PRESIDENTIAL ADDRESS

PRESIDENTIAL ADDRESS

Nicholas R. Miller

Public Choice Society

March 13, 2010

Charles E. Wilson

• President of General Motors

• Nominated by President-elect Eisenhower to be Secretary of Defense

Charles E. Wilson

• President of General Motors

• Nominated by President-elect Eisenhower to be Secretary of Defense

• “What’s good for the country is good for General Motors, and vice versa.”

Nelson W. Polsby

• Polsby’s Law: “What‘s bad for the political system is good for political science, and vice versa.”

George C.

Edwards III

WHY THE ELECTORAL COLLEGE IS GOOD FOR

POLITICAL SCIENCE

WHY THE ELECTORAL COLLEGE IS GOOD FOR

POLITICAL SCIENCE

(AND PUBLIC CHOICE)

My Take on the Electoral College• I am at best ambivalent about whether the Electoral

College is bad (or good) for the political system.– On the whole, I regard it as a problematic but

serviceable institution.

• But I’m sure of two things:– The EC makes Presidential elections a lot more

interesting, and– The EC is terrific for political science research (and

teaching).

• Let us count the ways.

Ways in Which the Electoral College Is Good for Political Science

• The original Electoral College illustrates one way to design of voting system to select one winner out of a potentially large field of candidates concerning whom voter preferences are likely to be widely dispersed.

• But this system had a interesting and fatal flaw, because the framers did not understand “Schattschneider’s Law” as supplemented by “Duverger’s Law.”

• The original EC system rapidly transformed into an electoral system quite different from what the Framers intended, but by the 1830s it had stabilized into a position of institutional equilibrium.

Ways in Which the Electoral College Is Good for Political Science (cont.)

• This transformation turned the top tier of the EC system into a weighted voting system, which has provided an excellent empirical case to which various measures of voting power can be applied.– Although it recent decade it has had substantial competition from

the EU Council of Ministers.

• The transformed Electoral College provides usefully distinct example for analysis “partisan bias” and the “swing ratio” in electoral systems.

– The “partisan bias” and “swing ratio” concepts were developed in the context of British-style SMD parliamentary systems, to which the EC provides a useful contrast because the “districts” (i.e., states)

• are relatively few and large, and• have different populations and voting weights.

Why the Electoral College is Good for Political Science (cont.)

• The contemporary EC has a number of problematic features that raise interesting theoretical and empirical questions:

– The Voting Power Problem. Does the Electoral College system (as it has operated since the 1830s) give voters in different states unequal voting power?

• If so, voters in which states are favored and which disfavored and by how much?

– The Election Inversion Problem. The candidate who wins the most popular votes nationwide may fail to be elected.

• How likely is such an event and what circumstances affect its likelihood?

– The Electoral College Deadlock Problem, i.e., the House contingent procedure in the event no candidate wins 270 electoral votes.

• Implications of the 23rd Amendment (electoral votes for DC).


• Because of these and other problems, numerous variations (“reforms”) of the EC have been proposed, with respect to which – we can powerfully demonstrate Duverger’s mechanical effects

[i.e., that different electoral systems may translate the same votes into different winners], and

– we can constructively speculate about Duverger’s psychological [or strategic] effects [i.e., that different electoral systems may induce different choices by voters, candidates, and parties].

• Moreover, each of these variants can be analyzed theoretically and (to some extent) empirically, with respect to– the voting power problem,– the election inversion problem, and– the Electoral College deadlock problem.


• Finally, the proposed National Popular Vote Plan potentially illustrates how institutional rules can be circumvented by a binding agreement among (some) participants (in this case, by an interstate compact among states controlling at least 270 electoral votes).

Ingberman, D. E., and Yao, D. A. "Circumventing Formal Structure Through Commitment: Presidential Influence and Agenda Control," Public Choice, 1970.

The Original Electoral College

• The original Electoral College proposal was put together by the Committee on Postponed Matters over a period of a few days and accepted by the Convention (with one modification) within the last couple of weeks of the Convention.

– In Federalist 68, Hamilton claims that “if the manner of it be not perfect, it is at least excellent.”

