The Future of Partisan Symmetry as a Judicial Test for Partisan Gerrymandering … · ELECTION LAW JOURNAL ... The Future of Partisan Symmetry as a Judicial Test for Partisan Gerrymandering

ELECTION LAW JOURNALVolume 6, Number 1, 2007© Mary Ann Liebert, Inc.DOI: 10.1089/elj.2006.0000

The Future of Partisan Symmetry as a Judicial Test forPartisan Gerrymandering after LULAC v. Perry

BERNARD GROFMAN and GARY KING

ABSTRACT

While the Supreme Court in Bandemer v. Davis found partisan gerrymandering to be justi-ciable, no challenged redistricting plan in the subsequent 20 years has been held unconsti-tutional on partisan grounds. Then, in Vieth v. Jubilerer, five justices concluded that somestandard might be adopted in a future case, if a manageable rule could be found. When ger-rymandering next came before the Court, in LULAC v. Perry, we along with two of our col-leagues filed an Amicus Brief (King et al., 2005), proposing the test be based in part on thepartisan symmetry standard. Although the issue was not resolved, our proposal was discussedand positively evaluated in three of the opinions, including the plurality opinion, and for thefirst time for any proposal the Court gave a clear indication that a future legal test for parti-san gerrymandering will likely include partisan symmetry. A majority of Justices now appearto endorse the view that the measurement of partisan symmetry may be used in partisan ger-rymandering claims as “a helpful (though certainly not talismanic) tool” (Justice Stevens,joined by Justice Breyer), provided one recognizes that “asymmetry alone is not a reliablemeasure of unconstitutional partisanship” and possibly that the standard would be appliedonly after at least one election has been held under the redistricting plan at issue (Justice

Bernard Grofman �http://www.socsci.uci.edu/�bgrofman/� is Professor of Political Science at the University ofCalifornia, Irvine. The Supreme Court, as well as many lower federal courts, have cited his research on racial votingpatterns and other topics related to elections on numerous occasions, perhaps most notably in Thornburg v. Gingles,478 U.S. 30, 52–53 & n. 20 (1986), one of the roughly twenty voting rights cases in nearly a dozen states where he hasserved as an expert witness. Grofman has also twice been a consultant to the Special Master in the Federal DistrictCourt, Southern District of New York, in cases where the failure of the legislator and governor to reach agreementforced the court to propose a congressional redistricting plan of its own for the State of New York.

Gary King �http://GKing.Harvard.edu� is David Florence Professor of Government, and Director of the Institutefor Quantitative Social Science, at Harvard University. The methods he and his coauthors developed are widely usedby courts and experts in redistricting litigation. So that he and others could implement these methods, he wrote andfreely distributes the software programs JudgeIt (along with Andrew Gelman), for measuring partisan bias and elec-toral responsiveness in districting plans, and EI, for measuring racially polarized voting from available electoral andcensus data. Both are widely used in academia, redistricting processes, and redistricting litigation. He has served asan expert witness or consultant in about a third of the U.S. states during their redistricting processes. He can bereached at 1737 Cambridge Street, Harvard University, Cambridge MA 02138; [email protected], 617-495-2027.

We are indebted to Justin Nelson for assistance with an Amicus Brief on Behalf of Neither Party which we sub-mitted (along with Andrew Gelman and Jonathan Katz) to the U.S. Supreme Court in Jackson v. Perry, to CloverBehrend-Gethard for secretarial assistance in preparing this paper, and to the Library of Congress (PA#NDP03-1), theNational Science Foundation (SES-0318275, IIS-9874747), and the National Institutes of Aging (P01 AG17625-01) forresearch support. We are also indebted to Marshall Hurley Esq. for having provided us updated information on therules for election of Superior Court judges in North Carolina.

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INTRODUCTION

THE U.S. SUPREME COURT declared partisangerrymandering claims justiciable in Davis

v. Bandemer,1 but in the subsequent twodecades no redistricting plan has been struckdown as an unconstitutional partisan gerry-mander. In Vieth v. Jubilerer,2 five Justices con-curred that the challenged Pennsylvania con-gressional plan was not, on the evidence beforethe Court, to be regarded as a partisan gerry-mander, and four also asserted that, hence-forth, partisan gerrymandering should be re-garded as nonjusticiable. The four remainingJustices, who were in favor of further proceed-ings in the case, could not agree how to mea-sure the severity of partisan gerrymandering orunder what circumstances a plan was so egre-gious that it should be considered unconstitu-tional. The “swing” member on this case, Jus-tice Kennedy, concurred on the merits of thedecision finding the Pennsylvania congres-sional plan to be constitutional (asserting thatthe absence of agreed upon comprehensive andneutral principles for evaluation made it im-possible to reach a judgment that the plan wasunconstitutional), but opposed overturningBandemer’s holding that partisan gerrymander-ing was justiciable, in the hope that sometimein the future there might arise a clearly man-ageable standard that the Court could adopt.

In Spring 2006, the Supreme Court heard LULAC v. Perry,3 where it addressed, amongother things, the legal claim that the 2003 re-re-districting of congressional lines in the State ofTexas is an unconstitutional partisan gerry-mander.4 The Court majority rejected two typesof partisan gerrymandering claims: (1) thatmid-decennial re-redistricting is inherently un-constitutional, and (2) that redistricting donefor no motive other than partisan gain is in-

herently unconstitutional. Even the combina-tion of a mid-decadal re-redistricting and theabsence of motivation other than partisan gainwere held not to present a constitutional issue.5However, though the 2003 Texas congressionalplan was not found to be an unconstitutionalpartisan gerrymander, five members of the

PARTISAN SYMMETRY AND GERRYMANDERING 3

Kennedy, joined by Justices Souter and Ginsburg). We use this article to respond to the re-quest of Justices Souter and Ginsburg that “further attention . . . be devoted to the adminis-trability of such a criterion at all levels of redistricting and its review.” Building on our pre-vious scholarly work, our Amicus Brief, the observations of these five Justices, and asupporting consensus in the academic literature, we offer here a social science perspective onthe conceptualization and measurement of partisan gerrymandering and the development ofrelevant legal rules based on what is effectively the Supreme Court’s open invitation to lowercourts to revisit these issues in the light of LULAC v. Perry.

1 Davis v. Bandemer, 478 U.S. 109 (1986).2 Vieth v. Jubilerer, 541 U.S. 267 (2004).3 LULAC v. Perry, 126 S. Ct. 2594 (2006). This case con-solidated Nos. 05-204, 05-254, 05-276, and 05-439. It wasdecided on June 28, 2006.4 The plan used for the 2002 congressional elections inTexas was a court-drawn plan whose constitutionalitywas upheld by the Supreme Court in Balderas v. Texas, 536U.S. 919 (2002). When the 2002 elections resulted in a shiftof the state into Republican control of both branches ofthe state legislature as well as control of the governorship,after much travail involving Democratic legislators whofled the state to break legislative quorum requirements,the Republican-controlled legislature passed a plan in2003 which resulted in six additional Republican mem-bers of congress being elected in 2004. The near farcicalelements of the initial Democratic attempts to prevent theTexas legislature from voting on that new congressionaldistricting plan led one political satirist to characterize thesituation after the 2004 congressional elections in Texasas: “For the Democrats, reredistricting temporarily de-layed became reredistricting DeLayed, but never denied.”(A Wuffle, personal communication, April 1, 2005). In Ses-sion v. Perry, 298 F. Supp. 2d 451 (E.D. Tex.) (three-judgecourt) (per curiam), summarily vacated sub nom. Jacksonv. Perry, 543 U.S. 941 (2004), the District Court for theEastern District of Texas, after hearing argument on thisissue, said the 2003 Texas plan was not an unconstitu-tional gerrymander. (The District Court also rejected theclaim that the plan violated Section 2 of the Voting RightsAct.) That decision was vacated and remanded to the Dis-trict Court in the light of Vieth, 541 U.S. 941 (2004). Aftera reexamination of the political gerrymandering claimsthe District Court again held for the defendants in Hen-derson v. Perry, 399 F. Supp. 756 (2005), and that decisionwas appealed to the Supreme Court, on a variety ofgrounds, under the name LULAC v. Perry.5 “The sole-intent standard . . . is no more compellingwhen it is linked to the circumstances that Plan 1374C ismid-decennial legislation.” LULAC, 126 S. Ct. at 2602(opn. of Kennedy, J.).

Court reiterated the holding in Vieth that par-tisan gerrymandering can, in principle, be rec-ognized as a violation of equal protection, andtwo others (Chief Justices Roberts and JusticeAlito) took no position on that question.6

Although, “as in Vieth,” there existed “nomajority for any single criterion of impermissi-ble gerrymander,”7 this case marks a potentialsea change in how the Supreme Court adjudi-cates partisan gerrymandering claims. For thefirst time, a criterion for detecting and mea-suring gerrymandering—known as partisansymmetry—attracted considerable positive at-tention by the Justices. The potential impor-tance of the partisan symmetry criterion wasargued for by us and two of our colleagues inan Amicus Brief submitted in that case (on be-half of neither party).8 The ideas in that Ami-cus Brief were discussed in three of the opin-ions, including the plurality opinion written byJustice Kennedy.9 A majority of Justices nowappear to endorse our view that the measure-ment of partisan symmetry can be used as partof a broader test in resolving partisan gerry-mandering claims. This case marks the firsttime that a majority of the Court has agreed onthe potential use of any criterion for measuringthe effects of partisan gerrymandering. (This ofcourse merely recognizes current practice inmany lower courts where the vast majority ofexperts routinely compute and often presentresults on the partisan fairness of redistrictingplans based on the concept and measures ofpartisan symmetry we describe here.)

Two Justices (Stevens and Breyer) see it as “a helpful (though certainly not talismanic)tool.”10 Speaking for himself alone, JusticeStevens identifies departure from partisansymmetry as one of eight criteria he wouldmake use of in determining effects-based vio-lations of equal protection in the context of par-tisan gerrymandering claims,11 and he explic-itly finds that the challenged plan violates apartisan symmetry test.12 Moreover, JusticeStevens asserts that the “symmetry standard . . .is undoubtedly ‘a reliable standard’ for mea-suring a ‘burden . . . on the complainants’ rep-resentative rights.’ ”13

Two Justices (Souter and Ginsburg) look tothe future and indicate that they “do not ruleout the utility of a criterion of symmetry as a

test.”14 And most importantly, they explainthat “interest in exploring this notion is evident[on the Court].”15

A fifth Justice, Justice Kennedy, also does notrule out use of this criterion, adding twocaveats: that “asymmetry alone is not a reliablemeasure of unconstitutional partisanship” andthat the Court may need to administer the standard retrospectively rather than prospec-tively.16 Justice Stevens characterizes JusticeKennedy’s view as one of “leaving the dooropen to the use of the standard in futurecases.”17

Furthermore, two additional justices, ChiefJustice Roberts, joined by Justice Alito, whileasserting that appellants have not yet provided“a reliable standard for identifying unconstitu-tional gerrymanders”18 leave open the questionof an appropriate standard.19

GROFMAN AND KING4

6 LULAC, 126 S. Ct. at 2652 (opn. of Roberts, C. J.).7 LULAC, 126 S. Ct. at 2647 (opn. of Souter, J.).8 Amicus Brief in Jackson v. Perry Submitted on Behalf ofNeither Party by Gary King, Bernard Grofman, AndrewGelman, and Jonathan Katz in the U.S. Supreme Court(No. 05-276), henceforth King et al. (2005). See�http://gking.harvard.edu/projects/red.shtml�.9 Although there was majority agreement on each of theissues raised in the case, those majorities were not alwaysmade up of the same set of Justices, and the case had sixseparate opinions.10 LULAC, 126 S. Ct. at 2638 (n.9) (opn. of Stevens, J. P.,joined by Breyer, S).11 LULAC, 126 S.Ct. at 2641 (opn. of Stevens, J. P.).12 “Plan 1374C [the challenged plan] is inconsistent withthe symmetry standard . . . .” (LULAC, 126 S. Ct. at 2637(n. 8) (opn. of Stevens, J.).13 LULAC, 126 S. Ct. at 2637 (opn. of Stevens, J.), with in-ternal quotes citing to ante (opinion of Kennedy, J.).14 LULAC, 126 S. Ct. at 2647 (opn. of Souter, J.).15 LULAC, 126 S. Ct. at 2647 (opn. of Souter, J.), with in-ternal quotes citing to the opinion of Kennedy, J. and tothe opinion of Stevens, J.16 LULAC, 126 S. Ct. at 2611 (opn. of Kennedy, J. joinedby Justices Souter and Ginsburg), emphasis added.17 LULAC, 126 S. Ct. at 2638 (n.9) (opn. of Stevens, J.), withinternal cite to opinion of Kennedy, J. See also RichardBriffault, LULAC on Partisan Gerrymandering: Some Clar-ity, More Uncertainty, 105 Mich. L. Rev. First Impressions58, 61 (2006).18 LULAC, 126 S. Ct. at 2651 (opn. of Roberts, C.J.), withinternal cite quoting from the opinion by Kennedy, J., anteat 2612.19 Only Justice Scalia, joined by Justice Thomas, wouldvote to reverse Bandemer. These Justices reiterate theirview in Vieth that, since “no party or judge has put fortha judicially manageable standard . . . we should simplydismiss appellants’ claims as nonjusticiable.” LULAC, 126S. Ct. at 2663 (opn. of Scalia, J.).

We find the openness of a majority of the Jus-tices to making use of measures of partisan bias(a deviation from partisan symmetry) as partof a standard for unconstitutional partisan ger-rymandering to be an extremely promising de-velopment for reining in abuses of gerryman-dering in American democracy.20 We use thisarticle to respond to the suggestion of JusticesSouter and Breyer that “further attention . . . bedevoted to the administrability of such a crite-rion at all levels of redistricting and its re-view.”21 In the process of so doing we commenton the three specific new ideas raised by Jus-tice Kennedy’s discussion in LULAC of possi-ble tests for partisan gerrymandering: his sug-gestion that a “challenge could be litigated ifand when the feared inequity arose” ratherthan on the basis of “unfair results that wouldoccur in a hypothetical state of affairs;”22 hissuggestion that we need to look comparativelyto judge relative magnitudes of partisan bias inalternative plans (an idea which parallels how courts have investigated ill-compactnessclaims based on state constitutional chal-lenges), and his specific suggestion to distin-guish the case where a majority party has itsvoting strength exaggerated (which is how hecharacterizes the 2003 plan, based on the actualresults in 2004, with the Republicans as the ma-jority party) from the case where a party thatis in the process of becoming a minority interms of voting support uses redistricting to en-trench itself in power over the remainder of thedecade (which is how he characterizes the 1991Texas congressional plan, with the Democratsseen as a once dominant party which losesvoter support over the course of the decade).23

We also address the concerns of JusticeKennedy and other Justices that a partisan sym-metry test can only be effectively used if thereis a specified threshold to distinguish uncon-stitutional gerrymandering from mere politicsas usual.24 But we share the view of JusticeStevens that, even if the Court fully adopts theconcept of partisan symmetry as one that islegally relevant, and recognizes the potentialusefulness of the specific methodology that canbe used to measure levels of partisan bias thatwe discuss below and in our previous writings,it is for the Court to make the critical judgmentsabout what would constitute unconstitutional-

ity or legally actionable thresholds and stan-dards: “Justice Kennedy faults proponents ofthe symmetry standard for ‘not providing astandard for deciding how much partisan biasis too much’ (ante at 13). But it is this Court, notproponents of the symmetry standard, that hasthe judicial obligation to answer the questionof how much unfairness is too much.”25 Al-though we believe that the choice of legally ac-tionable thresholds for violations of partisansymmetry is the Court’s purview, social scien-tists can be helpful by clarifying the logical pos-sibilities—which we also do here.

The remainder of this article consists of fourparts: In Section II we expand and clarify thearguments laid out in King et al. (2005) as tothe potential usefulness of the measurement ofpartisan symmetry, and we identify and rebuta number of common misconceptions about thepartisan symmetry standard, most of which aregiven airing in various of the briefs filed in LULAC. Then, in Section III, we consider ways


20 The consequences of partisan gerrymandering are ar-guably exacerbated in situations of razor thin legislativemajorities and high ideological polarization. (See B.Grofman and G. Jacobson, Amicus Brief in Richard Vieth,et al., v. Robert C. Jubelirer, et al., 541 U.S. 267 (2004); S.Hirsch, The United States House of Unrepresentative: WhatWent Wrong in the Latest Round of Congressional Redistrict-ing, 2 Election Law Journal 179–216 (2003).21 LULAC, 126 S. Ct. at 2647 (opn. of Souter, J.). We alsonote that, in Justice Stevens’ view, “Part III of the Court’sopinion and . . . my own opinion demonstrate [that] as-sessing whether a redistricting map has a discriminatoryimpact on the opportunities for voters and candidates ofa particular party to influence the political process is amanageable judicial task.” LULAC, 126 S. Ct. at 2636 (n.5) (opn. of Stevens J.).22 LULAC, 126 S. Ct. at 2611 (opn. of Kennedy, J.).23 In Justice Kennedy’s view: “A test that treats these sim-ilarly effective power plays in such different ways doesnot have the reliability that appellants ascribe to it.” LULAC, 126 S. Ct. at 2610 (opn. of Kennedy J.).24 However, while this article is directly relevant to theempirical questions posed by this case related to partisangerrymandering—in particular to the conceptualizationand measurement of partisan bias—since we have notfully reviewed the evidentiary record nor conducted in-dependent empirical investigations of our own, we ex-pressed in our Brief and express here no views about thelevel of partisan bias in the redistricting plan that was atissue nor that in previous plans, nor do we express anopinion as to which party ought to have prevailed in LU-LAC with respect to the issue of unconstitutional partisangerrymandering. 25 LULAC, 126 S. Ct. at 2638 (n. 9) (opn. Kennedy, J.).

in which courts might address the issue of set-ting a prima facie legal threshold for when thelevel of partisan gerrymandering rises to a mat-ter of legal concern—so as to distinguish egre-gious and unconstitutional gerrymanderingfrom politics as usual. Next, in Section IV, weconsider how partisan symmetry can be made acomponent of a broader multi-criteria standardfor partisan gerrymandering that deals with bothoverall equal protection and matters specific toparticular districts.26 Finally, in Section V, weprovide a concluding discussion that looks to thefuture of partisan gerrymandering claims.

