Modeling the Institutional Foundation of Parliamentary Government Formationmattgolder.com/files/research/jop1.pdf · 2015-05-28 · Modeling the Institutional Foundation of Parliamentary

Modeling the Institutional Foundation ofParliamentary Government Formation

Matt Golder Pennsylvania State University

Sona N. Golder Pennsylvania State University

David A. Siegel Florida State University

That neither the assumptions nor the predictions of standard government formation models entirely correspond toempirical findings has led some to conclude that theoretical accounts of government formation should bereconsidered from the bottom up. We take up this challenge by presenting a zero-intelligence model of governmentformation. In our model, three or more parties that care about office and policy make random governmentproposals. The only constraints that we impose on government formation correspond to the two bindingconstitutional constraints that exist in all parliamentary systems: an incumbent government always exists and allgovernments must enjoy majority legislative support. Despite its deliberately limited structure, our model predictsdistributions over portfolio allocation, government types, and bargaining delays that approach those observed in thereal world. Our analysis suggests that many formation outcomes may result from the institutional foundation ofparliamentary democracies, independent of the strategic behavior of party leaders.

The legislative elections in Israel in 2009 failedto produce an obvious government coalition.1

Instead, the leaders of the two largest parties,Kadima and Likud, both claimed victory and begannegotiating with potential coalition partners over cab-inet positions and the policies that any new governmentwould pursue. This initial period of negotiationsprovided some information about the viability ofvarious potential government coalitions. The head ofstate then appointed the leader of the conservative LikudParty as formateur because he seemed more likely thanthe centrist Kadima leader to be able to successfully puttogether a coalition that would enjoy the support of alegislative majority. The negotiations over the new Israeligovernment lasted seven weeks, during which time theincumbent Kadima prime minister remained in power.

This Israeli example highlights some importantfeatures of how governments form in parliamentarydemocracies. First, it is often the case that there is noobvious government alternative and politicians will ex-plore a great many options before arriving at a finalgovernment. Given that it is not unusual for a legislatureto have five or more parties, many potential coalitions willtypically be considered. Although some will be instantly

rejected, others will be investigated, and this process takestime. Delays often occur because party elites are consid-ering different options, trying to obtain the most advanta-geous coalition. During this time, the incumbentgovernment stays in office in a caretaker capacity. Eventhough caretaker governments are typically not expectedto implement new policies, it is almost certainly the casethat having the incumbent Kadima party remain in officewas likely to please some legislative parties more thanothers. For example, we suspect that Kadima members,who were expecting to soon move into the opposition,had a higher tolerance for a prolonged government for-mation period in this instance than Likud members did.

Contrast this Israeli example (or many othergovernment formation stories we could have told)with standard theoretical accounts of the governmentformation process. The typical approach is based onthe canonical (closed-rule) Baron-Ferejohn model inwhich three legislative parties bargain over forming anew government by making alternating offers (Baronand Diermeier 2001; Baron and Ferejohn 1989).A proposer (formateur) is first selected using an exog-enous selection mechanism. This proposer then hasthe sole right to make a proposal, typically involving

The Journal of Politics, Vol. 74, No. 2, April 2012, Pp. 427–445 doi:10.1017/S0022381611001654

� Southern Political Science Association, 2012 ISSN 0022-3816

1The data and all computer code necessary to replicate our results are publicly available on the authors’ homepages: https://files.nyu.edu/mrg217/public/, https://files.nyu.edu/sln202/public/, and http://myweb.fsu.edu/dsiegel/.

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some distribution of office benefits and a governmentpolicy position, to the other parties. The leaders ofthese other parties cannot hold their own negotiationsor make alternative proposals. All parties then vote onthe proposal made by the formateur. If the proposalreceives majority support, then a new governmentforms and implements its policy immediately. If theproposal does not receive majority support, then theexogenous selection mechanism is called upon againto designate a new proposer and the process beginsonce more. Prior to the proposal of a new governmentbeing accepted, all parties are assumed to receiveidentical payoffs, often normalized to zero.