The Original Electoral College (cont.)• The EC proposal created a (potentially) two-stage election

process.– Each elector was required to cast two equal and unranked votes

for President,• for two different candidates (unlike cumulative voting),• at least one of whom was not a resident of the elector’s state.

– In the event no candidate was supported by a majority of electors, (i.e., > 25% of the electoral votes) or in the event that two candi-dates with the required majority were tied, there would be a “runoff election” in Congress among the top five electoral vote getters or between the tied candidates.

• The Committee proposed that the runoff be in the Senate.• The Convention considered changing this to the House or to Congress as a

whole by joint ballot.• It ended up changing the locus of the runoff to the House, voting one vote per

state delegation.

The Original Electoral College (cont.)• The first stage of the original EC process bears some resemblance to Approval

Voting, but with these differences:– electors were required to cast exactly two votes (whereas AV allows voters to cast

any number of votes);– the out-of-state stipulation was imposed on these votes; and– advocates of Approval Voting view it as a way of avoiding any type of runoff.

• Because the first-stage and second-state electorates are different (indeed, required to be disjoint), the overall process bears some resemblance to a screening or nominating process as analyzed by Barberá and Coelho.– Member of the convention certainly thought about interactions between the two

stages.– They spoke of usually “nominating” and the Senate/House “electing” the President.

Salvador Barberà and Danilo Coelho, On the Rule of k-Names” and “How to Choose a Non-controversial List with k Names,” SC&W, June 2008.

The Original Electoral College (cont.)

• Madison, whose Virginia Plan provided that states be represented proportionally to population but who subsequently turned against election of the President by Congress (as proposed in the VA Plan), nevertheless preferred the runoff to take place in the Senate [or the House voting by state delegations], rather than by joint ballot of Congress as a whole [or the House voting by members].

– Mr. Madison considered it as a primary object to render an eventual resort to any part of the Legislature improbable. He was apprehensive that the proposed alteration [election by joint ballot of Congress as a whole] would turn the attention of the large States too much to the appointment [nomination] of candidates, instead of aiming at an effectual appointment of the officer, as the large States would predominate in the Legislature which would have the final choice out of the Candidates. Whereas if the Senate [or the House voting by delegations] in which the small States predominate should have this final choice, the concerted effort of the large States would be to make the appointment in the first instance conclusive. [Madison’s Notes, September 5]

– Evidently, Madison understood the concepts of strategic voting and subgame perfect equilibrium.

The Fatal Flaw in the Original Electoral College

• The Committee on Postponed Matters believed a second office had to be at stake to induce electors to take their second votes seriously.– Thus they created the office of Vice President,

• but did this only to make the Presidential selection process work.

• This turned out to be the fatal flaw in their plan,– once Washington retired and the Schattschneider and Duverger

effects came to fore.

• Schattschneider’s Law: If you have elections, you get political parties, i.e., – organized attempts to win elections by concentrating votes [by a

nomination process] on a few candidates.

• Duverger’s Law: If you have single-winner elections, you get two political parties – no more and no fewer, i.e.,– two rival organized attempts, each trying to concentrate votes on

a single candidate.

The Fatal Flaw (cont.)• The effect of Duverger’s Law was to realize Madison’s

expectation (and hope) that “the concerted effort of the large States would be to make the appointment in the first instance conclusive,” – except that concerted effort was by parties, not by big states.

• But the original EC did not quite create single-winner elections– but rather single-plus-a-bit-winner elections, – and this led to severe problems as shown below.

• These problems produced the 12th Amendment.

The Transformation of the Electoral College

• Electors become instructed party delegates, rather than uninstructed local trustees.

• Electors are popularly elected.• Electors are popularly elected on a “general ticket” (“winner-take-all”)

basis.

• The movement to the general ticket system was driven initially by the efforts of competing parties to concentrate votes:– Madison to Monroe (1800): “All agree that an election by districts

would be best if it could be general, but while ten states choose either by their legislatures or by a general ticket, it is folly or worse for the other six not to follow.”