II. CONCEPTUALIZING ANDMEASURING PARTISAN FAIRNESS

We now explain the concept of partisan sym-metry as a standard for partisan fairness, andthen the measurement of how redistricting plansmay deviate from this fairness standard. We alsodiscuss whether measures of partisan fairnessshould be imposed prospectively, before an elec-tion is held under a redistricting plan, or retro-spectively, and finally we clarify some commonmisunderstandings about partisan symmetry.

Conceptualization

As we wrote in King et al., “The symmetrystandard requires that the electoral system treatsimilarly-situated parties equally, so that eachreceives the same fraction of legislative seatsfor a particular vote percentage as the otherparty would receive if it had received the samepercentage [of the vote].”27 Social scientistshave long recognized partisan symmetry as theappropriate way to define partisan fairness inthe American system of plurality-based elec-tions,28 and for many years such a view hasbeen virtually a consensus position of the schol-arly community. We are aware of no publisheddisagreement or even clear misunderstandingin the scholarly community about partisansymmetry as a standard for partisan fairness inplurality-based American elections since theclarification and measures introduced by GaryKing and Robert X. Browning in DemocraticRepresentation and Partisan Bias in CongressionalElections.29 This level of consensus is explicitlyacknowledged by Justice Stevens, who writes

in his opinion in LULAC that “this standard iswidely accepted by scholars as providing ameasure of partisan fairness in electoral sys-tems.”30 Indeed, as Justice Stevens pointed out,

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26 Such a standard can satisfy the desire of the pluralityin Davis v. Bandemer, 478 U.S. 109 (1986), for “a showingof more than a de minimis effect” (at 134) such that “anactual or projected history of disproportionate results ex-ists, and that the electoral system is arranged in a man-ner that will consistently degrade a voter’s or a group ofvoters’ influence on the political process as a whole.” (at132). In the language of Justice Kennedy in LULAC, itmust “show a burden, as measured by a reliable standard,on the complainants’ representational rights.” (at 2602)(opn.of Kennedy, J.).27 2005, 4–5; op cit.; quoted in LULAC, 126 S. Ct. at 2637(opn. of Stevens, J.).28 Although the literature on the fair translation of seatsinto votes can be traced back more than a century, themost prominent early studies in the modern literature in-clude Edward R. Tufte, The Relationship Between Seats andVotes in Two-Party Systems, 67 Am. Pol. Sci. Rev. 540–554(1973), and Bernard Grofman, Measures of Bias and Pro-portionality in Seats-Votes Relationships, 9 Political Method-ology 295–327 (1983).29 81 Am. Pol. Sci. Rev. 1251 (1987).30 Justice Stevens then cites (at pp. 21–22) to a number ofthe references given in King et al. (2005) in support of thisproposition, including Edward R. Tufte, The RelationshipBetween Seats and Votes in Two-Party Systems, 67 Am. Pol.Sci. Rev. 540–554 (1973); Gary King and Robert X. Brown-ing, Democratic Representation and Partisan Bias in Con-gressional Elections, 81 Am. Pol. Sci. Rev. 1251 (1987); An-drew Gelman & Gary King, A Unified Method of EvaluatingElectoral Systems and Redistricting Plans, 38 Am. J. Pol. Sci.514 (1994); Dennis Thompson, Election Time: Normative Im-plications of Temporal Properties of the Electoral Process in theUnited States, 98, Am. Pol. Sci. Rev. 51 (2004); and Erik J.Engstrom & Samuel Kernell, Manufactured Responsiveness:The Impact of State Electoral Laws on Unified Party Controlof the Presidency and House of Representatives, 1840–1940, 49Am. J. Pol. Sci. 531 (2005). As explained elsewhere,“[s]cholars have reached near consensus on partisan sym-metry as a standard of partisan fairness and have madegreat progress on developing measures that can be usedto see whether electoral systems and districting plansmeet this standard.” Gary King, John Bruce & AndrewGelman, “Racial Fairness in Legislative Redistricting,” inClassifying by Race 85, 85 (Paul E. Peterson, ed., 1996).There are many other references we could give (see e.g.,Ernesto Calvo & Maria Victoria Murillo, Who Delivers?Partisan Clients in the Argentine Electoral Market, 48 Am. J.Pol. Sci. 742 (2004); and Thomas W. Gilligan & John G.Matsusaka, Structural Constraints On Partisan Bias UnderThe Efficient Gerrymander, 100 Pub. Choice 65, (1999)) tofurther support this claim. The only alternative standardof fairness that exists in the political science literature isproportionality of seats and votes, but it is widely recog-nized that a proportionality standard is simply not ap-propriate for use as a legal standard in plurality basedelections, since plurality elections cannot be expected toyield proportional results.

“the symmetry standard was not simply pro-posed by an amicus to the Court [in LULAC], itwas also used by the expert for plaintiffs andthe expert for the state in assessing the degreeof partisan bias in Plans 1151C [the 2001Balderas court-drawn plan] and Plan 1374C [the2003 plan under challenge].”31 Moreover, neu-tral officials such as courts and non-partisanmembers of redistricting commissions havealso regularly made use of it.32

The concept of partisan symmetry is broadlyapplicable, in that it applies not only to two-party legislative elections, but also to multi-party systems,33 and even non-legislative elec-tions.34 For simplicity of exposition, however,we focus here only on the simple and impor-tant case of two-party (Democratic and Re-publican) contests in single-member, pluralitywinner legislative districts.

For the purpose of this article, we define anelectoral system as a set of specific legal rulesthat govern an election—such as winning byplurality, who has the franchise, where the vot-ing machines are located, etc.—as well as thelegislative districting plan.35 The key to thesymmetry definition of fairness is that it eval-uates the electoral system as a whole by eval-uating how voter preferences statewide aretranslated into the division of legislative seatsbetween the parties. It is also a simple and di-rect generalization of the symmetry standarduniversally applied to candidates in winner-take-all plurality elections in individual single-member legislative districts. We explain thedefinition of fairness in this simple single-dis-trict context first and then discuss the general-ization that works for collections of districts inevaluating entire state electoral systems in thecontext of redistricting.

The electoral rule in the simple context of a single member legislative district is thatwhichever candidate receives a plurality of thevotes wins the legislative seat. It is importantto recognize that this obvious definition of fair-ness requires no knowledge of the vote out-come or who actually will win the election;rather it evaluates fairness by setting rules forallocating all possible vote outcomes to seat out-comes, and refers to candidates only by theirvote totals and not by their names or attributes.In particular, the reason it is considered fair for

one candidate to win the seat if he or she winsa plurality of the votes is not because of whathappened in the election, but rather because ofwhat would happen under the symmetric butopposite hypothetical outcome: if the othercandidate had received a plurality of votes in-stead, he or she would win the seat. An unfairsystem would be one where we know the op-posite hypothetical would not occur.

Thus, the symmetry standard in this casemerely involves the comparison of one hypo-thetical outcome to another. Fairness is definedin this context by each party’s candidate beingtreated equally under the law by rules that pro-vide an equal opportunity to compete for theseat. Symmetry is thus a way of ensuring“anonymity,” the fairness criterion that pre-vents electoral system rules from referring topolitical parties by name rather than in termsof how many votes they receive in the election.


31 LULAC, 126 S. Ct. at 2637 (opn. Stevens J.), citing toApp. 34–42 (report of Professor John R. Alford, expert forAppellants), and id. at 189–193, 216 (report of ProfessorRonald Keith Gaddie, expert for the State). Here wewould call special attention to Graph 2 in the Alford re-port, and Fig. 1 in the Gaddie Report.32 See, e.g., Page v. Bartels, 144 F. Supp. 2d 346 (D.N.J.2000). However, many uses of seats-votes curves bycourts and redistricting commissions do not take advan-tage of the most recent methodological improvements inevaluating partisan symmetry found in the political sci-ence literature. (See below.)33 See, e.g., Gary King, Electoral Responsiveness and Parti-san Bias in Multiparty Democracies, 15 Legislative StudiesQuarterly, 159, 163–65, 181 (1990).34 For example, partisan symmetry, and associated mea-sures, have been applied to the Electoral College (AndrewGelman, Jonathan Katz, and Gary King, “EmpiricallyEvaluating the Electoral College,” Chapter 5, pp. 75–88,in Ann N. Criegler, Marion R. Just, and Edward J. Mc-Caffery, eds., Rethinking the Vote: The Politics and Prospectsof American Electoral Reform, (New York: Oxford Univer-sity Press, 2004, �http://gking.harvard.edu/files/abs/rethink-abs.shtml�); Bernard Grofman, Thomas Brunell,Janet Campagna, Distinguishing Between the Effects ofSwing Ratio and Bias on Outcomes in the U.S. Electoral Col-lege, 1900–1992, 16(4) Electoral Studies 471–487 (1997); andto delegate selection in presidential election nominationcontests (Stephen Ansolabehere and Gary King, Measuringthe Consequences of Delegate Selection Rules in PresidentialNominations, 52(2) Journal of Politics 609–621 (May, 1990),�http://gking.harvard.edu/files/abs/pri-abs.shtml�.35 For a more general discussion of the various types ofelectoral laws, see Bernard Grofman and Arend Lijphart(eds.), “Introduction,” in Electoral Laws and Their PoliticalConsequences, esp. pp. 1–3 (New York: Agathon Press,1986).

Anonymity is ensured by partisan symmetrysince if we take an electoral result and switchthe names of the parties that received the par-ticular vote outcomes, the seat outcomes wouldalso switch.

This basic symmetry definition given above isapplicable to each individual district in all sin-gle-member, plurality winner, district-based leg-islative election contests in the U.S. Any electoralrule that would require one candidate in a dis-trict to garner more votes to win than anothercandidate, or which refers to the names or at-tributes of the candidates in deciding the winnerwould obviously not last long in any U.S. courtwith appropriate jurisdiction. The rule is also aclear reflection of fundamental tenets of Ameri-can representative democracy and culture.

The definition of partisan symmetry in thecontext of redistricting takes this same venera-ble principle and slightly generalizes it to ap-ply to the relevant group of districts, such asan entire state legislature or all the congres-sional districts within a state. For this group ofdistricts, the symmetry standard requires thatthe number of seats one party would receive ifit garnered a particular percentage of the votebe identical to the number of seats the otherparty would receive if it had received the samepercentage of the vote, or in other words thatoutcomes not depend upon party names. Forexample, suppose the Democratic Party re-ceives an average of 55% of the vote totals in astate’s legislative district elections and, becauseof the way the district lines were drawn, it wins70% of the legislative seats in that state. Is thatfair? That question cannot be answered basedon this one piece of evidence alone. It dependson a comparison with the opposite hypotheti-cal outcome: It would be fair only if the Re-publican Party would also have received 70%of the seats in an election where it had receivedan average of 55% of the vote totals in districtelections. This electoral system would be bi-ased against the Republican Party if it wouldgarner fewer than 70% of the seats and biasedagainst the Democratic Party if the Republicanswould garner more than 70%. In other words,partisan symmetry requires that “each politicalgroup in a State has the same chance to electrepresentatives of its choice as any other polit-ical group.”36

The key idea is that candidates of each politi-cal party should have equal opportunity in trans-lating voter support into the division of legisla-tive seats between the parties: as we notedpreviously, symmetry requires that the electoralsystem treat similarly-situated political partiesequally. Partisan symmetry says nothing aboutwhich candidates should be elected, and it is notconditioned on any particular vote division: itonly says that if a party is able to muster a cer-tain fraction of votes, then it should get the samenumber of seats as the other party would if thatparty had received the same voter support. Sym-metry thus evaluates partisan gerrymanderingonly by its consequences.

Other features of the electoral system thathave sometimes been used as proxies for par-tisan gerrymandering are only relevant to thisdefinition insofar as they affect the partisansymmetry of the electoral system. These otherfactors—such as who drew the district lines,whether there was proper citizen input, orwhether the districts are compact, split localpolitical subdivisions, or maintain communi-ties of interest—may in fact be of interest tocourts or to the legislature for other reasons, oras values in and of themselves, but in terms offairness to political parties, they are only rele-vant under this standard if they have an effecton making the electoral system deviate frompartisan symmetry. (Of course, the Court mayalso wish to require some of these other crite-ria to hold as well.)

Measuring symmetry and partisan bias doesnot require “proportional representation”(where each party receives the same proportionof seats as it receives in votes). Of course, anelectoral system that is proportional, like anyelectoral system, may treat the parties sym-metrically and thus fairly.37 Yet symmetry can

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36 Davis v. Bandemer, 478 U.S. at 162 (Powell, J., concur-ring in part and dissenting in part).37 Electoral systems that mandate versions of propor-tional representation do not necessarily produce partisansymmetry. For example, many European nations that useproportional representation have electoral rules that, asapplied, generate electoral systems with sometimes con-siderable partisan bias. This may occur in a multi-partysystem when very small parties fall below legal thresh-olds and so get no seats and as a result larger parties gainmore than a proportional share of seats.

exist (or not exist) in all types of electoral sys-tems. Because most electoral systems in theUnited States are single-member districts that arewinner-take-all, in practice they normally give a“bonus” of varying sizes (above proportionality)in seats to the party that wins a majority of thevotes across a state. So long as this bonus isawarded based on whoever wins the majority,rather than to a specific party by name, it wouldbe fair under the partisan symmetry standard de-spite giving non-proportional results.

The range of electoral systems that are sym-metric can be ordered by the degree of electoralresponsiveness. Electoral responsiveness—alsoreferred to as the “bonus” for the majorityparty, the “swing ratio,” or the “degree of rep-resentation”—quantifies this idea by askinghow much the seat division between the par-ties change as the vote proportions change. Apurely proportional system is one in which aone percent increase in the votes for a partyleads to a one percent increase in seats for thatparty. Statistical models of plurality-based elec-tions have demonstrated that plurality-basedelections are only rarely proportional, i.e., theyexhibit an electoral responsiveness that is dif-ferent from one. If, for example, the electoralresponsiveness were 2, and there were onlytwo political parties, this would mean that, onaverage, for every one percentage point gain invote share above but near 50% a party couldexpect to gain an additional 2 percentage pointsof seat share in the legislature, e.g., for a voteshare of 60 percent, a party could expect to con-trol roughly 70 percent of the seats in the leg-islature. This common pattern violates propor-tional representation but does not violatesymmetry, so long as whatever party wins amajority of the votes gets the bonus. Undersymmetry, there is nothing necessarily unfairabout one party winning a greater proportionof seats than the other, so long as that “oneparty” is not any particular party. An electoralsystem may have any degree of partisan bias,no matter what level of responsiveness hap-pens to exist.

Electoral responsiveness is often regarded asa normatively good feature of elections. Cer-tainly elections in which the seat division be-tween the parties did not respond at all tochanges in voter preferences would not be de-

mocratic. Low levels of responsiveness can beproduced by a legislative redistricting plan, orby other features of elections, such as high lev-els of incumbency advantage, many uncon-tested elections, weak candidates, or a politicallypolarized electorate. Most scholars therefore re-gard electoral systems with higher levels of elec-toral responsiveness as better,38 and this is oneof the reasons many favor the American systemof district-based elections, since it tends to pro-duce a higher level of responsiveness than othersystems. A few state constitutions favor what wethink is properly conceptualized as high levelsof electoral responsiveness, i.e., a preference forcompetitive seats, but it is not clear that theSupreme Court has addressed this issue otherthan to explain that in making partisan gerry-mandering justiciable, they were not favoringproportional representation. That makes a greatdeal of sense in this context, because requiringproportional representation in the Americancontext of single member district plurality-basedelections is effectively synonymous with requir-ing low levels of electoral responsiveness, some-thing that few favor and something that has lit-tle basis in American law.

Measurement

The concept of partisan symmetry explicatedabove is important in and of itself, but even aclear concept that everyone accepts as relevantdoes not immediately suggest a specificmethod of measuring that concept, or any rulethat would necessarily apply in the legal set-ting. These two additional goals of measure-ment and legal application require, first, a sta-tistical measure of the deviation of an electoralsystem from partisan symmetry; in otherwords, we need a measure of partisan bias. (Forsome purposes we describe below, we may alsodesire a measure of electoral responsiveness,which distinguishes different types of fair elec-toral systems.) Second, the Court will then alsoneed to determine how to make use of such


38 An exception is Thomas L. Brunell, Rethinking Redis-tricting: How Drawing Uncompetitive Districts EliminatesGerrymanders, Enhances Representation, and Improves Atti-tudes Toward Congress, 39(1) PS: Political Science & Poli-tics 77–85 (January, 2006).

measures, but that is a separate issue we deferuntil Section III.