Although this approach to modeling governmentformation has contributed greatly to our knowledgeand does particularly well in highlighting the strategicinteractions that are possible between parties, it hasseveral limitations. One is that the structure of thebargaining game, in which a single actor has themonopoly power to make proposals at any given pointin time, does not accurately reflect how party leadersactually bargain over who gets into government. Thoughall models are necessarily simplifications of reality, thefact that the removal of the alternating bargainingassumption from these models results in their beingunable to produce equilibria is obviously problematicgiven the failure of this assumption to hold empirically.More importantly, standard models lead to equilibriumpredictions that are often at odds with the empiricalevidence from parliamentary democracies that has accu-mulated over the last six-and-a-half decades. The standardpredictions are that governments will be minimal win-ning, that ministerial portfolios are allocated in a non-proportional manner, and that governments form swiftly.In reality, minority and surplus majority governmentsform quite regularly (Laver and Schofield 1998; Strøm1990); cabinet portfolios are nearly always allocatedproportionally (Warwick and Druckman 2001, 2006);and there is significant variation in how long it takesgovernments to form (Diermeier and van Roozendaal1998; Golder 2010; Martin and Vanberg 2003).2

That neither the assumptions nor the predictionsof the current theoretical approach correspond closelyto the empirical findings has led some to suggest that itmight be fruitful to consider a different approach tomodeling government formation. For example, Laver,de Marchi, and Mutlu emphasize the gap betweenstandard models of government formation and theempirical evidence when they remark that ‘‘the pro-fession’s canonical theory of bargaining in legislaturesis contradicted by one of the profession’s strongest andmost robust empirical laws [Gamson’s Law]’’ (2011,288). They conclude that the topic of governmentformation ‘‘must be reconsidered from the bottomup.’’ We take up this challenge by presenting a new typeof government formation model.

A key feature of any government formationmodel has to do with how parties negotiate. Existingmodels typically assume that party leaders are utility-maximizing agents who make optimal choices as theynegotiate strategically using very specialized bargain-ing protocols. The problem is that almost nothingsubstantive is written on how parties actually bargainover who gets into government and what policy shouldbe implemented. One reason for this is that analysts areseldom party to the secretive backroom dealings thatunderpin the typical government formation process.In our model, we circumvent this problem by placingno constraints on the types of government proposalsthat can be made. In this way, our model bears somesimilarity to those presented in Schofield and Sened(2006) and Penn (2009). Specifically, our model, liketheirs, diverges from the standard approach andviews government formation as a lottery over possi-ble coalitions, policies, and distributions of perqui-sites (in our case, cabinet ministries).

The only constraints we impose on governmentformation correspond to the two constitutional con-straints that exist in all parliamentary systems: (1) anincumbent government always exists, and (2) allgovernments, in addition to having the support oftheir member parties, must enjoy majority legislativesupport. Our model represents a ‘‘null’’ model in thatany model of parliamentary government formationmust impose these constraints and any model differentfrom ours must add at least some additional structure.Our goal in this article is to abstract away from theexact details of the bargaining process and insteadexamine how the two constitutional constraints thatare common to all parliamentary democracies shapegovernment formation.

To do this, we draw on the economics literaturedealing with ‘‘zero-intelligence agents,’’ which indi-cates that the institutional structure of markets can

2We recognize that some models in the Baron-Ferejohn traditionproduce something other than the standard predictions thatempirical scholars typically associate with this area of research. Forexample, Carroll and Cox (2007) and Morelli (1999) both presentmodels in which portfolios are allocated proportionally in someequilibria. Similarly, there are models that produce governmentsother than minimal winning coalitions (Bandyopadhyay and Oak2008; Baron and Diermeier 2001; Diermeier and Merlo 2000), oneof which also predicts delays in government formation (Diermeier,Eraslan, and Merlo 2003). That said, we know of no existingmodel that simultaneously produces predictions that approximateempirical distributions of government delay, government type, andportfolio allocation.

428 matt golder, sona n. golder, and david a. siegel

itself determine outcomes (Bosch and Sunder 2000;Farmer, Patelli, and Zovko 2005; Gode and Sunder1993, 1997). A zero-intelligence agent is one who actsrandomly subject to minimal constraints.3 In theirseminal article, Gode and Sunder (1993) reportresults from an experiment in which human tradersare replaced by zero-intelligence agents that submitrandom offers. Gode and Sunder demonstrate thatthe efficiency of auctions can be raised close to 100%simply by imposing a budget constraint—not per-mitting traders to sell below their costs or buy abovetheir values. They conclude that ‘‘the allocativeefficiency of a double auction derives largely fromits structure, independent of traders’ motivation,intelligence, or learning’’ (1993, 119).