– Virginia switched from districts in 1796 to winner-take-all in 1800.• If it had not, the Republicans would almost certainly lost the

1800 election.

Transformation of the Electoral College (cont.)

• The party driven trans-formation was reinforced by voting power calcula-tions implicitly made by state legislatures (that have the power to determine how electors are selected).

• Even if “all agree that an election by districts would be best,” – states have an incentive

to switch to winner-take-all, since

– switching to winner-take-all increases the voting power of the state’s voters.

Winner-Take-All Is “In Equilibrium”

• By the 1830s, all states are winner-take-all.

• In the mid-1990s, the Florida state legislature seriously considered switching to the Modified District Plan.

• Although small states are penalizing by the winner-take-all system, they are further penalized if the unilaterally switch to districts.– So even if a district system

is universally agreed to be socially superior (as Madison considered it to be), states will not voluntary choose to move that direction.

– States are caught in a Prisoner’s Dilemma.

A Priori Voting Power and the Electoral College• At least one delegate to the Conventional understood that the

concentration of votes affects voting power.– Luther Martin: Even if the States who had the most inhabitants ought to have the

greatest number of delegates [to the proposed House of Representatives], yet the number of delegates ought not to be in exact proportion to the number of inhabitants because the influence and power of those states whose delegates are numerous will be greater, when compared to the influence and power of the other States, than the proportion which the numbers of their delegates bear to each other.

• William Riker discovered Martin’s argument, he thought it sufficiently insightful to be characterized as “the first power index.” – In fact, under the provisional apportionment of House seats to which

Martin referred, each state’s share of Banzhaf voting power is closely aligned with its seat share.

– However, if Martin had focused on the two-stage voting power of individual members of the House, his objection would have been well founded.

– While Martin’s expectation that state delegations in the House would act as blocs was not borne out, state electoral votes would soon be cast in blocs, and the U.S. Electoral College has subsequently been one of the principal institutions to which voting power analysis has been applied.

William Riker, “The First Power Index,” Social Choice and Welfare, 1986.

A Priori Voting Power (cont.)• “A Priori Voting Power and the U.S. Electoral College” on the PCS

website.• Felsenthal and Machover instruct us that the Absolute Banzhaf

Power Measure should be used to assess voting power in the Electoral College.– A voter’s absolute Banzhaf voting power is the probability that

he/she casts a decisive vote in a “random” or “Bernoulli” election.

– Therefore we can calculate the overall voting power of an individual in a two-tier voting game as the

the probability that the voter cast a decisive vote in the state election

times

the probability that the state casts a decisive (bloc of) votes in the Electoral College,

given a Bernoulli election.

Dan S. Felsenthal and Moshé Machover, The Measurement of Voting Power: Theory and Practice, Problems and Paradoxes, 1998.

A Bernoulli Election (from The New Yorker, 1937)

Dennis and Robert Leech’s Website:Computer Algorithms for Voting Power Analysis

Voting Power and the Electoral College• The Voting Power Problem. Does the Electoral College

system (as it has operated since the 1830s) give voters in different states unequal voting power?– If so, voters in which states are favored and which disfavored

and by how much?

• With respect to this question, directly contradictory claims are commonly expressed as result of the failure many by many commentators to make two related distinctions:– the theoretical distinction between

• voting weight and • voting power, and

– the practical distinction between • how electoral votes are apportioned among the states (which

determines their voting weights), and • how electoral votes are cast by states (which influences their

voting power).

There is a significant small-state advantage with respect to the apportionment of electoral votes.

Which is more than counterbalanced by the large-state advantage resulting from winner-take-all,.

Absent the small-state apportionment advantage, the overall large-state advantage would be far more extreme.

Electoral College Variants• Almost all Electoral College variants (proposed “reforms”)

have the effect of allowing the small-state apportionment advantage to translate into a substantial overall small-state voting power advantage.– The Pure District System (Madison)– The Modified District System (used by ME and NE)– The Pure Proportional System (recently reinvented as “Weighted

Vote Shares” by Barnett and Kaplan) – The Whole-Number Proportional System (Colorado Proposition 36

in 2004)

• The one exception is the National Bonus System,– which equalizes voting power as the size of the national bonus

increases.