Over the many years in which scholars haveworked on defining fairness as partisan sym-metry, they have also developed a sequence ofsteadily improving statistical approaches de-signed to measure the degree of partisan biasin elections and in proposed legislative redis-tricting plans. These now highly mature statis-tical methods rely on well-tested and well-ac-cepted statistical procedures.

Estimating partisan bias and electoral re-sponsiveness both first require studying howthe statewide average district vote for Demo-cratic candidates (which in our simple two-partyrunning example is 100% minus the fraction forthe Republican candidates) will translate intothe expected statewide fraction of seats for theDemocratic Party. The relationship betweenthese two variables is typically summarizedwith the seats-votes curve, which traces out theexpected statewide seats division as a functionof each possible value of the average district vote(i.e., for each average district vote percent forthe Democrats between 0% and 100%, or atleast near the middle of that scale where realresults occur more commonly). Once we havetraced out the seats-votes curve, we can computepartisan bias by directly examining how eachparty would fare in obtaining seats for any givenvote fraction. For example, we could literallyread off the expected seat proportion the Dem-ocrats would likely receive if they won 55% ofthe vote in the average of the districts in the state,and the seat proportion for the Republicans ifthey received 55% of the vote. Similarly, theseats-votes curve also reveals the level of elec-toral responsiveness by the slope of the line nearthe middle of the curve where most electionstake place: steeper slopes mean that a smallchange in the average district vote (for eitherparty) would yield a larger change in the seat di-vision between the parties than if the seats-votescurve were flatter. It is important not to confuseelectoral responsiveness, which refers to the slopeof seats-votes curves and helps to distinguish dif-ferent types of fair systems, with partisan bias,which refers to the degree to which an electoralsystem deviates from partisan symmetry. Thetwo are totally distinct concepts.

Because we can measure both partisan biasand electoral responsiveness directly from the

seats-votes curve, all that remains is to (a) iden-tify a method of estimating the seats-votes curvefrom the data we observe, and (b) specify a sta-tistical methodology that allows us to estimatethe margin of error that exists in the measure-ments we derive from the seats-vote curve.

Historically, four general categories of meth-ods have been used to measure seats-votescurves, each one better than the previous.39 Tooffer intuition about how one can estimate therelationship from real data, and also to give asense of the real scientific progress made in thisfield, we now briefly describe each approach.

The first method developed to measure aseats-votes curve was to take a number of elec-tion results and to plot the actual statewide av-erage district vote by the statewide seat propor-tions, with one point representing each election.The strategy is then to fit some type of linear ornonlinear regression to these points and use thatestimated regression line as the seats-votescurve. (The margin of error in the seats-votescurve measured this way is estimated from howclosely the points fit the curve.) This approachworks fine in principle, except that there are usu-ally five or fewer elections between redistrict-ings, which is too few to pin down the seats-votescurve with much certainty. More importantly,this approach cannot be applied directly to eval-uate redistricting plans before they are put intoeffect or even before the next redistricting isabout to take place, and so it is useful only forhistorical and comparative purposes.40

A second strategy for measuring the seats-votes curve is to use a key relationship evidentin the vast majority of district election data to construct the hypothetical relationships be-

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39 Andrew Gelman and Gary King, Estimating the ElectoralConsequences of Legislative Redistricting, 85(410) Journal ofthe American Statistical Association 276 (June 1990).40 See M.G. Kendall and A. Stuart, The Law of Cubic Pro-portions in Electoral Results, 1 British Journal of Sociology193–196; James G. March, Party Legislative Representationas a Function of Election Results, 21(4) Public Opinion Quar-terly 512–542 (Winter 1957–58); Phillip A Schrodt, A Sta-tistical Study of the Cube Law in Five Electoral Systems, 7 Po-litical Methodology, 31–53; Bernard Grofman, Measures ofBias and Proportionality in Seats-Votes Relationships, 9 Po-litical Methodology 295, 327 (1983); Richard G. Niemi andPatrick Fett, The Swing Ratio: An Explanation and an As-sessment, XI,1 Legislative Studies Quarterly 7590 (Febru-ary, 1986); Gary King and Robert X. Browning, Democra-tic Representation and Partisan Bias in CongressionalElections, 81 Am. Pol. Sci. Rev. 1251 (1987).

tween votes and seats from the district-levelvotes in only one election. The idea is to plot firstthe one point representing the observed propor-tion of seats and of votes in the one actual elec-tion. Then one assumes that, if the swing in votesfor the Democratic Party statewide increased by(say) one percentage point, the same uniformswing would occur in every district within thestate. We can use this “uniform partisan swing”assumption by adding one percentage point toeach district in the state and then declaring thecandidates “winners” in each district based onthese new hypothetical vote results; this pro-duces one additional point on the seats-votesplot. The same procedure is repeated by adding(and subtracting) a large range of values uni-formly one at a time to all districts and recom-puting the statewide seat totals. In this way, wecan reconstruct an entire seats-votes curve basedon this one assumption.41

This uniform partisan swing strategy is an im-provement since by marshaling district-leveldata, it productively uses much more informa-tion than the first cross-election approach, andyet it requires only a single actual election. Un-fortunately, the approach still has three seriousflaws for use in evaluating redistricting. First, itdoes require this one election, and so we couldnot evaluate the consequences of redistrictingplans with this approach until after the first elec-tion held under the new plan. Second, althoughit is remarkable that the uniform partisan swingassumption does hold approximately in a vastarray of democratic elections in the U.S., world-wide, and throughout history,42 the assumption(which requires uniform swing to hold exactly)is violated to a degree by almost all actual elec-tion data. And finally, the assumption of exactuniform partisan swing implies a zero marginof error in terms of predictive accuracy, whichis always unrealistic in social science analyses.Newer methods address one or all of these threedisadvantages.

The third approach to estimating the seats-votes curve eliminates the need to wait until af-ter the first election. The idea is to create hy-pothetical votes in districts under the newredistricting plan by using the actual votes castin a previous election for some statewide race(often a low visibility race, such as state trea-surer or board of regents) and breaking themdown into the new districts.43 The assumption

here is not that the votes in the statewide raceare the same as those that would be receivedby the legislative candidate in the district elec-tion, but rather only that the relationship be-tween votes and seats can be estimated in thisway. This assumption corresponds to the ideathat, if you ranked the degree to which districtswere Republican based on legislative electionsor elections to a statewide office, the rank order,and not necessarily the actual vote, would beapproximately the same. This assumption is of-ten accurate, but never exactly of course. Forexample, the incumbency status of the legisla-tors, and their typical electoral advantage, is ig-nored, as are many other important politicaldifferences in each legislative district election.The lack of a realistic (nonzero) margin of er-ror is also not fixed by this approach. Thus,even though this method sometimes providesa reasonable measure of the seats-votes curve,and in turn the degree and direction of parti-san bias and the extent of electoral responsive-ness, this method can be improved on.

The fourth and current state of the art ap-proach, developed in a sequence of articles byGary King and Andrew Gelman,44 builds on


41 David E. Butler, Appendix, The British General Electionof 1950, H. G. Nicholas, Ed., pp. 305–333 (London: Macmil-lan, 1951).42 See Gary King; Ori Rosen; Martin Tanner; and Alexan-der F. Wagner, Ordinary Voting Behavior in the Extraordi-nary Election of Adolf Hitler, �http://gking.harvard.edu/files/abs/naziV-abs.shtml�, which offers examples ofuniform partisan swing in the U.S. Congress, the Okla-homa State House, the Weimar Republic, and the Parlia-ment of the Russian Federation.43 See C. Backstrom, L. Robins, and S. Eller, Issues in Ger-rymandering: An Exploratory Measure of Partisan Gerry-mandering Applied to Minnesota, 62 Minnesota Law Review1121–1159 (1978).44 This approach was built over four successive articles,each which improved on the previous: Gary King, Repre-sentation Through Legislative Redistricting: A StochasticModel, 33(4) Am. J. Pol. Sci. 787–824 (November, 1989);Andrew Gelman and Gary King, Estimating the ElectoralConsequences of Legislative Redistricting, 85(410) Journal ofthe American Statistical Association 274–282 (June, 1990);Gary King and Andrew Gelman, Systemic Consequences ofIncumbency Advantage in U.S. House Elections, 35(1) Am. J.Pol. Sci. 110–138 (February, 1991); and Andrew Gelmanand Gary King, A Unified Method of Evaluating ElectoralSystems and Redistricting Plans, 38(2) Am. J. Pol. Sci.514–554 (May, 1994). The method in the latter article isimplemented in the open source and free software called“JudgeIt: A Program for Evaluating Electoral Systems andRedistricting Plans,” by Andrew Gelman and Gary King�http://gking.harvard.edu/stats.shtml#judgeit�.

the insights of the above earlier methods inthree key ways. First, instead of assuming thatuniform partisan swing holds exactly, it onlyrequires the statistical assumption of approxi-mate uniform partisan swing. This more realisticassumption has been shown to fit electoral datavery closely in a vast array of elections, and sois appropriate to evaluate almost all Americanlegislative electoral systems. In fact, the samepattern holds for elections of all kinds in theU.S., and even elections in other countries. Forexample, we may not have any idea how thenext presidential elections will turn out but,whatever the exact results for elections in thisdecade, we know with a high degree of cer-tainty that the overall vote in Utah will be moreRepublican than that in Massachusetts. In Re-publican years, both will typically becomemore Republican, and in Democratic years theywill both usually become more Democratic but,whatever the nationwide swing, the orderingof and distance between the two will remainroughly the same.

This insight is a key empirical generaliza-tion that applies to all elections in the U.S. andmost other democracies: the statewide or na-tionwide swing in elections is highly variableand difficult to predict, but the approximaterank order of districts is highly regular andstable. The rank order is not perfectly fixed,and local political changes can and regularlydo affect them, but this uncertainty is reflectedin the statistical assumption of approximateuniform partisan swing, and the changes inthe ranking of different areas is usually rela-tively small and within predictable margins oferror.45 Fortunately, the methodology neces-sary to estimate partisan bias requires no pre-dictions about the swing, and indeed is not af-fected by whether it is a Democratic orRepublican year or whether one will be moreprevalent than the other. It is instead basedonly on this regular feature of elections thathelps establish the relationship between anyparticular vote outcome and the likely result-ing seat division.

The second advantage of this new approachis that it does not require assuming that votesin statewide elections for statewide candidateshave any particular ex ante relationship withvotes for legislative candidates. Instead, this

methodology has adapted, incorporated, andextended standard statistical approaches(based on linear regression, one of the mostcommonly used methodologies in the socialsciences) to measure what seat outcomeswould be like given particular average districtvote proportions by estimating outcomes fromthe available historical data. Estimatingwhether such a relationship exists, and what itis, is a strategy in stark contrast to previousmethods, which had merely assumed that thevote for a statewide office would be a perfectpredictor of results in legislative districts. Infact, the new method allows the use of anyavailable information about the determinantsof partisan voting strength in the new districts,including recent election results, the presenceof an incumbent in the district, and whether therace is contested. Other factors may includeparty registration data, prior party control ofthe district, incumbency status, candidate qual-ity, or demographic characteristics of the vot-ing age population.

The first three approaches to estimatingseats-votes curves also have the disadvantageof being sensitive to the choice of election dataused and other inputs to the calculations, be-cause, for example, you must choose whichstatewide office to use for the elections understudy. These methods will sometimes producevery different estimates of partisan bias with adifferent choice of statewide office. The state ofthe art fourth approach does not have this dis-advantage, because all available data may beused, we do not need to assume that peoplevote the same way for statewide offices as inlegislative elections, actual election data fromthe legislature under study are used, and spe-cial statistical procedures are introduced thatmake the method work even when highly pre-dictive variables are not available. Imple-mented properly, estimates of partisan bias fora particular redistricting plan tend to be quitesimilar, and within the margin of error, even if

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45 A partial exception is when we have a massive re-alignment under way, but in many such situations, it isusually the case that, within any given state, electoraltides are moving generally in the same direction and sothe assumption still holds.

available explanatory variables change to alarge degree.46

The final advantage of the new approach isthat allowing approximate uniform partisanswing also turns out to provide accurate sta-tistical measures of the “margin of error,” sothat we can know how confident we can be inthe values we get for partisan bias. In this way,courts can be aided in determining the weightto give an expert’s testimony about the magni-tude of partisan bias.

In its present form, this standard methodol-ogy for measuring symmetry and partisan biasis well-established, widely accepted, peer-re-viewed, and highly reliable.

Prospective versus retrospective tests

The durability of partisan gerrymandering ef-fects. The approach to partisan gerrymander-ing based on symmetry allows us to deal notonly with the issue of severity in the form ofthe magnitude of partisan bias, but also withthe issue of the expected durability of partisangerrymandering effects that was raised by theBandemer plurality.47 The Bandemer Court re-quired that gerrymandering be durable in itseffects before it could rise to the level of a con-stitutional violation (the redistricting must“consistently degrade” a voter’s or group ofvoters’ influence on the political process as awhole). In effect, under that standard, plaintiffsmust show that they have little or no hope ofovercoming the plan’s discriminatory bias.

It is sometimes claimed that we do not needto worry about a redistricting’s partisan im-pacts because these will “wear off” over thecourse of a decade. In general, that need not betrue. It is certainly true, of course, that those at-tempting gerrymandering do not alwaysachieve the effects they intend. And, if theymake a mistake gerrymandering, the partisaneffects of their efforts can wear off over time,or even be reversed.48 But that gerrymander-ing does not always work, or even that it some-times fails over time, certainly does not meanthat there can be no such thing as a successfulpartisan gerrymander. The methodology wepropose allows us to distinguish those cases inwhich a gerrymandering might have been at-tempted but was not very well done from those

cases in which the partisan bias imposed bygerrymandering is expected to be both sub-stantial and long-lasting. While measures ofpartisan bias involve “if, then” scenarios ratherthan crystal ball gazing, there are special cir-cumstances in which it may be possible to an-ticipate durable partisan biases that lock-in par-ticular outcomes or ranges of outcomes.

Journalistic accounts of partisan gerryman-dering often describe it as a process of packingone’s opponents into as few districts as possi-ble and seeking to win the remaining districtsby the barest of margins. While there is a gooddeal of truth in this portrait, more sophisticatedanalyses have shown it to be flawed. “Efficient”partisan gerrymandering is forward looking,and seeks to take into account the magnitudeof longer run “electoral tides.”49 Thus, skilledgerrymanderers draw districts for the party in-tended to be the beneficiary of the gerryman-der with expected margins that are largeenough to insulate those districts from ex-pected changes over times in voter preferences.


46 In any challenge to a plan as an unconstitutional parti-san gerrymander courts will apply the traditional criteriafor admitting expert evidence and determine in each case(1) whether the experts are qualified; and (2) whether theirparticular analyses are reliable. Indeed, as noted earlier,courts regularly use statistics in a number of different ar-eas of voting rights law. For example, statistical measuresare commonly used to determine levels of racial bloc vot-ing and to help decide whether a minority group can electa candidate of its choice (see Thornburg v. Gingles, 478 U.S.30, 52–53 (1986)). In each instance, the court must makea judgment about the expert and the methodology. For athorough discussion of the different statistical standardsused to determine whether a plaintiff has met the Ginglestest and their reliability, see Bone Shirt v. Hazeltine, 336 F.Supp. 2d 976, 995–1005 (D.S.D. 2004) (discussing the var-ious standards and surveying cases that apply these stan-dards).47 Davis v. Bandemer, 478 U.S. 109 (1986).48 Indeed, failure to take into account anticipatablechanges over time in voter support (i.e., failing to readthe “handwriting on the wall”) can convert a plan thatwas intended to have been gerrymandered to favor PartyA into a plan whose actual consequences are to favorparty B. See Bernard Grofman and Tom Brunell, “The Artof the Dummymander: The Impact of Recent Redistrict-ings on the Partisan Makeup of Southern House Seats,”in Peter Galderisi (Ed.), Redistricting in the New Millenniumpp. 183–199 (Lexington Press, 2005).49 For a discussion of efficient partisan gerrymanderingsee Guillermo Owen and Bernard N. Grofman, Optimalpartisan gerrymandering, 7(1) Political Geography Quar-terly 5–22 (1988).

That is, they attempt to draw districts so as to re-sult in high levels of partisan bias in their favor andlow levels of electoral responsiveness.

When we have skillful partisan gerryman-dering, we see low levels of electoral respon-siveness being implemented by the party do-ing the gerrymandering protecting incumbentsof its own party with safe seats, and packingpartisans of the opposing party into seats thatcan be confidently expected to be very safe forthe minority party candidate in the district overthe course of a redistricting decade. Thus, whenwe have sufficiently skillful partisan gerry-mandering, rather than the constituents choos-ing their legislator, those drawing the lineschoose each legislator’s constituents in such afashion that the non-term-limited legislator canexpect to be safe as long as the legislatorchooses to run for reelection, unless there is atruly enormous voter swing.50 Indeed, if theyare given a district free of competition from afellow legislator of their own party, sometimesself-interested incumbent legislators of the mi-nority party are very happy with the results ofa partisan gerrymander for the other party be-cause their own seats have been made so safe.51

But party leaders of the minority party, espe-cially those from outside the legislature, arelikely to be left very unhappy because the wayin which lines have been drawn essentiallyfreezes in the minority party’s status as a mi-nority party. Fortunately, the same concepts ofbias and responsiveness, and the methodologyused to measure them that we have described,can be used to assess both the bias of a planand the expected durability of its effects.