We apply the same basic approach to investigatehow the institutional structure of parliamentary de-mocracies influences government formation. Specifi-cally, we present a model in which parties that care aboutoffice and policy make random government proposals,but only those proposals that are both preferable to thestatus quo government for the proposer and receivelegislative majority support are enacted.4 By allowing allparties to make proposals simultaneously and averag-ing across a great many formation opportunities, anypatterns that emerge should be the consequence of thecommon institutional foundation shared by all parlia-mentary democracies.

Our choice of how to model ‘‘bargaining’’ mayseem unusual for a model aiming at empirical verity.Given that our approach diverges quite markedlyfrom that observed in much of the formal literature,we should reiterate the purpose of our model. Ourmodel makes no pretense to accurately describe orexplain the bargaining behavior of actors involved inthe government formation process (Gode and Sunder1997, 604). We hold no illusions, for example, thatparty leaders really gather together and simultane-ously announce randomly chosen coalitions andgovernment policy. And surely more goes into thechoice of government than a comparison to the statusquo. Moreover, we do not see our model as a directchallenge to existing models that rely on utilitymaximization and strategic behavior. Instead, thegoal of our model is simply to discover whether the

two constitutional constraints that exist in all parlia-mentary systems are sufficient to generate empiricallyrealistic predictions about the types of governmentsthat form, portfolio allocation, and delays in govern-ment formation, independent of context-specificfactors, norms of behavior, or bargaining protocolsthat limit the variance in the types of proposals thatparties can make.5

In the next section, we outline what we knowempirically about parliamentary government forma-tion. We present our model in section three. Thefourth section is devoted to discussing the model’spredictions and investigating how well they compareto real-world data. Given the bare bones nature of oursetup, it is quite remarkable how well the predictions ofour model match what is observed in the real world.Our model suggests that the two institutional con-straints that characterize parliamentary governmentformation—the existence of an incumbent govern-ment and the requirement that governments enjoymajority legislative support—can generate many ofour most robust empirical regularities, independent ofthe strategic behavior of party leaders and theirbargaining protocols. In addition to showing thesimilarity between our results and real-world data,we also illustrate how each of our major results varieswith factors such as party system diversity, partysystem size, and the weight that parties assign to policyrelative to office. We do this not only to help explainwhat is necessary for our model to produce the resultsthat it does, but also to display the wide range oftheoretical and empirical questions that are opened upby our model.

What We Know Empirically AboutGovernment Formation

In what follows, we draw on the vast empiricalliterature addressing parliamentary government

3Gode and Sunder (1993) were the first to use the term ‘‘zerointelligence.’’ Their highly cited article has led to a large andgrowing literature on zero-intelligence agents in economics,computer science, and other fields. To our knowledge, weprovide the first zero-intelligence model in political science.

4Although we situate our model in the zero-intelligence liter-ature, we should note that our random proposal mechanism canbe justified on other grounds (Compte and Jehiel 2004).

5Note that we are not claiming that context-specific factors,norms of behavior, and alternative bargaining protocols areunimportant. Even if our model were to produce results thatclosely matched empirical regularities, we recognize that therewould likely remain a significant role for these other factors inpredicting government outcomes. Indeed, Gode and Sunder’s(1993) market-constrained zero-intelligence agents produce var-iance in outcomes far greater than human market agents, therebyimplying that additional, unmodeled factors must account for thereduction in variance. Along similar lines, it is entirely plausiblethat a norm toward fairness could constrain the variance around,say, the proportionality of cabinet portfolio allocation producedby our model.

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formation to outline what we know about both theprocess by which governments form and the associ-ated outcomes of this process.

The Government Formation Process

In parliamentary democracies, the government com-prises the prime minister and her cabinet. New govern-ments emerge either because an election occurs orbecause an incumbent government resigns. But what isthe structure of the government formation process?Any answer to this question must start with theconstitutional constraints that bind in any formationprocess.