Arnold Barnett, and Edward H. Kaplan, “A Cure for the Electoral College?” Chance, 2007

The Pure District System

The Modified District System

(Pure) Pure Proportional System

The Whole-Number Proportional Plan

The Whole-Number Proportional Plan

From Claus Beisbart and Luc Bovens, “A Power Analysis of the Amend-ment 36 in Colorado,” University of Konstanz, May 2005; subsequently published in Public Choice, March 2008.

National Bonus Plan (Bonus = 101)

National Bonus Plan (Varying Bonuses)

The Probability of Election Inversions• The Election Inversion

Problem. The candidate who wins the most popular votes nation-wide may fail to be elected.– How likely is such an

event and what circumstances affect its likelihood?

• One approach is literally probabilistic (though May’s probabilistic approach was different).

Probability of Election Inversions (cont.)• Based on very large-scale (n = 1,000,000) simulations of Bernoulli

elections, if the number of equally populated districts/states is modestly large (e.g., k > 20), about 20.5% of such elections produce reversals.

Feix, Lepelley, Merlin, and Rouet, “The Probability of Conflicts in a U.S. Presidential Type Election,” Economic Theory, 2004

• If the districts are non-uniform (as in the Electoral College), the probability of an election reversal is evidently slightly greater.

• Simulations of 32,000 Bernoulli elections for each of three EC variants:

A Sample of 32,000 Simulated Elections Based on Perturbations of the 2004 PVEV

Estimated (Symmetric) Probability of Election Reversals By Popular Vote (Based on the 2004 PVEV)

Estimated (Symmetric) Probability of Electoral Vote Ties By Popular Vote (Based on 2004 Landscape)

A Empirical Approach to Election Inversions

• Construct the “Popular Vote into Electoral Votes” (PVEV) step function for any Presidential election. – This in effect assumes the Democratic (as the following charts

are constructed) popular vote swings up or down uniformly over all states.

– Note: the “slope” of the function in the vicinity of PV = 50% is (in effect) the Electoral College “swing ratio” in that election.

– David E. Butler, “An Examination of the Results,” Appendix to H. G. Nichols, The British General Election of 1950, 1951.

– Neal R. Peirce and Lawrence D. Longley, The People’s President: The Electoral College in American History and the Direct Vote Alternative, rev. ed., 1981 [“The Bischoff Method”]

– Carleton W. Sterling, “Electoral College Misrepresentation: A Geometric Analysis,” Polity, 1981.

The PVEV Step Function for 1988

Zoom in on the Inversion Interval

Magnitude and Direction of Election Inversion Intervals

First Source of Possible Election Reversals

• The first source of possible election reversals is invariably present.

• An election reversal may occur as a result of the (non-systematic) “rounding error” (so to speak) necessarily entailed by the fact that the PVEV function moves up in discrete steps. – In any event, a given PVEV function allows (in a sufficiently

close election) a “wrong winner” of one party only.– But small perturbations of such a landscape allow a “wrong

winner” of the other party.• The 1988 chart (and similar charts for all recent elections

[including 2000]) provide a clear illustration of election reversals due to “rounding error” only.– So if the election had been much closer (in popular votes) and

the electoral landscape slightly perturbed, Dukakis might have been a wrong winner instead of Bush.

Highly Asymmetric PVEV Function in 1940

1860 Election

The Even More Asymmetric PVEV Function in 1860

Two Distinct Sources of Bias in the PVEV

• Asymmetry or bias in the PVEV function can result either or both from two distinct phenomena:– distribution effects.– apportionment effects (which can be further subdivided into

different components, e.g., turnout effects, etc.).

• Either effect alone can produce an election inversion, and– they can either reinforce or counterbalance each other.

• A perfectly apportioned system is (a hypothetical) one in which every state’s electoral vote is precisely propor-tional to its popular vote (and apportionment effects are thereby eliminated).