Hypothetical, versus directly observed, un-equal treatment. Justice Kennedy makes itclear in his opinion that he is bothered by thefact that estimates of partisan bias commonlyrely on projecting previous information fromprevious elections into the future: “Even as-suming a court could choose reliably amongdifferent models of shifting voter preferences,we are wary of adopting a constitutional stan-dard that invalidates a map based on unfair re-sults that would occur in a hypothetical stateof affairs.”52 Consequently, as noted earlier, hisopinion suggests that litigation might be betterdelayed until levels of partisan bias could be

observed directly from one or more electionsunder a given plan. We do not wish to dis-courage partisan gerrymandering law suits be-ing brought after an election had taken placeunder a new plan, since then any harm fromthe redistricting plan can in fact be judged withsomewhat less uncertainty after the election.Moreover, if the Court required partisan sym-metry to be part of the judicial standard of par-tisan gerrymandering only after the first elec-tion, redistricters would surely anticipate thisin drawing the districts in the first place, espe-cially since it is so easy to assess the plan be-fore the election. Nevertheless, there exist anumber of reasons to think that the pluralitylanguage in Bandemer53 allowing for reliance oneither an “actual” or a “projected” history ofdisproportionate results is to be preferred to aninsistence that only evidence from electionsconducted under a plan be regarded as proba-tive. We outline those reasons here.

First, as noted above, use of a partisan sym-metry test does not involve predicting actualelection outcomes in the form of vote shares.The redistricting plan itself, which is the docu-ment that to be declared constitutional or not,exists prior to the election and observing it involves no hypotheticals or counterfactuals.Moreover, the effect of the redistricting plancan be directly estimated before the electionbased on conditional, statistically grounded as-sertions about what would happen to outcomesif any particular aggregate vote share percent-

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50 The minority party members are given really safe seatswith the intention of concentrating the votes of theirparty’s supporters in as few seats as possible; but themembers of the majority party are also given safe seats,now with the intention of making sure that those seats re-main safe over the course of subsequent elections.51 As noted in the plurality opinion in Vieth at 571–2, “ef-forts to maximize partisan representation statewide mightwell begin with packing voters of the opposing party intothe districts of existing incumbents of that party. By thismeans an incumbent is protected, a potential adversaryto the districting mollified, and votes of the opposingparty are diluted.”52 LULAC, 126 S. Ct. at 2611 (opn. of Kennedy, J.). JusticeBreyer in Vieth refers to situations where a majority partyin votes has twice been denied a majority of seats as ev-idence which might compensate for the absence of otherindicia of unjustified entrenchment of a minority party inpower.53 Davis v. Bandemer, 478 U.S. 109, 140 (1986).

age were achieved by a given political party’scandidates. Measurements by experts aboutpartisan bias in a redistricting plan are thus notefforts to divine the future. For example, in asingle district election, the claim that “electoralrules declare whichever candidate who garnersa plurality of the vote the winner of the seat”is an example of an if-then statement, and re-quires no prediction about or knowledge ofwhich party will win the vote plurality. Simi-larly, the statements required in ascertainingpartisan bias are statements about what levelof asymmetry can be expected in translating thevotes for the Democratic and Republican can-didates in a legislature into seats in that legis-lature if, in the future, there were to exist a par-ticular level of voter support for each party. Thelevel of support that voters give to the partiesis the voter’s own business and is not stipu-lated ex ante as part of this definition of fair-ness. Rather, by examining all the relevant dataand the potential seat divisions that would oc-cur for particular vote divisions, social scien-tists can compare the potential scenarios anddetermine the consequences for partisan bias ofa map, separating out other potentially con-founding factors. The question is not whethera particular party will win; it is whether the re-districting plan on the table has stacked thedeck to such a degree that the plan burdens theother party’s “rights of fair and effective rep-resentation.”54

Second, as also noted above, the assumptionsused are relatively weak ones, involving onlyrelative propensities of the voters within a par-ticular geographic area in a state to vote for agiven political party as compared to voterswithin some other geographic area. It is an em-pirical question as to whether units of geogra-phy can be distinguished in their partisanpropensities, and thus whether partisan gerry-mandering is even possible. But if partisan ger-rymandering is possible, then systematic mea-surement of it is possible. Just as raciallypolarized voting is a “linchpin” of racial votedilution claims, even though vote dilution andracial polarization are completely distinct con-cepts, so the empirical claim that partisanpropensities exist in a jurisdiction that arestrong enough to allow us to roughly rank or-der units of geography in their expected parti-

sanship is a necessary predicate of any parti-san gerrymandering claim.55

Third, when we look at actual evidence aboutthe predictive power of this methodology weare reassured about its usefulness. For exam-ple, in expert witness testimony in a Californiacongressional districting case of the 1990s byBernard Grofman, specific claims were made in1994 about a “Democratic lock” that would beexpected to last the rest of the decade barringsubstantial changes in California statewide vot-ing patterns. These observations turned out tobe highly accurate.56 Similarly, predictionsgiven in expert witness testimony in FederalDistrict Court by Gary King for every districtelection in the Ohio State House and Senatealso proved highly accurate.57

Fourth, the use of this methodology by theexperts for opposing sides who testified aboutpartisan gerrymandering in the cases consol-idated into LULAC (Professor Alford and Pro-fessor Gaddie) were in remarkable agreementabout the partisan implications of the planswhose partisan bias they investigated. As Jus-tice Stevens points out: “According to Pro-fessor Gaddie, the State’s expert, Plan 1374Cgives Republicans an advantage in 22 of 32congressional seats. The plaintiffs’ expert . . .agreed. [That expert] added that in his view,the only surprise from the 2004 elections was‘how far things moved’ toward achieving a


54 Vieth, 541 U.S. at 312 (Kennedy, J., concurring in thejudgment).55 A variant of this point is made by Justice Souter (joinedby Justice Ginsburg) in their dissenting opinion in Vieth,at 602, who argue that, to bring a successful partisan ger-rymandering claim, it must be shown that plaintiffs are amember of a politically “cohesive” group. However, wewould emphasize that the test we propose, based on be-havior at the level of units of geography, is less restric-tive than that suggested by Justices Souter and Ginsburg,since our test refers only to the potential for partisan ger-rymandering based on geographically-based districts,and does not require analysis at the individual voter level.56 See Bernard Grofman, Declarations in Badham v. Eu (ex-cerpts), PS 544–549, 573–574 (Summer 1985); cf. BernardGrofman, Introduction to Minisymposium on Political gerry-mandering: Badham v. Eu, Political science Goes to Court, PS538–543 (Summer 1985).57 These predictions were reported in Andrew Gelmanand Gary King, A Unified Method of Evaluating ElectoralSystems and Redistricting Plans, 38(2) Am. J. Pol. Sci.514–554 (May, 1994).

22-10 pro-Republican split ‘in a single electionyear.’ ”58

While such congruence among experts foropposing sides cannot prove that the method-ology for determining partisan symmetry isvalid for predictive purposes, it enhances ourconfidence that courts can find credible expertwitness testimony to give reliable estimatesthat can be helpful in resolving partisan gerry-mandering cases. The assertions that using as-sessments of hypotheticals based on previouselection results (and some statistical calcula-tions) to calculate levels of partisan bias is be-yond the competence of expert witness testi-mony, or results in claims whose credibilitycannot be evaluated by courts, is simply wrong.In cases involving racial vote dilution claimsunder the 14th Amendment or under Section 2of the Voting Rights Act of 1965 as amended in1982, for almost forty years, expert witnesseshave been routinely making use of hypotheti-cals in a very similar way to what would be re-quired in calculations of partisan bias. What ex-perts in these racial cases have done is useprevious election outcomes and knowledge ofracial demography to calculate the hypotheti-cal minority population proportion needed toprovide minorities a realistic opportunity toelect candidates of choice with votes entirelyfrom within the minority group, and/or the hypothetical minority population proportionneeded to provide minorities a realistic oppor-tunity to elect candidates of choice if there is agiven level of reliable white crossover voting.

Fifth, in voting rights cases, courts com-monly make what we might think of as “pre-sumptive” findings of statutory or constitu-tional violations. For example, in looking atplans under the Voting Rights Act, it is almostinevitable that a plan will be evaluated for Sec-tion 5 compliance before any elections havebeen held under the plan. There is no obviousreason why an analogous rule should not ap-ply to partisan gerrymandering.

Finally, and relatedly, there are also goodreasons to think that a gerrymandering stan-dard that is addressed to prospective harmsrather than to harms already committed can belawful. Consider, for example, a claim that acontractor has violated fiduciary obligations orbeen guilty of wrongful neglect by using a ce-

ment mix that is likely to crumble over time.We would not want to have to wait until thebuilding collapsed to compel a remedy. Norwould we need to know exactly when the dis-aster was going to occur as long as its occur-rence could be reliably predicted. Moreover, inthe context of redistricting, once lines havebeen redrawn to favor a given party, the elec-toral advantage of incumbency will be con-ferred on the winners, who will then carry thisadvantage into new elections, which may makeit harder to undo the damage from an illegalpartisan gerrymander than if the problem wereavoided in the first place. In addition, the mi-nority party “will surely have a more difficulttime recruiting strong candidates, and mobi-lizing voters and resources, in these . . . safedistricts.”59

Avoiding common misunderstandings

We conclude this section by discussing andclarifying ten misunderstandings about sym-metry and partisan bias that should be avoided.We have drawn our illustrations of these mis-understandings primarily from the briefs ofvarious of the Appellees and amici in Jackson v.Perry, one of the cases consolidated under thename LULAC v. Perry. We believe the discus-sion below can be helpful to courts reviewingexpert witness testimony and legal argumentsabout the nature of partisan bias and partisanfairness.

First, it is sometimes claimed, as in the Briefof Appellees Tina Benkiser, Chairman, Repub-lican Party of Texas, and John DeNoyelles inJackson v. Perry,60 that the methods describedabove cannot be applied because results will beso dependent upon which particular electionsand other data are used that no meaningful cal-culations about the magnitude of partisan bias

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58 LULAC, 126 S. Ct. at 2626-2637 (n. 6) App. to Juris State-ment at 225a (declaration of John R. Alford, Ph.D.). Jus-tice Stevens (n. 7 at p. 20) notes that Republicans won “21of the 22 seats that had been designed to favor Republi-cans in Plan 1374C,” and goes on to comment that the ev-idence suggests that the lone exception, RepresentativeEdwards, who won by only 51% of the vote, may not besafe in 2006.59 LULAC, 126 S. Ct. at 2640 (opn. of Stevens, J.).60 At pp. 18–19, n.10.

can be provided. Given modern technology,that claim is false. Experts can disagree aboutwhich set of input data is relevant for a givencase, but the resulting measures of partisan biasnormally will not differ to any significant de-gree because the best current methods are quiterobust to changes in model specification. Be-cause social scientists studying partisan biasrely on the symmetry standard as the baselinefor attempting to calculate the degree of bias,differences of opinion between experts will belimited in scope. In practice, differences acrossexperts in the academic literature, and eventhose on opposite sides in redistricting litiga-tion have usually been minor, especially whenconsidering the margin of error properly cal-culated. We expect that the methodology of as-certaining the seats-votes curve from real data,and then measuring partisan bias (and electoralresponsiveness, if desired) will continue to im-prove, but the current state-of-the art method-ology has now matured to the point where thevast majority of the available relevant infor-mation is now incorporated in the methods,and so future improvements will likely be in-cremental, such as helping to handle specialcases or unusual situations.

Second, some make the claim that the sym-metry standard is yet another version of a pro-portionality rule.61 This assertion is factuallyincorrect.62 Those making such a claim are con-flating two very different concepts, propor-tionality and symmetry, by confusing electoralresponsiveness with partisan bias. Perfect pro-portionality is allowed as one possible fair sys-tem under the symmetry definition of fairness,but symmetry does not require proportional-ity. Fairness in the form of symmetry can existin electoral systems that are far from propor-tional. In particular we can have the absence ofpartisan bias (or its presence at only very lowlevels) in systems such as plurality elections inthe U.S. that have electoral responsiveness val-ues that are very far from one. On the otherhand, limiting the level of partisan bias in a sys-tem has no necessary effect on the system’slevel of electoral responsiveness, and thus willhave no necessary effect on the degree to whicha system is proportional.

Third, not all methods of analyzing seats-votes curve are equally useful to the courts. As

demonstrated in the discussion of the evolutionof the social science literature on this subject,the statistical technology to investigate seats-votes relationships has now matured to thepoint where it can be counted on to provide re-liable information for public policymakers, thecourts, and others involved in redistricting.However, when laypersons are discussing dataon seats-votes curves they sometimes presentand analyze that data in a misleading way. Forexample, in the State Appellees Brief in Jacksonv. Perry, and in the Republican Party of TexasBrief in Jackson v. Perry, data are reported onstatewide vote shares and on statewide seatoutcomes and the two numbers are comparedto provide an indicator of partisan fairness.63

But, this simplistic mode of analysis makes itvirtually impossible to distinguish discrepan-cies between seat share and vote share that arecaused simply by levels of electoral respon-siveness higher than one from discrepanciesthat are caused by actual partisan bias.


61 See e.g., State Appellees Brief in Jackson v. Perry, at p.46.62 In the plurality opinion in Vieth authored by JusticeScalia, the Court reiterates its long standing view that “theConstitution provides no right to proportional represen-tation.” This is a legal conclusion, and so not in ourpurview, but in any case, not one with which we woulddisagree. Indeed, we would note that the use of pluralityelections in single seat and multi-seat districts (and in at-large elections) at the time of the founding reinforces theview that the Constitution has no mandate for propor-tional representation in either method or result, and thecontinued use of plurality-based elections after the pas-sage of the Civil War Amendments further reinforces thisconclusion. However, the plurality opinion in Vieth, alsoasserts that the claim that a map is unconstitutional be-cause it “can thwart the plaintiffs’ ability to translate amajority of votes into a majority of seats” is equivalent torequiring proportional representation. That is a statementabout political science methodology, and one that is er-roneous. Nonetheless, we should also be equally clear thatin this article we are not asserting that any plan thatthwarts a party’s ability to translate a majority of votesinto a majority of seats must necessarily be held uncon-stitutional. Rather, we are simply proposing a way tomeasure the magnitude of partisan bias, and leaving itentirely up to the Supreme Court to determine the mag-nitude of (durable) partisan bias that rises to the level ofa (prima facie) constitutional violation. See extended dis-cussion of the issue of thresholds and manageable stan-dards in Section IV.63 Brief of Appellees Tina Benkiser, Chairman, Republi-can Party of Texas, and John DeNoyelles in Jackson v.Perry, at pp. 21–26).

A fourth empirical misunderstanding isfound in the statement in the plurality opinionin Vieth, that, “even if a majority party couldbe identified, it would be impossible to assurethat it won a majority of seats unless the States’traditional election structures were radically re-vised.”64 This point is linked to an importantinsight into a statistical feature of plurality elec-tions discussed above, namely that plurality-based elections cannot be expected to generateproportional outcomes because of what issometimes referred to as the “bonus effect,”and hence it is inappropriate to use propor-tionality in the outcomes of plurality-basedelections as a test for partisan fairness or of theequality of treatment of the voters who are thesupporters of the (two) parties. But, as we em-phasized earlier, from the fact that we cannotexpect plurality-based plans to be proportional,it does not follow that we cannot apply thequite different concept of partisan bias to eval-uate plans that use plurality based elections(see further discussion of crafting of judiciallymanageable standards in Section IV below). Infact, since partisan symmetry does not implyproportionality, the problem identified is not aproblem.

A fifth misunderstanding is found in the plu-rality opinion in Vieth that begins with the fun-damentally sound insight into real world poli-tics that “a person’s politics is rarely as readilydiscernible—and never as permanently dis-cernible—as a person’s race. Political affiliationis not an immutable characteristic, but mayshift from one election to the next; and evenwithin a given election, not all voters follow theparty line. We dare say (and hope) that the po-litical party which puts forward an utterly in-competent candidate will lose even in its reg-istration stronghold.”65 Considerable literaturein political science supports this claim of thefour Justices in the Vieth plurality that voterchoices may vary from election to another, andthat there are idiosyncratic reasons why onecandidate of a party may do well and anotherdo badly. But they go too far when they alsoclaim that these facts make “it impossible to as-sess the effects of partisan gerrymandering, tofashion a standard for evaluating a violation,and finally to craft a remedy.”66

That claim does not follow from the empiri-

cal regularity noted, four sub-points aboutwhich are critical.

A. As noted earlier, the empirical findingsnecessary for experts to demonstrate partisangerrymandering are directed at characteristics ofthe electoral system, and thus based on “if, then”scenarios, not on predictions about vote shares.

B. The second point has to do with drawingthe correct implications of the fact that partisanpropensities are not fixed, immutable featuresof human beings. Far from this being a prob-lem for using the methodology used to calcu-late partisan bias, it is precisely this mutabilitythat allows us to make use of the standard so-cial science methodology necessary for mea-suring partisan bias.67

C. Regarding the mutability of partisanship,the partisan bias methodology we propose ismakes only a very weak assumption, namelythat different units of geography can be ap-proximately rank ordered in terms of their av-erage partisan propensities.