Imperfect Apportionment• The U.S. Electoral College system is (substantially) imperfectly

apportioned, for many reasons. – House (and electoral vote) apportionments are anywhere from two (e.g.,

in 1992) to ten years (e.g., in 2000) out-of-date.– House seats (and electoral votes) are apportioned on the basis of total

population, not on the basis of• the voting age population, or• the voting eligible population, or• registered voters, or• actual voters in a given election.• All these factors vary considerably from state to state.

– House seats (and electoral votes) must be apportioned in whole numbers and therefore can’t be precisely proportional to anything.

– Small states are guaranteed a minimum of three electoral votes.

• Imperfect apportionment may or may not bring about bias in the PVEV function.– This depends on the extent to which states (districts) having greater or

lesser weight than they would have under perfect apportionment is correlated with their support for one or other candidate or party.

1988 PVEV Based on Perfect vs. Imperfect Apportionment


Apportionment Effects in 1860

• The 1860 election was based on highly imperfect apportionment.– The southern states (for the last time) benefited from the 3/5

compromise pertaining to apportionment.

– The southern states had on average smaller populations than the northern states and therefore benefited disproportionately from the small-state guarantee.

– Even within the free population, suffrage was more restricted in the south than in the north.

– Turnout among eligible voters was lower in the south than the north.

• But all these apportionment effects favored the south and therefore the Democrats.

• Thus the pro-Republican reversal of winners was entirely due to distribution effects.– The magnitude of the reversal of winners in 1860 would have been even

greater in the absence of the countervailing apportionment effects.


Distribution Effects and the Schattschneider’s 25%-75% Rule

• Distribution effects in districted electoral system result from the winner-take-all at the district/state level character of these systems.– Such effects can be powerful even in

• simple districted (one district-one seat/electoral vote) systems, and• perfectly apportioned systems.

• The most extreme example of an election reversal in perfectly apportioned system results when– one candidate or party wins just over 50% of the popular votes in just

over 50% of the (uniform) districts or in non-uniform districts that collectively have just over 50% of the electoral votes.

– These districts also have just over 50% of the popular vote (because apportionment is perfect).

– The winning candidate or party therefore wins just over 50% of the electoral votes with just over 25% (50+% x 50+%) of the popular vote and the other candidate with almost 75% of the popular vote loses the election.

– The election inversion interval is (just short of) 25 percentage points wide.

E.E. Schattschneider, Party Government, 1942, p. 70 (also May, p. 204)

The 25%-75% Rule in 1860 • In the 1860 Lincoln vs. anti-Lincoln scenario, the popular vote

distribution approximated the 25%-75% pattern quite well.– Lincoln would have carried all the northern states except NJ, CA,

and OR • which held a bit more than half the electoral votes (and a larger

majority of the [free] population),

• generally by modest popular vote margins.

– The anti-Lincoln opposition would have• carried all southern states with a bit less than half of the electoral

votes (and substantially less than half of the [free] population)

• by essentially 100% margins; and

• lost all other states other than NJ, CA, and OR by relatively narrow margins.

• If the most salient characteristic of the Electoral College is that it may produce election inversions, one’s evaluation of the EC may depend on whether one thinks Lincoln should have been elected President in 1860.

Distribution Effects (cont.)• The Whole Number Proportional and Districts Plans do not eliminate

distribution effects, and so– they permit election reversals (even with perfect apportionment);

indeed– the District Plans permit election reversals at the state as well as

national levels.• The Pure Proportional Plan for casting electoral votes eliminates

distribution effects entirely.– But election reversals could still occur under the Pure Proportional Plan due to

apportionment effects.

– The reversals would favor candidates who do exceptionally well in small and/or low turnout states).

– However, the Pure Proportional Plan combined with perfect apportionment would be equivalent to direct national popular vote,

– so election reversals could not occur, and

– individual voting power would be equalized (and maximized).

In Conclusion

• Whatever the merits of the Electoral College as an institution, it is terrific as a subject for political analysis.– Indeed, in this respect, we may say (quoting

Hamilton) that, if the Electoral College is not perfect, it is at least excellent.

• Thank you.

Documents

PRESIDENTIAL ADDRESS