D. Finally, because measuring deviationsfrom symmetry requires understanding hypo-thetical scenarios about the consequences ofchanges in partisan vote shares, in order forpartisan bias calculations based on such sce-narios to be meaningful, these changes in voteshares must, at least in principle, be feasibleones.68 For example, consider a state where theDemocrats consistently receive 80% of the av-erage district vote in election after election,decade after decade, and where we thereforehave no experience of the Republicans evercoming close even remotely to a majority, muchless 80%. In this situation, even though the con-cept of partisan symmetry still applies in the-ory, ascertaining what would happen to theseat division in symmetric situations where

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64 Vieth, 541 U.S. 267 at 552.65 Vieth, 541 U.S. 267 at 286 (internal citations omitted).66 Vieth, 541 U.S. 267 at 287.67 Put differently, a partisan symmetry test for the mag-nitude of partisan bias is easy to apply in normal, healthy,democratic electoral systems. That is because in such sys-tems, not everyone always votes consistently for the sameparty.68 Similarly, as we discuss in Section V, applying the sym-metry methodology to evaluate the equality of treatmentfor groups with fixed characteristics, such as race, is notsensible.

each party in turn received some fixed per-centage of the vote would be so far from thehistorical experience that no empirical methodcould be reliably used to ascertain the degreeof partisan bias.69 Thus, the methodology wepropose is intended only for jurisdictionswhere the politics is competitive enough that itis empirically feasible to develop reliable ex-pectations what each party would receive inseats if it won a given sized majority of thevotes.70 Because we are not proposing to applythis methodology in every situation, but onlyin potentially competitive jurisdictions, wherethe consequences of gerrymandering might beespecially onerous in thwarting the will of themajority, the burden on courts of seeking to ap-ply our methodology is correspondingly lim-ited.71 Which settings are appropriate (in a statistical sense) for application of the method-ology used to establish partisan fairness is ap-propriately a topic for expert witness testi-mony, but in most jurisdictions which go tolitigation this issue is likely to prove completelyunproblematic.

A sixth and related error about the partisanbias approach has to do with claims that it re-quires us to consider empirically implausibleas well as purely hypothetical outcomes. StateAppellees in their Brief72 claim that the sym-metry standard is “designed to address onlythe rare if not unprecedented situation of anelectorate shifting near instantaneously from amajority (of 58% or more) of one party to acomparable majority of another.” Of course,this clever phrasing is a complete mischarac-terization of how deviations from partisansymmetry are established. The symmetry defi-nition does not, in any way, envision instanta-neous shifts of huge magnitude. Rather, it con-siders possible outcomes in the range whereelections are reasonably competitive (such asfrom 40% to 60% for a party). Moreover, as em-phasized earlier, we only propose to apply themethodology to jurisdictions where it is factu-ally reasonable to assume that elections can becompetitive somewhere within this range.

A seventh and related mistake was madewhere they claim that “[b]y definition, [thesymmetry standard] does not assess the elec-toral results that will actually be produced bya plan, but makes its validity turn on theoreti-

cal results that might occur if political circum-stances significantly change.”73 As we haveemphasized, there is no way to determine the“electoral results that will actually be producedby a plan” without knowing how voters actu-ally voted. Even when there has been an elec-tion under a plan, court determination aboutthat redistricting plan still involves case factsthat turn on hypotheticals about how the planwill operate in future elections.

The key assumption behind using hypothet-icals in calculating partisan bias is simply thatit is possible to approximately rank order unitsof geography in terms of their partisan propen-sities.74 But, that is exactly what gerrymander-ers must do when they decide how to constructtheir gerrymanders. When we use the method-ology described above to calculate partisan biaswe are merely positing that it is realistically


69 The problem of counterfactuals (or hypotheticals)posed so far from the data that measurement is difficultor impossible is an important general issue in statisticalanalysis. See for example Gary King and Langche Zeng,The Dangers of Extreme Counterfactuals, 14(2) Political Anal-ysis (2006); Gary King and Langche Zeng, When Can His-tory be Our Guide? The Pitfalls of Counterfactual Inference,International Studies Quarterly (2006, forthcoming).70 Applying the symmetry standard to a political systemwith consistent one-party control is not feasible or rele-vant. In electoral systems that do not function as democ-racies, or have some non- or semi-democratic featuressuch as de jure or de facto one-party rule, or the total ab-sence of partisan competition, other features of the elec-toral system would need to be studied (or remedied) be-fore it would be reasonable to assess the degree anddirection of partisan bias.71 However, one qualification is necessary. For state re-districting of Congressional elections, since Congresscould be nationally competitive while locally uncompet-itive, or nationally uncompetitive while locally competi-tive, in these situations, we would propose to apply themethodology where either consideration was applicable.However, we recognize that the choice as to how to de-limit the domain of cases to which the partisan biasmethodology would be applied is ultimately a legal issueeven though some restrictions (e.g., to settings that arepotentially competitive) are necessary for purely statisti-cal reasons.72 In Jackson v. Perry, at p. 47.73 In the Brief of Appellees Tina Benkiser, Chairman, Re-publican Party of Texas, and John DeNoyelles (at p. 18).74 As suggested earlier, courts often rely on expert wit-ness testimony to do just that. For example, in Balderas v.Texas, 536 U.S. 919 (2002), the district court used the num-ber of districts leaning in favor of each party based onprior election results to estimate which congressional dis-tricts could be expected to lean toward each party.

possible to construct a partisan gerrymander byputting together different units of geography.75

An eighth error is found in the State Ap-pellees claim76 that the symmetry standarddoes not “account for the heterogeneous dis-tribution of population and political prefer-ence.” This assertion is false. The symmetrydefinition of fairness applies directly andstraightforwardly no matter how heteroge-neous are the voter populations or their parti-san preferences. Moreover, the methods thathave been developed to measure partisan biasexplicitly take into account heterogeneity indistrict votes, and cause no difficulties for ei-ther conceptualization or measurement.

A ninth point of confusion is found in thecomplaint of the State Appellees77 that “nostandard exists in the [social science] literatureas to how much partisan bias is unconstitu-tional.” While we have no quarrel with that as-sertion, this brief is obviously confusing issuesthat are properly in the domain of the courtswith those that fall within the expertise of po-litical scientists and other social scientists. Con-sensus among political scientists about issuesin constitutional law is not of legal relevance;78

consensus among political scientists about is-sues of conceptualization and measurement ofpartisan bias would, on the other hand, behighly relevant were courts to adopt a test thatmakes use of information about levels of par-tisan bias, because the fact of such a consensusinforms the Court about the likelihood that re-liable empirical evidence can be introducedinto the record by competent experts about themagnitude of partisan gerrymandering effects.

Similarly, the fact that there is no consensusamong political scientists as to what level ofpartisan bias is unconstitutional does not, asthe State Appellees claim,79 “merely restate thefundamental quandaries that left the Court inVieth searching for a substantive measure offairness.” Rather, as we show in the next sec-tion, if partisan bias were to be adopted as akey component of a legal test for unconstitu-tional partisan gerrymandering, the SupremeCourt could draw on its jurisprudence in othervoting rights areas to establish appropriateconstitutional thresholds and to evaluate em-pirical evidence for unconstitutional effects ina fashion that is readily judicially manageable.

Having an unambiguous, generally accepted,and easy to apply definition of partisan fairnessin redistricting will make devising a legal stan-dard for unconstitutional partisan gerryman-dering much more straightforward.

A final and related source of confusion aboutthe partisan bias methodology is the claimmade by the State Appellees in their Brief inJackson v. Perry, at p. 47 that “adopting an over-all goal of ‘symmetry’ would require con-structing maps that take no account of other,more traditionally meaningful redistrictingvalues.” That claim is flatly wrong. As we dis-cuss in Section IV, by drawing on well-estab-lished approaches in other domains of votingrights case law, standard redistricting criteriacan easily be incorporated into legal review ofpartisan gerrymandering claims, especially asthey involve consideration of defenses againsta finding of partisan bias that rely on the State’sclaimed need to satisfy standard districting cri-teria, and issues of constructing judicial reme-dies if unconstitutional partisan gerrymander-ing is found. More generally, we would notethat the fact that there are competing legitimate(or even constitutionally grounded) criteriawhich courts must balance when consideringpartisan gerrymandering is no different fromthe task confronting courts in many other ar-eas of constitutional and statutory jurispru-dence involving various aspects of the Bill ofRights or the Civil War Amendments.

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75 Justice Souter’s opinion in Vieth, 158 L. Ed. 2d 546, at602, cites to various sources supporting the view that par-tisan gerrymandering has been made easier given mod-ern computer technology (e.g., R. Pildes, Principled Limi-tations on Racial and Partisan Restricting, 106 Yale L. J. 2505,2553–2554 (1997) (“Recent cases now document in [mi-croscopic] detail the astonishing precision with which re-districters can carve up individual precincts and distrib-ute them between districts with confidence concerningthe racial and partisan consequences”); and Morrill, “AGeographer’s Perspective,” in Political Gerrymandering andthe Courts 213–214 (B. Grofman ed. 1990) (noting that ger-rymandering can produce “high proportions of very safeseats”).).76 In their Brief in Jackson v. Perry, at p. 47.77 In their Brief in Jackson v. Perry, at 46–47.78 Whatever might be our views as citizens, as social sci-entists, we deliberately chose not to advocate a specificthreshold test for egregious partisan gerrymandering,since we regard setting this threshold as a matter of con-stitutional interpretation best left to the courts.79 In their Brief in Jackson v. Perry, at p. 46.

III. OPTIONS IN SETTING LEGALTHRESHOLDS FOR PRIMA FACIE

UNCONSTITUTIONAL PARTISAN BIAS

We have argued that the now well-devel-oped statistical methodology used in the schol-arly literature to measure partisan bias andelectoral responsiveness can readily form theevidentiary basis for a metric that can be usedto measure partisan gerrymandering effects,80

and it can allow courts to craft a “clear, man-ageable, and politically neutral” measure of“the particular burden a given partisan classi-fication imposes on representational rights.”81

The level of partisan bias (which can be calcu-lated as the difference between the seat sharesthat each of the two parties would receive ifthey each had received identical shares of thevote) can be used to evaluate the extent towhich “each political group in a State [has] thesame chance to elect representatives of itschoice as any other political group.”82

However, as we have emphasized earlier,while partisan bias can provide the basis ofmeasuring the magnitude of inequality of treat-ment, the issue of when inequities rise to thelevel of a constitutional violation is a quite dis-tinct question. In this section we focus on fivepotential approaches to craft a judicially man-ageable standard for unconstitutional partisangerrymandering that build on the concept ofpartisan bias to identify legal thresholds forprima facie evidence of equal protection viola-tions. Each of these approaches can be seen asstraightforward adaptations of constitutionalor statutory standards that the Supreme Courthas adopted in other areas of voting rights caselaw. The latter two arise from ideas in JusticeKennedy’s opinion in LULAC.

Require plans with as little partisan bias as practicable

The Supreme Court could adopt a rule thatrequires plans that create as little partisan biasas practicable. Such a rule could be adaptedfrom the Supreme Court’s jurisprudence inthe area of standards for acceptable deviationsfrom population equality in the context ofCongressional districting. In the one-person,one-vote context, the Supreme Court has re-

quired zero population deviation for Con-gressional districts, while still permitting thestate to justify minor population deviances byshowing a compelling need.83 Moreover, thestate need only achieve complete populationequality “as nearly as practicable.”84 So longas a state attempts in good faith to create equaldistricts, the plan passes constitutionalmuster.85

If this were the approach taken by theCourt, states would need to make a good-faitheffort to achieve as little partisan bias as pos-sible. States can comply with the “as little aspossible” rule quite simply. The sophisticationof computer mapping technologies allowsstates to evaluate partisan bias in creating aredistricting plan. States may then attempt tojustify deviations from political symmetry bypointing to a legitimate interest such as com-pactness, respecting municipal boundaries,minority rights, or respecting communities ofinterest.86

Disqualify plans with partisan bias that deviatefrom symmetry by at least one seat

The Supreme Court could adopt a rule thata plan can be overturned as an unconstitutionalpartisan gerrymander only if it can be shownthat the plan locks in political advantage forone political party of one or more legislativeseats as compared to a plan that was symmet-ric with respect to the parties. Through the useof experts, a plaintiff would have to prove thata map would cause a group to lose at least oneseat. Such a rule could be adapted from theSupreme Court’s jurisprudence in the area of


80 The courts have frequently made use of statistical con-cepts adapted from the social sciences in devising votingrights standards, e.g., Thornburg v. Gingles, 478 U.S. 30,55–61, 74–77 (1986) (using statistics to determine the ex-istence of racial bloc voting, a necessary part of any § 2claim); or Brown v. Thomson 462 U.S. 835 (1983) (measur-ing the total population deviation to adjudicate one person,one vote claims).81 Vieth, 541 U.S. 267 at 307–308 (Kennedy, J., concurringin the judgment).82 Davis v. Bandemer, 478 U.S. at 124.83 See, e.g., Karcher v. Daggett, 462 U.S. 725, 740–41 (1983).84 Id. at 730.85 Id. at 730–31.86 Cf. id. at 740.

standards for minority vote dilution in the con-text of Section 2 of the Voting Rights Act.87

Disqualify only those plans with egregious levelsof partisan bias (defined in terms of a specifiedpercentage point threshold)

The Supreme Court could adopt a rule set-ting a standard for egregious gerrymanders, byspecifying a threshold level of partisan bias inpercentage point terms such that plans whichexhibit levels of bias below that threshold areregarded as prima facie constitutional, andwhich requires that plans with partisan biasabove that threshold to be justified in terms ofcompelling, legitimate, and rational state poli-cies and interests. Such a rule could be adaptedfrom the Supreme Court’s jurisprudence in thearea of standards for acceptable deviationsfrom population equality in the context of stateand local districting.88

In this third approach, if the average differ-ence in the seat percentage between the twoparties, given an empirically reasonable valueof the average district vote, is above a particu-lar threshold (whether it be 3, 5, or 10 percent-age points), the plan would be prima facie un-constitutional. For example, suppose the courtset the standard at 10 percentage points. In thissituation, a plan would not be unconstitutionalunless one party could be expected to capture10 percentage points more seats than the otherparty even if the two parties received identicalshares of the vote.89 This unconstitutional levelwould be reached if the Democrats received65% of the seats if they received 55% of thevotes, but the Republican Party received 75%of the seats given the same 55% vote share.

Each of the three approaches above is basedon a different but easy-to-manage judicial stan-dard, and one that has been applied in otherareas of the law. For example, since states knowthe total population before redistricting, andbecause application of the one-person, one-votestandard is straightforward, relatively little lit-igation results. Similarly, whenever a state re-districts and uses existing computer technol-ogy so that we can match (past) electionoutcomes to geographic units, measuringprospectively or retrospectively the partisanbias of a plan is also straightforward.90

Disqualify only those plans that (can be expectedto) translate a minority of the votes into amajority of the seats

In general, it is not possible to directly inferthe existence of partisan bias from the fact that agiven party receives a lower seat share than itsvote percentage. That is because, as we havepointed out earlier, seats-votes relationships area combination of electoral responsiveness andpartisan bias, the two components of which mustbe jointly estimated by appropriate statisticalmethodology. Only statistical analyses that makeuses of election outcomes in particular units ofgeography aggregated to the level of the indi-vidual districts can give us the appropriate mea-surements of these key parameters.

But there is one situation in which it is pos-sible simply by comparing vote share and seatshare to reliably infer partisan bias in an elec-tion that has already occurred, namely a twoparty contest in which a party with a majorityof the votes gets less than a majority of theseats. As long as this difference cannot be ruledout on the basis of random variability that isnot likely to persist in subsequent elections (aproblem easily avoided with the methods out-lined above), we can think of such a situation

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87 Cf. Thornburg v. Gingles, 478 U.S. at 44–46 (imposing atest for justiciability under § 2 of the Voting Rights Act,42 U.S.C. § 1973, that requires a showing that the minor-ity population is “sufficiently large and compact to con-stitute a majority in a single-member district” so there ex-ists a potential remedy plan with at least one morereasonably compact district in which minorities have a re-alistic opportunity to elect candidates of choice than isfound in the challenged plan).88 Cf. Brown v. Thompson, 462 U.S. 835 (1983) (above 10%population deviation is prima facie unconstitutional forstate legislative districts); id. at 852 (outlining test for de-termining when a plan is unconstitutional).89 This ten percentage point range threshold would cor-respond to a bias of five percentage points in that, if oneparty gets five percentage more and one party five per-centage points less than the symmetric outcome, this givesus a difference between the seat shares of the parties (rel-ative to symmetry) of ten percentage points.90 Cf. Karcher at 733 (noting that in 1983, “[t]he rapid ad-vances of computer technology and education during thelast two decades make it relatively simple to draw con-tiguous districts of equal population and at the same timeto further whatever secondary goals the State has.”).91 As far as we are aware, the majoritarian criterion is firstproposed—but not under that name—in Bernard N. Grof-man, Criteria for districting: A social science perspective, 33(1)UCLA Law Review 77–184, Table 1, p. 174 (1985).

as violating a fundamental tenet of majorityrule which we may call the majoritarian crite-rion.91

In such a situation there must be partisan biasagainst the party winning the majority of thevotes. This situation may be thought of as dis-tinct from other examples of partisan bias be-cause majoritarian ideas are so deeply engrainedin our political system. It somehow seems moreheinous to prevent a majority from exercising itsmandate, then merely to exaggerate the size of amajority. Moreover, exaggerating the size of themajority is virtually inevitable under plurality-based legislative elections because of electoral re-sponsiveness values above one (the bonus ef-fect). As we have previously remarked, JusticeKennedy, in his LULAC opinion (at p. 12) viewsthese two types of outcomes (vote majorities intoseat minorities; vote majorities into even largerseat majorities) as conceptually distinct. He alsoclearly regards the former case as the potentiallymore serious violation of equal protection interms of the impact of partisan bias in generat-ing the outcome.92

If we take this distinction seriously, and re-gard only the former type of outcome as (po-tentially) constitutionally violative it suggestsa distinct (prima facie) test for when partisangerrymandering rises to the level of an uncon-stitutional violation, namely that the level ofpartisan bias must be such as to (reliably) con-vert a minority party in terms of votes into amajority party in terms of seats. Because thiscondition will only rarely be found in situationsinvolving partisan gerrymandering—after all,normally the party which controls the district-ing is a majority party and it will merely drawplans that will extend the magnitude of itsdominance—under this test, even a prima faciefinding of unconstitutional partisan gerryman-dering might be very rare. Nonetheless, hadthis standard been in place earlier, however,the evidence reviewed in Justice Kennedy’sopinion suggests that the 1991 pro-Democraticgerrymander might have been struck down inmid-decade or later in looking at the results ofelections that took place under that plan.93 Thisdistricting was one whose circumstances couldgive rise to a violation of the majoritarian cri-terion because it was a partisan plan drawn bya party in power able to control districting

whose leadership was, arguably, aware of theelectoral tides running against the party andwho sought to preserve that party’s dominancethrough creative gerrymandering. Thus, even


92 In Vieth, Justice Breyer has taken a similar view of theimportance of majority representation:

At the same time, these considerations can help iden-tify at least one circumstance where use of purely po-litical boundary-drawing factors can amount to a se-rious, and remediable, abuse, namely the unjustifieduse of political factors to entrench a minority inpower. By entrenchment I mean a situation in whicha party that enjoys only minority support among thepopulace has nonetheless contrived to take, and hold,legislative power. By unjustified entrenchment I meanthat the minority’s hold on power is purely the re-sult of partisan manipulation and not other factors.These “other” factors that could lead to “justified”(albeit temporary) minority entrenchment includesheer happenstance, the existence of more than twomajor parties, the unique constitutional requirementsof certain representational bodies such as the Senate,or reliance on traditional (geographic, communitiesof interest, etc.) districting criteria.

The democratic harm of unjustified entrenchmentis obvious. As this Court has written in respect topopularly-based electoral districts:

“Logically, in a society ostensibly grounded on rep-resentative government, it would seem reasonable thata majority of the people of a State could elect a major-ity of that State’s legislators. To conclude differently,and to sanction minority control of state legislative bod-ies, would appear to deny majority rights in a way thatfar surpasses any possible denial of minority rights thatmight otherwise be thought to result. Since legislaturesare responsible for enacting laws by which all citizensare to be governed, they should be bodies which arecollectively responsive to the popular will.” Reynolds,377 U.S. at 565, 84 S. Ct. 1362, 12 L. Ed. 2d 506.

Vieth, at 360.

93 Justice Kennedy reports (at p. 4) that “[t]he 1991 plan‘carefully constructs Democratic districts “with incredi-bly convoluted lines” and packs “heavily Republican”suburban areas into just a few districts.’ ” Henderson v.Perry, 399 F. Supp. 2d 756, 767 n. 47 (2005); quoting M.Barone and R. Cohen, Almanac of American Politics, p. 1510(2003). His opinion notes further that “Voters who con-sidered this unfair and unlawful treatment sought to in-validate the 1991 plan as an unconstitutional partisan ger-rymander, but to no avail. See Terrazas v. Slagle, 789 F.Supp. 828, 833 (W.D. Tex. 1992); Terrazas v. Slagle, 821 F.Supp. 1162, 1175 (W.D. Tex. 1993). The 1991 plan realizedthe hopes of Democrats and the fears of Republicans withrespect to the composition of the Texas congressional del-egation. The 1990’s were years of continued growth forthe Texas Republican Party, and by the end of the decadeit was sweeping elections for statewide office. Nonethe-less, despite carrying 59% of the vote in statewide elec-tions in 2000, The Republicans only won 13 congressionalseats to the Democrats; 17. Henderson, supra, at 763.”

under this remarkably strict standard sug-gested by some of Justice Kennedy’s observa-tions about partisan bias, there is no reason tothink that partisan gerrymandering would re-main a legal “dead letter.”94

Disqualify only those plans whose partisan bias isboth severe and greater than that in the planbeing replaced

A central issue with respect to any standardfor equal protection is the specification of abaseline against which equal treatment is to bejudged. As long as the U.S. makes uses of plu-rality-based single seat districts for its most im-portant elections, the issue of determining abaseline will be with us. For two party compe-

tition, a good way to specify such a baseline isto look at deviations from symmetry in trans-lating votes into seats at the point where eachparty receives exactly 50 percent of the vote.Equal treatment is this context implies that eachparty would get an (approximately) equalshare of the seats. Another approach, sug-gested by ideas in Justice Kennedy’s opinion,is to compare the magnitude of the deviationsfrom partisan symmetry found in the chal-lenged plan with that found in its immediatepredecessor (or predecessors). A possible testbased on this idea would give us a prima faciecase for unconstitutional partisan gerryman-dering only if the plan’s deviations from sym-metric treatment were both severe and moreegregious than those in previous plans.95

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94 Also we would emphasize that this test directly in-volves what we may think of as a special case applica-tion of the symmetry standard.95 Justice Kennedy’s opinion (at pp. 4–6) seems to indi-cate that he regarded the LULAC challenge to the 2003Texas congressional plan as failing this test. For example,at p. 5, he quotes the Henderson court’s views that the“practical effect” of the 2001 Balderas court-drawn plan,was to “leave the 1991 Democratic gerrymander largelyin place as a ‘legal plan.’” Henderson v. Perry, 399 F. Supp.2d 756, 763 (2005). And, as we earlier noted, JusticeKennedy apparently views the 1991 plan, with its per-ceived perpetuation of a minority party in power, aslegally more heinous than what he sees as the 2003 plan’sexaggeration of the voting strength of a majority party.We would point out, however, that there is dispute aboutthe partisan nature of the 2001 plan. In his opinion (at pp.5–6), Justice Stevens disputes Justice Kennedy’s charac-terization of the 2001 plan, and argues that it was, in fact,a politically neutral plan. Thus, in Justice Stevens’ view,the comparison that Justice Kennedy makes between a2001 plan that is essentially the legacy of a blatant Dem-ocratic gerrymander and a 2003 plan biased in favor ofRepublicans is inapposite. Justice Stevens also quotes ex-tensively to the Henderson court’s characterizations of the2001 plan, and reminds us (at p. 6) that, at the conclusionof its line-drawing, the Balderas court believed that it hadfashioned a map that was “likely to produce a congres-sional delegation roughly proportional to the party vot-ing breakdown across the state.” App. to Juris. Statement,at 209a. In this context we might note that neither Dem-ocrats nor Republicans challenged the Balderas plan as apartisan gerrymander. Justice Stevens (at p. 6) goes on tosuggest, however, that insofar as the 2001 plan was bi-ased, the bias was in a pro-Republican and not a pro-Democratic direction. On that page he quotes the Sessioncourt for the proposition that: “reflecting the growingstrength of the Republican party, the District Court’s plan,1151, offered that party an advantage in 20 of the 32 con-gressional seats. See Session, 298 F. Supp. 2d, at 471 (de-

scribing 1151C).”1 Justice Stevens (id.) also quotes theview of the state’s expert in the litigation involving theBalderas plan, Professor Ronald Keith Gaddie, that theBalderas plan was not biased in favor of Democrats, andthat it was “ ‘[m]aybe slightly biased’ in favor of Re-publicans.” App. 224. Justice Stevens then goes on tonote (at p. 6): “In the 2002 congressional elections, how-ever, Republicans were not able to capitalize on the ad-vantage that the Balderas plan had provided them. Anumber of Democratic incumbents were able to attractthe votes of ticket splitters (individuals who voted forcandidates from one party in statewide elections andfor a candidate from a different party in congressionalelections) and thus won elections in some districts thatfavored Republicans. As a result, Republicans carriedonly 15 of the [32] districts drawn by the Balderas court.”In the footnote following (n. 9 at pp. 6–7) Justice Stevensfurther observes: “It was apparently these electoral re-sults that later caused the District Court to state that thepractical effect of Plan 1151C ‘was to leave the Democ-ratic party gerrymander largely in place,’ ” Henderson at768 n. 2—the language quoted in Justice Kennedy’sopinion. But in that footnote Justice Stevens goes on tofurther argue that “the existence of ticket-splitting vot-ers hardly demonstrates that plan 1151C was biased infavor of Democrats.” The apparent factual disagree-ment between Justice Stevens and Justice Kennedy re-flects the different ways in which each treated incum-bency advantage. In effect, the analyses relied on byJustice Stevens looked at the plan as if all seats wereopen seats, while Justice Kennedy paid attention to theeffects of Democratic incumbencies in seats that mightotherwise be held by Republicans. The JudgeIt programallows courts to evaluate plans either with or withouttaking incumbency advantage into account. Which isthe correct approach in our view is, ultimately, a legaljudgment. However, we would note that incumbentsmay retire or be swept away by a strong electoral tideif their safety margins are cut too thin. See B. Grofmanand T. Brunell, “Art of the Dummymander,” 2005 op cit.

Just as most of the prima facie tests for ger-rymandering that we identified above are in-spired by other areas of voting rights case law(e.g., standards used for one person, onevote), so this latter test could be thought of asinspired by how courts have often dealt withthe issue of compactness when it arises incases involving state constitutional require-ments. While there are many measures ofcompactness, for none of them is there a clearmetric to determine what is egregiously ill-compact.96 In coping with this problem,courts frequently compare the compactness ofa given plan (or given districts) to that of com-peting plans (or districts within the same orother plans) or to compactness measurementsin a predecessor plan. Here, analogously,what we would be doing is comparing the(absolute) magnitude of deviation from par-tisan symmetry in a challenged plan fromwhat was found in earlier plans—usuallyplans that had been held to be constitu-tional.97

***We take no position on which of these five ap-

proaches is constitutionally most appropriate orwhich best fits the notion of “egregious” un-constitutionality first enunciated in Bandemer.98

As noted earlier we regard that determinationas a legal issue that is outside the purview ofthis article, and a choice the Supreme Court canand should make. Whichever of these legalthresholds is adopted, it will be straightforwardto determine if a constitutional violation has oc-curred (at least prima facie), and states and thosedrawing the lines in each state will know in ad-vance whether any plan they propose is likelyto pass court review.

For purposes of empirical calibration, wewould note, however, that studies of past par-tisan gerrymanders have shown that mostgerrymanders have a partisan bias of 1–3 per-centage points in favor of the party control-ling the redistricting. This effect is typicallypersistent over the decade following the re-districting, and accounts for measurable dif-ferences in the representation of the state’spopulation in the state legislature or Con-gress. Occasionally, the difference is greaterthan 5 percentage points, and only in rare

cases does a gerrymander results in a differ-ence of over 10 percentage points.99

IV. USING PARTISAN BIAS AS ACOMPONENT OF A JUDICIALLYMANAGEABLE STANDARD FORDETECTING AND MEASURING

UNCONSTITUTIONAL PARTISANGERRYMANDERING

Section I of this article demonstrates that par-tisan symmetry is a substantive definition offairness in districting that commands generalassent in the scholarly community. Section IIshows how measuring the deviation of an elec-toral system from partisan symmetry, to deter-mine partisan bias, is at least as empiricallystraightforward and conceptually clear as theconcepts used to evaluate districting plans


96 See Richard G., Niemi, Bernard Grofman, Carl Carlucciand Thomas Hofeller, Measuring compactness and the roleof a competent standard in a test for partisan and racial ger-rymandering, 52(4) Journal of Politics 1155–1181 (1990).97 Cf. Hofeller, Thomas and Bernard Grofman, “Compar-ing the compactness of California congressional districtsunder three different plans, 1980, 1982 and 1984,” inBernard Grofman (ed.), Political Gerrymandering and theCourts (NY: Agathon Press, 281–288 1990).98 See Vieth, 541 U.S. at 316 (Kennedy, J., concurring inthe judgment).99 Andrew Gelman & Gary King, Enhancing DemocracyThrough Legislative Redistricting, 88 Am. Pol. Sci. Rev. 541,546 fig. 2 (1994) (showing 15 states over a twenty-year pe-riod where the partisan bias rarely exceeded 5% and neverexceeded 10%); Robert X. Browning & Gary King, Seats,Votes, and Gerrymandering: Estimating Representation andBias in State Legislative Redistricting, 9 Law & Pol. 305, 318(1987) (examining the Indiana plan in the 1980s that wasthe subject of Davis v. Bandemer and concluding that theHouse plan had a bias of 6.2% while the Senate plan hada bias of 2.8%); King & Browning, Democratic Representa-tion, 81 Am. Pol. Sci. Rev. at 1262 Fig. 5 (showing bias inall states, with the plurality showing little if any bias, thevast majority falling within 5 percentage points, a few be-tween 5 and 10, and even fewer above 10); id. at 1269 (list-ing bias figures for all states and showing only one statewith a bias of above 10 percentage points); Gary W. Cox& Jonathan N. Katz, Elbridge Gerry’s Salamander: The Elec-toral Consequences of the Reapportionment Revolution 57–59(2002) (finding extreme cases of gerrymandering at asmuch as 8 percentage points). We might also note that inthe supposedly bipartisan gerrymander Connecticut inthe early 1970s that was at issue in Gaffney v. Cummings,412 U.S. 735 (1973), Gary King, Representation through Leg-islative Redistricting: A Stochastic Model, 33 Am. J. Pol. Sci.787, 814 (1989) finds partisan bias of 3%.

found in some other areas of voting rights andwhich the Supreme Court have found to be ju-dicially manageable.100

But, while social science can offer a defini-tion of partisan fairness and a methodology forcalculating partisan bias which is well-estab-lished and whose fundamentals are essentiallyundisputed within the political science litera-ture, only the courts can devise an appropriateconstitutional standard for egregious and un-constitutional partisan gerrymandering, andset appropriate thresholds as to evidentiaryburdens. In Section III of this article we haveshown how courts (building on what theSupreme Court said in LULAC) might draw onideas from other areas of voting rights case lawto set a plausible threshold test for prima facieunconstitutional partisan gerrymandering thatmakes use of the concept of partisan symme-try (either prospectively or retrospectively). Weuse this section to contribute to the ongoing de-bate about exactly how partisan bias can bemade part of a broader legal test for unconsti-tutional partisan gerrymandering.101

Looking at the views in LULAC expressedby Justices Souter, Breyer, Stevens and Gins-burg in conjunction with those of JusticeKennedy, we see clear signs that such a test canbe devised in a fashion that will command amajority of the present members of the Court.We argue that there almost certainly will be amulti-step process in evaluating claims of un-constitutional partisan gerrymandering. Wesuggest that one key element of such a processwould be based primarily on prima facie evi-dence for violations of some form of partisansymmetry test, and rebuttal thereto based onclaims of competing and overriding legitimateconsiderations.

Moreover, we suggest that issues relevant tothe remedy phase of a partisan gerrymander-ing claim will be somewhat different than is-sues relevant to the liability phase, and willlikely focus on the characteristics of particulardistricts, even though the level of partisan biasstatewide remains central in all phases of thecase. Also, while we will argue that there areseveral characteristics of the concept of parti-san bias that give rise to distinctive aspects ofits incorporation into a constitutional test forequal protection (see discussion below of dif-

ferences between racial gerrymandering andpartisan gerrymandering), we also believe thatthe manageable standards for unconstitutionalpartisan gerrymandering needed by the Courtcan draw on parallels with its successful ju-risprudence in other domains of voting rights.Finally, we suggest, that issues relating to thesatisfaction of traditional districting criteriamay be relevant to the issue of partisan intenteven if not directly relevant to the issue of par-tisan effects. Thus, while in our view partisanfairness, and its direct measurement in the formof a symmetry test applied jurisdiction wide,should remain at the heart of any partisan ger-rymandering claim, adopting this position doesnot in any way preclude a look at various spe-cific features of a redistricting plan (or pro-posed remedies) such as compliance with stan-dard redistricting norms like contiguity orcompactness.

We begin our discussion of how the SupremeCourt might usefully learn from its own suc-cesses in other domains of voting rights caselaw with “one person, one vote” case law, fo-cusing on one particular case, Brown v. Thom-son.102 Some key language from Brown (at p.852) illustrates how, in the context of one per-son, one vote, the Supreme Court has success-fully integrated concepts and measurement, le-gal rules involving thresholds, and evidenceabout ancillary factors into a multi-part butnonetheless unified legal approach. In that

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100 See, e.g., Shaw v. Reno, 509 U.S. 630, 646–49 (1993) (ex-plaining how to decide whether a race is a preponderantmotive, and examining “appearance,” among other fac-tors), and Georgia v. Ashcroft, 539 U.S. 461, 480 (2003) (dis-cussing the concept of minority influence and noting that“[t]he ability of minority voters to elect a candidate oftheir choice is important but often complex in practice todetermine”).101 While our expertise is primarily in the social sciences,because we each have served as expert witnesses in manysituations where we must use our social science knowl-edge to address legal issues, in this section we proposeseveral different ways in which the Supreme Court mightdraw upon the concept of partisan bias to craft a consti-tutional standard for partisan gerrymandering. We dothis by looking at how the Court has already successfullycrafted judicially manageable standards in other areas ofvoting rights.102 462 U.S. 835 (1983).

case, the court wrote (internal cites included asgiven):

Our cases since Reynolds have clarified thestructure of constitutional inquiry intostate legislative apportionments, settingup what amounts to a four-step test.

First, a plaintiff must show that the devi-ations at issue are sufficiently large tomake out a prima facie case of discrimi-nation. We have come to establish a roughthreshold of 10% maximum deviationfrom equality (adding together the devia-tions from average district size of the mostunderrepresented and most overrepre-sented districts); below that level, devia-tions will ordinarily be considered de min-imis. Ante, at 842–843; Connor v. Finch, 431U.S. 407, 418 (1977); White v. Regester, 412U.S. 755, 763–764 (1973).

Second, a court must consider the qualityof the reasons advanced by the State to ex-plain the deviations. Acceptable reasonsmust be “legitimate considerations inci-dent to the effectuation of a rational statepolicy,” Reynolds, supra, at 579, and mustbe “free from any taint of arbitrariness ordiscrimination,” Roman, supra, at 710. SeeMahan v. Howell, 410 U.S. 315, 325–326(1973).

Third, the State must show that “the statepolicy urged . . . to justify the divergences. . . is, indeed, furthered by the plan,” id.,at 326. This necessarily requires a showingthat any deviations from equality are notsignificantly greater than is necessary toserve the State’s asserted policy; if anotherplan could serve that policy substantiallyas well while providing smaller deviationsfrom equality, it can hardly be said that thelarger deviations advance the policy. See,e.g., Kilgarlin v. Hill, 386 U.S. 120, 123–124(1967); Mahan, supra, at 319–320, 326; Con-nor, supra, at 420–421.

Fourth, even if the State succeeds inshowing that the deviations in its plan arejustified by their furtherance of a rational

state policy, the court must neverthelessconsider whether they are small enough tobe constitutionally tolerable. “For a State’spolicy urged in justification of disparity indistrict population, however rational, can-not constitutionally be permitted to emas-culate the goal of substantial populationequality.” Mahan, supra, at 326.

This language, as we demonstrate below, pro-vides a number of important clues as to howto craft a manageable standard for partisan ger-rymandering. Moreover, the Brown v. Thomsonmulti-part approach will allow us, in large part,to reconcile the seemingly incompatible viewsof the four dissenting justices in Vieth.

First, it identifies a specific threshold forwhen a one person, one vote violation becomesprima facie unconstitutional. Second, it recog-nizes that, even though one person, one voteissues are fundamentally about populationequality, other considerations can also play arole in deciding such cases. Third, it allows fora process of burden shifting. In the initial phaseof the case, the key element for the plaintiffs isto show a sufficiently large (legally significant)deviation from one person, one vote. Once thatis shown, the burden shifts to the defendant ju-risdiction to make a case that the deviations inquestion are legitimated by a rational state pur-pose. Fourth and finally, that evidence is, inturn, rebuttable, especially as to whether thestate’s justifications are compelling ones giventhe nature and magnitude of the demonstrateddeviation from population equality.

Of course, we are not proposing that theBrown v. Thomson standard be adapted “as is”with partisan bias merely substituted for devi-ation from equal population. For example, aswe showed in Section III, the voting rights caselaw suggests several different ways courtsmight specify a threshold as to when the levelof partisan bias was constitutionally rele-vant.103 Similarly, we regard the last three ele-


103 Our discussion of threshold standards in this previoussection focused primarily on the first part of the four parttest for one person, one vote violations laid down in Brownv. Thomson 462 U.S. 835 (1983) from which we quote above,namely the part which establishes a threshold for identify-ing a potential one person, one vote constitutional violation.

ments of the Brown test as suggestive, ratherthan determinative, of how to proceed vis-à-vispartisan gerrymandering. The key, as illus-trated in the long quote from Brown v. Thomsonwith which we began this section, is the recog-nition that identifying a legally relevant con-cept, showing how to measure it empirically,and specifying a threshold for which it becomeslegally relevant, while necessary conditions forcrafting a legal standard in the context of vot-ing rights claims, do not end legal delibera-tions. Other ancillary considerations may comeinto play, especially at the remedy phase of atrial, or in attempts to justify grounding of aplan in a legitimate and compelling state in-terest, or in assessing whether partisans haveintentionally gone well beyond “normal” re-districting in pursuit of partisan advantage toengage in deliberate egregious manipulation ofdistrict boundaries. Relatedly, both statewideand constituency specific characteristics of aplan may also enter into a determination of thelegitimacy of choices made by line-drawers interms of establishing impermissible intentand/or in terms of justifying their choices asrational state action.

Below we will consider how ideas from thelast three components of the Brown v. Thomsonapproach to the crafting of a legal standard toestablish a violation of constitutionally pro-tected voting rights, and that of other votingrights approaches, might be combined in thecontext of partisan gerrymandering claims.

Integrating a symmetry standard withcompactness and other traditional districting criteria

The role of compactness and maintenance ofprevious boundaries in effects-based stan-dards of unconstitutional partisan gerryman-dering. Criteria such as compactness and re-spect for existing political boundaries are oftenused as proxies for partisan gerrymandering,but they are typically not very good proxies.One of us has previously emphasized the im-portant point made in the plurality opinion inVieth that “packing and cracking, whether in-tentional or not, are quite consistent with ad-herence to compactness and respect for politi-cal subdivision lines.”104 The fundamental

issue in partisan gerrymandering cases interms of effects is whether a districting plan un-fairly burdens the representational rights of aparticular political group, not whether or notdistricts look pretty.

Moreover, partisan bias is certainly not theonly issue in gerrymandering cases. As JusticesStevens and Souter argued in Vieth, satisfyingcompactness considerations and other com-mon districting criteria, such as respect for ex-isting jurisdictional boundaries or not splittingcommunities of interest, are often important inand of themselves.105 That is, while violation ofneutral standards such as compactness andcontiguity are not, in and of themselves, directevidence of partisan gerrymandering effects,106

using them can satisfy other legal rules and re-quirements and as such can enter into legal re-view of claims of the legality of a redistrictingplan, once a prima facie level of unconstitutionalpartisan bias has been established.107 This can

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104 Vieth, 158 L. Ed. 2d, at 565. See Bernard Grofman, Cri-teria for Redistricting: A Social Science Perspective, 33U.C.L.A. Law Review 77–184, 88–93 (1985). Also, as leg-islators employ more and more sophisticated tools for re-districting, they can comply quite easily with some ofthese objective criteria while still burdening the right tofair and effective representation through political gerry-mandering.105 See Vieth, 541 U.S. at 335 (Stevens, J., dissenting); id. at347–48 (Souter, J., dissenting). See also Davis v. Bandemer,478 U.S. 109, 165 (1986) (Powell, J., dissenting) (looking tothe “configurations of districts, the observance of politi-cal subdivision lines, and other criteria that have inde-pendent relevance to the fairness of districting”).106 As we have previously emphasized, only partisan biasis a direct measure of partisan gerrymandering effects.107 Other districting criteria, such as similar treatment ofeach party’s incumbents, may also be relevant. Those do-ing gerrymandering will often seek to eliminate the seatsof one or more incumbents of the other party by drasticredrawing of districts lines or by pairing incumbents inthe same district. The exact way in which incumbent pair-ings and redrawing of lines to affect incumbents of oneparty more than incumbents of the other party can im-pact on partisan bias is a complex topic, and best left tocase-specific analysis. Suffice it to note that in the contem-porary U.S., in congressional and legislative election in vir-tually any constituency, on average, incumbents run betterthan do candidates of the same party who are not incum-bents. Numerous studies have been done of the magnitudeof this incumbency advantage. See e.g., Andrew Gelman andGary King, Estimating Incumbency Advantage Without Bias,34(4) Am. J. Pol. Sci. 1142–1164 (November, 1990)�http://gking.harvard.edu/files/abs/inc-abs.shtml�.However, since incumbents, per se, have no legal “right”to their seats, the legal relevance for partisan gerryman-

happen in two different ways: (a) when the bur-den shifts to the state to justify the level of par-tisan unfairness found in a plan, and the stateargues that features of the plan that led to par-tisan bias were necessitated by the state’s com-pliance with neutral districting principles suchas compactness (cf. part 2 through 4 of the four-part test from Brown v. Thomson quoted at thebeginning of Section IV),108 or (b) when we en-ter the remedy phase of a trial if a court is facedwith the task of drawing a plan of its own, orevaluating alternative proposed remedialplans.109

The role of standard districting criteria inassessing partisan intent. We would point outthat issues relating to the satisfaction of tradi-tional districting criteria, both at the level of individual districts and in terms of overall fea-tures of a plan (e.g., average level of compact-ness, number of unnecessary crossings of po-litical subunit boundaries) may be directlyrelevant to the issue of partisan intent even ifnot directly relevant to the issue of partisan ef-fects. In Bandemer, the Supreme Court pluralityregarded proof of intent to achieve partisan ad-vantage as at best a minor and probably evenan irrelevant part of a partisan gerrymander-ing claim, because the partisan concerns of linedrawers who were placed by the political situ-ation in a position to advantage their partisancause via redistricting could more or less betaken for granted. But even if we grant that fact,exactly how legislators seek to achieve partisanadvantage can still be relevant to determiningintent to weight partisan considerations above

all others to a constitutionally impermissibledegree.

Here an analogy between redistricting andboxing may be helpful. In boxing, we take it forgranted that boxers are seeking to knock eachother’s heads off, yet we still distinguish be-tween a legitimate knockdown and one causedby a low blow.110 A review of the features of aplan in terms of standard districting criteria(both at the level of individual districts and inthe plan as a whole) can allow courts to assessintent so as to distinguish “normal” redistrict-ing in pursuit of partisan advantage from caseswhere partisans engage in deliberately inap-propriate and egregious manipulation of dis-trict boundaries—i.e., have sought to win bythe redistricting equivalent of an impermissi-ble low blow. In this context, Justice Stevenssuggests in his opinion in LULAC (at pp. 30–32)multiple violations of standard redistrictingcriteria, coupled with other indicia that pointto clear and unchecked partisan motive, maybe interpreted as evidence that unconstitu-tional intentional partisan gerrymandering isgoing on.

But, in our view, we would not need to getto issues of intent until we had established thata “knockdown” (i.e., a magnitude of partisanbias that, on its face, rises to the level of a con-stitutional violation) had occurred. Only thenwould we need to consider the constitutional“legitimacy” of that knockdown in terms of fac-tors such as motive. By leaving intent and otherissues having to do with the shapes of the dis-tricts until a later stage if the inquiry—a stagethat would not even be reached if there was not


dering claims of party-specific differences in the treat-ment of incumbents remains an open question. JusticeStevens (at n. 11, p. 28), uses the “placing of two incum-bents of the same party into a single district,” and the“number of districts that have been cracked in a mannerthat weakens an opposition party incumbent” as two ofhis eight indicia of partisan gerrymandering. Bernard N.Grofman, Criteria for Redistricting: A Social Science Per-spective, 33 U.C.L.A. Law Review 77–184, 117 (1985), wasone of the first studies to call attention to this incumbent-related aspect of efficient partisan gerrymandering—onewhich is still neglected in many studies of this topic. Grof-man used it as one of a dozen criteria he identified thatmight be indicative of gerrymandering.108 Indeed, Justice Stevens who sees compactness as serv-ing “important values in the districting process,” (LULAC,

126 S. Ct. at 2646), takes the very strong position that “aState that creates more compact districts should enjoy asafe harbor from partisan gerrymandering claims” (id.).109 Later in this section we will consider how neutral dis-tricting criteria play a somewhat different role in parti-san gerrymandering cases than they do in other areas ofvoting rights case law.110 We are indebted to A Wuffle (personal communica-tion, April 1, 2005) for suggesting this analogy. (A Wuf-fle, although not referred to by name in the decision, isbest known to the Supreme Court as the author of the po-etic pastiche about North Carolina’s 12th congressionaldistrict quoted in Justice Kennedy’s majority opinion inMiller. v. Johnson, 515 U.S. 900 (1995), 132 L. Ed. 2d 762 at796: “Ask not for whom the line is drawn; it is drawn toavoid thee.”).

a clear legal determination of a level of parti-san bias that met some prima facie standard of unconstitutionality—the courts consideringpartisan gerrymandering claims will have theirtask much simplified and made more manage-able in that many partisan gerrymanderingclaims are likely to be thrown out at a very earlystage in the proceedings.

Statewide versus district-specific measures of gerrymandering

Justice Breyer argued in Vieth for a state-wide test for partisan gerrymandering whileJustice Stevens and Justice Souter (joined byJustice Ginsburg) argued for a more district-specific approach. In LULAC, however, JusticeStevens, while suggesting both an effects andpurpose test of partisan gerrymandering thatcould apply to a single district (Part IV, pp.30–32), also proposed an effects test forstatewide partisan gerrymandering (Part III atn. 11, p. 28).111 In our view as social scientists,in an effects-based inquiry into gerrymander-ing, both approaches are needed—but at dif-ferent phases of the inquiry. Thus, with respectto the disagreements among the dissenting jus-tices in Vieth about whether a standard shouldlook statewide or be district-specific, substan-tial as this disagreement appears to be, we be-lieve that the disagreement can resolved.

To the extent that the Supreme Court adoptspartisan bias as a basis for estimating the mag-nitude of partisan gerrymandering effects, thetest would necessarily involve calculations andresults about the level of partisan bias in theplan as a whole. However, in reviewing the ev-idence for partisan gerrymandering, it is per-fectly reasonable for courts to look to seewhether particular districts in a plan exhibithigh levels of “packing” or “cracking,”112 solong as these techniques of gerrymanderinghave an effect in terms of the deviation frompartisan symmetry. Even more importantly,while partisan bias involves calculations for aplan as whole, judicial remedies for egregiouspartisan gerrymandering may often involve“unpacking” minority party voters and re-crafting particular sets of districts113 that havebeen the special targets of gerrymandering ef-forts.114

The legal specificity of a partisan gerrymanderingstandard

A number of features of partisan competitionforce the use of different methodologies fordefining and measuring partisan fairness than

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111 Justice Stevens (Part III, at n. 11, p. 28) identifies eightdifferent indicia: (1) the number of people who have beenmoved from one district to another, (2) the number of dis-tricts that are less compact than their predecessors, (3) thedegree to which the new plan departs from other neutraldistricting criteria, including respect for communities ofinterest and compliance with the Voting Rights Act, (4)the number of districts that have been cracked in a man-ner that weakens an opposition party incumbent, (5) thenumber of districts that include two incumbents from theopposite party, (6) whether the adoption of the plan gavethe opposition party, and other groups, a fair opportu-nity to have input into the redistricting process, (7) thenumber of seats that are likely to be safe seats for the dom-inant party, and (8) the size of the departure in the newplan from the symmetry standard.” Earlier work by oneof the present authors took a similar tack: See BernardGrofman, Criteria for Redistricting: A Social Science Per-spective, 33 U.C.L.A. Law Review 77–184, 88–93 (1985)(identifying twelve prima facie indicators of partisan ger-rymandering). That work remains relevant, but we wouldnow suggest that these indicators be taken to be ones thatcan largely inform us about improper partisan intent andlack of legitimate state purpose while partisan bias betaken to be the sole direct measure of partisan effects, al-though differential and discriminatory treatment of in-cumbents of opposite parties may also be relevant here—a legal issue which we see as not yet resolved.112 “Packing” and “cracking” are shorthand terms for twoof the fundamental tools of partisan gerrymandering,wasting the votes of one’s opponents in districts whichthey win by huge majorities (packing), and dispersing thevotes of one’s opponents in districts where these voteswill not be efficacious in electing candidates of choice(cracking). In addition, for at-large and multimember con-stituencies, a basic tool of vote dilution is “stacking,” i.e.,submerging opposition voters who would be largeenough and geographically compact enough to form themajority if they were to located within a single memberdistrict into a larger (multi-seat) constituency in whichthey are a clear minority, and in which their votes willnot be efficacious in electing candidates of choice. For ex-ample, virtually all of the Justice refer to issues involvedin the “cracking” of District #24, albeit only a minority ofthem would hold that cracking to be unconstitutional orillegal (see, e.g., Justice Souter’s opinion and JusticeStevens’ views in Part IV of his opinion).113 In the language used at some points in several of theLULAC opinions such district specific concerns are “gran-ular.”114 Of course, although these remedies to unconstitutionalpartisan gerrymandering, and indeed every individualboundary line drawn, involve specific districts, the ulti-mate criterion for assessing the fairness of a redistrictingplan to the political parties and their supporters is at thestatewide level. As we described in Section I above, the

we do for other violations of equal protection,such as the protection of racial groups or de-terminations of one person, one vote violations.Thus, it will be possible for courts to adopt ap-propriate tests of partisan bias and to incorpo-rate them into standards for unconstitutionalpartisan gerrymandering without any neces-sary need to rethink how the Supreme Courthas dealt with equal protection in other do-mains of voting rights in the light of the teststo be used in this area. Three key distinctionsare necessary here.

First, just as we previously showed that theconcept of partisan symmetry is only appro-priate for competitive situations where there isa potential for a change in partisan outcomes(majority control, in particular) as a result ofshifting electoral tides, a concept of “racialsymmetry” would not be the appropriate wayto evaluate equal protection claims involvingracial or ethnic groups with fixed ascriptivecharacteristics. To evaluate “ethnic group sym-metry” we would need to ask what would hap-pen to the seat division between the ethnicgroups if a state with, say, 10% African Amer-icans suddenly became 90% African American.But that really doesn’t make sense. While peo-ple regularly change their support for politicalparties on the basis of candidate qualities, is-sues, and the performance of incumbents, theydo not (or cannot) similarly switch ethnicgroup memberships. And although immigra-tion, emigration, birth, and death do producechanges in the ethnic composition of a state,these changes tend to be very gradual over timeand do not really make applying a symmetry

standard to racial categories something thatmakes conceptual sense.115

Second, and relatedly, because, as we notedabove, there is no direct analogue for measur-ing the impact of districting on racial groups tothe role that partisan bias plays as a direct mea-sure of partisan gerrymandering effects, wewould anticipate a more central role of sub-sidiary criteria such as geographic compactnessin the initial phase of voting rights claims thatinvolve racial impact than is found in the legalreview of claims related to partisan gerryman-dering. In the racial context, courts have ex-amined the shape and appearance of districtlines in order to resolve whether a state was en-gaging in a racial gerrymander.116 Similarly,the shapes of districts as they are related to thegeographic concentration of minority grouppopulations and to existing jurisdictionalboundaries has been found relevant in casesstemming from Shaw v. Reno,117 where the is-sue is inferring whether race has been a pre-ponderant motive in line drawing.118 But therole of these subsidiary criteria appear to bemuch less direct in cases involving partisangerrymandering since there we have, in parti-san bias, a direct measure of the consequenceswe are most concerned about vis-à-vis fairnessand equal treatment.

Third, whether for partisan or for racialgroups, we would emphasize that the conceptof symmetry is not an appropriate basis for ad-dressing equal protection claims in situationsinvolving pure at-large election systems, sinceabsent voter fraud, symmetry will essentiallyalways be satisfied for such at-large systems. In


legality of electoral systems requires rules be applied atthe individual district-level. But even after all individual-level rules are applied, we must look to the representa-tion of the state as a whole to determine fairness to thepolitical parties and their supporters. Fairness to the po-litical parties, partisan gerrymandering, and their mea-sures, partisan symmetry and partisan bias, are by theirnature concepts that apply to collections of districts ratherthan to each district separately. Indeed, democratic rep-resentation itself is by its nature a collective concept andthat is recognized in the concepts used to understand it,the legal rules that apply to it, and the techniques parti-sans use to affect it.115 For racial groups, methodology based on the well-es-tablished concept of vote dilution is well-established,where we also look to determine if there is racial polar-

ized voting necessary to substantiate a claim that a grouphas shared political interests and political identity that gobeyond merely sharing ascriptive characteristics. SeeBernard Grofman, Lisa Handley, and Richard Niemi, Mi-nority Representation and the Quest for Voting Equality (NewYork: Cambridge University Press, 1992). The problemswith “racial symmetry” and several other possible ab-solute standards for fairness to racial groups in redis-tricting are discussed in Gary King, John Bruce & AndrewGelman, “Racial Fairness in Legislative Redistricting,” inClassifying by Race 85, 85 (Paul E. Peterson, ed., 1996).116 See, e.g., Gomillion v. Lightfoot, 364 U.S. 339 (1960).117 Shaw v. Reno, 509 U.S. 630 (1993).118 In such cases, of course, establishing racial intent mayalso require addressing other issues, such as competingclaims about legislative motives.

pure at-large systems (i.e., one where the en-tire legislature is chosen from two competingpartisan slates, with each voter in the entirepolity having as many votes to cast as there areseats in the legislature), if voters cast all theirmultiple votes along partisan lines, thus elect-ing either an entire slate of Democrats or an en-tire slate of Republicans, changes in partisanvote share can affect partisan balance, but theydo not affect either partisan bias or electoral re-sponsiveness. That is because in such pure at-large systems there can be no partisan bias,since the two parties are treated symmetricallyin that each will win 100% of the seats with aplurality of the votes, and the level of electoralresponsiveness in pure at-large systems is ef-fectively infinite in that an infinitesimal changein party vote share from 50%� to 50%� willchange all the seats and thus change party con-trol.

In contrast, in districted systems that use plu-rality voting (including both ones where allseats elect a single representatives and ones in-volving multiple districts from some or all ofwhich different numbers of representatives areelected), changes in partisan vote share can af-fect both partisan bias and electoral respon-siveness.119 Thus, the possibility of long-termbias in a districted plan is completely differentfrom what we find in an at-large plan.120 In apure at-large election, if there are only twoslates, then, as shown above, bias is normallyzero, but electoral responsiveness is huge, be-cause there is either feast or famine—either aparty (the one with the majority of the votespolity-wide, however slight an edge they mighthave) wins all the seats, or it wins none.121

Synopsis

One way to think about the basic ideas in thisarticle about how social science can be usefulto the courts in making determinations aboutpartisan gerrymandering is in terms of four dif-ferent contributions, involving (1) conceptual-ization, (2) measurement, (3) legal relevance, and(4) legal specificity, respectively.

Conceptualization. We have shown that awidespread consensus exists in the social sci-ence literature supporting a specific defini-tion of partisan fairness in legislative redis-

tricting in plurality-winner district-basedelections based on the concept known as par-tisan symmetry.

Measurement. The social science literature of-fers statistically grounded, well accepted,and highly informative methods for measur-ing the deviation of a redistricting plan frompartisan symmetry. The degree of deviationfrom symmetry of treatment is known as par-tisan bias, and is easily quantified, and madespecific as to direction. Expert witness testi-mony can readily be obtained about the levelof partisan bias, and areas of disagreement

GROFMAN AND KING32

119 The discussion we give above is intended to apply onlyto districted systems of representation.120 The only electoral arrangement that has ever beenstruck down as unfair to a political party by any federalcourt was the state-wide (at-large) election scheme for Su-perior Court judges in the State of North Carolina thatwas overturned by a district court in Republican Party ofNorth Carolina v. Hunt. Because the empirical and legal is-sues at stake in Republican Party of North Carolina v. Huntinvolved a pure at-large (state-wide) election system, theissues in that case are almost totally distinct from thosethat apply to the districted elections for which themethodology we describe is intended. That trial court,whose ruling was sharply criticized by the plurality in Vi-eth (at n. 8), based its judgment about unconstitutionalpartisan gerrymandering by drawing on an analogy be-tween partisan and racial vote dilution. It found Repub-lican candidates historically experiencing a consistent andpervasive lack of success and exclusion from the electoralprocess as a whole. But, on appeal, the decision of the dis-trict court on how to remedy the unconstitutional vote di-lution it found was overturned when the U.S. Court ofAppeals took judicial notice of Republican success inelecting Superior Court judges statewide in an electionthat took place very shortly after the district court opin-ion was announced. The Appeals Court (Republican Partyof North Carolina v. Hunt, 1996 U.S. App. LEXIS 2029, No.94-2410, 1996 WL 60439 (4th Cir., Feb. 12, 1996) (per cu-riam) (unpublished), judgt. order reported at 77 F.3d 470.)remanded the case for further proceedings. However, theremand was mooted by a decision of the North Carolinalegislature to enact new legislation specifying district-based elections for Superior Court judgeships to be heldon a non-partisan basis (Marshall Hurley, attorney for theplaintiffs, personal communication, February 1, 2006). Buteven if this case had been decided otherwise, and even ifhad not involved an at-large election, its precedentialvalue would have been very limited since this case ini-tially presented an extreme factual situation, one whereno Republican judge had ever been elected statewide ina hundred years.121 At-large elections have been overturned as unconsti-tutional in settings where, due to polarized patterns ofvoting, they have been found, in the totality of the cir-cumstances, to minimize or cancel out the votes of mi-nority voters (see Thornburg v. Gingles, 478 U.S. 30 (1986)).

among competent experts about the magni-tude or durability of partisan bias will be lim-ited to fact-specific issues of a sort that courtsregularly deal with in the numerous domainswhere expert witness testimony is commonlyaccepted as relevant.

Legal Relevance. The social science concept ofpartisan bias is relevant to courts seeking tocraft legal standards for unconstitutionalpartisan gerrymandering because it is builton the most basic and common notions offairness in elections, and because it offers astraightforward and direct way to under-stand “equal protection” in the context of re-districting and political party competition.Thus, courts can draw on social science evi-dence in making fact-specific and case-spe-cific legal decisions. Of course, however, theultimate decisions need to be made by theSupreme Court about exactly what criteria,thresholds, and fundamental legal rulesshould guide lower courts.122

Legal Specificity. The menu of choices avail-able to the Court for defining unconstitu-tional gerrymandering, although based onideas of equal protection and fairness, arespecific to the domain of partisan gerryman-dering and do not necessarily carry over intoother domains of election law or legislativeredistricting. In particular, measures of sym-metry are less relevant in domains where wehave racial groups with fixed ascriptive char-acteristics and for which well-established le-gal concepts such as minority vote dilution areapplicable.123

V. CONCLUDING REMARKS

“The object of districting is to establish ‘fairand effective representation for all citizens.’ ”124

Partisan bias clearly offers a suitable metric tomeasure, in at least a preliminary fashion, the“burden a gerrymander imposes on represen-tational rights”125 because it is so clearly rootedin commonsense notions of fairness and equal-ity of treatment,126 and because it is directlylinked to the measurement of the effects of par-tisan gerrymandering. It is also a concept thatcan be clearly measured and about which evi-dence can be provided by competent social sci-

ence testimony.127 Now that members of theSupreme Court have singled out the deviationfrom partisan symmetry as a potential key in-dicator of partisan gerrymandering (with par-tisan bias arguably playing a role analogous tothe total population deviation in the one person,one vote cases), we anticipate that there will be new partisan gerrymandering challengesbrought. But since the bar has clearly been sethigh, with the Court’s refusal to invalidate theTexas congressional plan as an unconstitu-tional partisan gerrymander, we would not an-ticipate that there will be many such new chal-lenges. What we would expect, though, is thatmost new challenges will seek to attract thevotes of Justice Kennedy, as a pivotal memberof the Court, by basing their legal challenges toplans on results of elections already conductedunder that plan rather than on prospective as-sessments of expected severe long term parti-san bias. Either way, redistricters, and lawyers


122 Such determinations will, of course, be based on theSupreme Court’s own constitutionally- and historically-grounded jurisprudential analyses.123 See e.g., Thornburg v. Gingles, 478 U.S. 30 (1986). Forsocial science perspectives on Thornburg v. Gingles and theconcept of minority vote dilution see Bernard Grofman,Lisa Handley, and Richard Niemi, Minority Representationand the Quest for Voting Equality (New York: CambridgeUniversity Press, 1992, esp. Chaps. 2–3).124 Vieth, 541 U.S. at 307 (Kennedy, J., concurring in thejudgment) (quoting Reynolds v. Sims, 377 U.S. 533, 565–68(1964)).125 Vieth, 541 U.S. at 313 (Kennedy, J., concurring in thejudgment).126 As noted earlier, we take for granted that electionshave objective and symmetrical guidelines for determin-ing who wins: It would not be fair if one candidate couldwin with a plurality of votes but another candidate couldwin only if s/he obtained some supermajority of thevotes. Fairness requires that the political process treatseach candidate equally. The symmetry approach takesthis same principle and applies it to political groups (andtheir supporters) at the statewide or jurisdiction-widelevel by estimating the level of partisan bias in a plan.127 Moreover, since we propose to limit investigation ofpartisan gerrymandering claims to situations that are suf-ficiently competitive that control of a legislature (or ofCongress) is potentially at stake, and because we proposemeasurement criteria the results of which can readily beknown in advance, and because we make determinationof the magnitude of partisan bias the initial litmus testwhich will serve as an evidentiary hurdle for plaintiffs tosurmount to even be able to bring a case alleging uncon-stitutional partisan gerrymandering, the approach we ad-vocate will substantially limit the potential for an intru-sive judicial presence into an inherently political processabout which Justice Kennedy once expressed concern inhis opinion in Vieth.

arguing redistricting cases, would now be welladvised to use the best social science method-ologies to estimate the degree to which theirplan deviates from partisan symmetry.

As we have emphasized throughout this ar-ticle, the decision to make use of partisan biasas a prima facie measure of deviation from fair-ness and equality of treatment leaves openmany important legal questions. First, courtswill need to consider whether the only relevantevidence of partisan gerrymandering comesfrom elections actually held under a plan orwhether prospective evaluations based on pastelections in the same geographic areas mightalso be probative. This is a topic about whichwe briefly commented in Section II of our arti-cle. Second, courts will need to address thequestion of what is an appropriate legal thresh-old for a level of partisan bias that would trig-ger a prima facie claim of violation of equal pro-tection. This is a question for which weidentified various possible answers in SectionIII. Third, courts will need to address how othercriteria might enter as relevant at some phaseof the trial process. This is a topic on which wecommented in Section IV.

Now that the Supreme Court has providedthe first real guidance to lower courts abouthow to think about partisan gerrymanderingclaims based on Bandemer v. Davis, we antici-pate that the case law in the area of partisangerrymandering will evolve much as it has inother areas of voting rights—namely deliber-ately but steadily, and with only occasional fur-ther intervention by the Supreme Court to clar-ify inconsistencies that arise among lower courtjudgments.128 The plurality opinion in Viethquotes from an earlier statement by BernardGrofman: (“[A]s far as I am aware I am one ofonly two people who believe that Bandemermakes sense. Moreover, the other person,Daniel Lowenstein, has a diametrically op-posed view as to what the plurality opinionmeans”).129 We find nothing to argue with inthat statement, but take from it a very differentimplication than that drawn by the plurality inVieth. We believe that perhaps the single mostimportant reason that lower courts have not de-veloped a manageable standard for judicial re-view of partisan gerrymandering claims in thetwo decades since Bandemer is that Bandemerand subsequent Supreme Court decisions

about partisan gerrymandering failed to pro-vide lower courts adequate guidance about thedirections along which such standards mightdevelop.130 In our view, if we look closely atthe various opinions in LULAC, we can see thatthe Supreme Court has seeded the clouds afterthis 20 year drought.131 We think that, at last,

GROFMAN AND KING34

128 The Court was warned by Justice Frankfurter not toenter the “political thicket” of reapportionment becauseit would be unable to craft manageable standards or avoidchoosing between competing models of representation.Yet, if we look at how “one person, one vote” standardshave actually evolved, this is arguably the area of votingrights case law which is the clearest both in terms of thesignals it sends to legislatures as to what they need to doto meet a constitutional test, and to courts as to what theyneed to do in reviewing challenges based on populationinequalities. Early cases such as Reynolds v. Sims did notsettle the exact threshold for when unequal populationrises to the level of a constitutional violation. Yet, oncethe Supreme Court determined the general standards forpopulation equality in Reynolds v. Sims, 377 U.S. at 377,and Wesberry v. Sanders, 376 U.S. at 8, subsequent casessimply became legal arguments about exactly what levelof population deviation was unconstitutional in given cir-cumstances. Larios v. Cox, 305 F. Supp. 2d 1335 (2004), pro-vided a further complexity, but arguably, even that deci-sion was foreshadowed in earlier one person, one votecases.129 541 U.S. at 283, (quoting Bernard Grofman, An ExpertWitness Perspective on Continuing and Emerging VotingRights Controversies, 21 Stetson L. Rev. 783, 816 (1992)).130 Cf. Vieth, 541 U.S. at 312 (Kennedy, J., concurring inthe judgment) (suggesting that no manageable standarddeveloped after Davis v. Bandemer because lower courtscould do nothing except follow that decision); id. at 344–45(Souter, J., dissenting).131 The only real alternative explanation for the failure ofcourts to ever find an example of an unconstitutional par-tisan gerrymander in the nearly two decades since Ban-demer was decided is the one offered by UCLA Law Pro-fessor Daniel Lowenstein in an article, Vieth’s Gap: HasThe Supreme Court Gone From Bad To Worse On Parti-san Gerrymandering? forthcoming in 2006 in the CornellJournal of Law and Public Policy. Professor Lowenstein as-serts that the plurality opinion in Vieth is wrong in claim-ing partisan gerrymandering to be nonjusticiable due toa lack of a clear and manageable standard. In his view,Bandemer offers such a clear and legally manageable stan-dard, as shown by the results in the eighteen cases wherelower courts were asked to apply it. In Lowenstein’s view,Bandemer required a showing that a political party hadbeen subject to the same level of discrimination as onceoccurred with racial minorities—a total exclusion frompolitics. In his view, since none of the eighteen caseswhere lower courts failed to find an unconstitutional par-tisan gerrymander involved situations rising to this levelof discrimination, all these cases were thus properly de-cided under a judicially manageable standard. Of course,such an interpretation simply makes Bandemer a deadletter de facto instead of de jure.

there can now be a non-trivial probability ofrain, and as a result to a new flowering ofAmerican democracy less affected by the ills ofpartisan gerrymandering. It will now be up tolower courts in future cases to make concretethe ideas about tests for partisan gerryman-dering found in LULAC.

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