Binding Constitutional Constraints. There areonly two constitutional constraints that bind in anyparliamentary government formation process. Theseconstraints bind for all governments irrespective ofwhether the governments form in postelection orinterelection periods. The first constraint is that allgovernments, in addition to having the support oftheir member parties, must enjoy the support of alegislative majority. In some parliamentary democra-cies, the government must explicitly demonstrate thatit has majority legislative support in an investiture votebefore it can officially take office. But even if there isno formal investiture vote, all parliamentary govern-ments must enjoy at least the implicit support of alegislative majority due to the ability of the legislatureto call votes of no confidence. If a government everloses such a vote, because it cannot garner the supportof a legislative majority, then it must resign. Ulti-mately, a parliamentary government may be removedfrom office any time a majority of legislators decidesthat this is what should happen. As a result, anyincoming government must be able to survive a voteof no confidence and, hence, enjoy the support of alegislative majority even if it never has to explicitlydemonstrate this through an actual vote.

The second and final constitutional constraintthat binds any parliamentary government formationprocess is that there is always a government. Con-stitutionally, the incumbent government remains inplace until it is formally replaced by an alternative.Whether a government resigns or is defeated in a voteof no confidence, it remains in power as a caretakergovernment until a new duly mandated governmentreplaces it. Although there is variation in how muchnew policy a caretaker government can implement, itremains the case that the policies implemented by theincumbent government stay in place until they arereplaced by the policies of a new government. As aresult, the incumbent caretaker government always

represents the status quo or reversion point in anygovernment formation process.

‘‘Nonbinding’’ Modeling Constraints. Standardgovernment formation models impose additional‘‘nonbinding’’ constraints on how governments form.In general, these constraints come in the form oftechnical assumptions about the nature and sequenceof play in whatever bargaining model is beingemployed. One of the most distinctive constraintsimposed by many models is that there is a commonknowledge formateur who is exogenously determinedand who has the sole right to propose governments.In effect, these models assume that formateurs arechosen either sequentially in order of party sizestarting with the largest party (Austen-Smith andBanks 1988) or probabilistically where the likelihoodof being selected is proportional to the formateur’sshare of legislative seats (Baron and Ferejohn 1989).6

Empirically, though, few constitutions state howformateurs are to be selected. Although it might seemreasonable that formateurs will be selected in order oflegislative size as some models do, there are only twoEuropean countries—Greece and Bulgaria—that con-stitutionally require this. In some countries, such asItaly, Portugal, Austria, Finland, and France, the headof state has enjoyed considerable discretion overformateur selection. In other countries, such as theNetherlands and Belgium, the head of state appoints aninformateur who talks to party leaders and gathersinformation about viable governments. The head ofstate then chooses a formateur based on the informa-teur’s advice. In many cases, negotiations over govern-ment formation are simply described as ‘‘free-stylebargaining’’ among the various parties. In general, thevast majority of empirical evidence indicates thatformateurs emerge endogenously as part of the under-lying bargaining process.7 As a result, we do not

6Rarely is evidence provided to support either of these selectionmechanisms. Although Diermeier and Merlo (2004) claim that theprobabilistic selection rule receives empirical support, their analysisis open to question because they use Keesings to identify forma-teurs. Despite ‘‘sustained and determined efforts’’ to reconstructdata on formateurs using Keesings, Laver, de Marchi, and Mutlu‘‘concluded unambiguously that . . . it is not . . . systematicallypossible to observe ex ante exogenous formateur status in primarydata sources’’ (2011, 292). They go on to conclude that formateurselection rules ‘‘are not testable using a variable for exogenousformateur status, coded from historical sources.’’

7With the exception of Morelli (1999), Diermeier, Eraslan, andMerlo (2003), Yildirim (2007), and Bassi (2008), existing modelsof government formation adopt an exogenous selection mecha-nism for determining the formateur. For a far more completediscussion of the modeling literature in regard to the choice offormateur, see Penn (2009).


include an exogenous formateur selection rule in ourmodel.

Irrespective of how the formateur is chosen, it isalmost certainly unrealistic to expect that the forma-teur has a monopoly right on making governmentproposals and that other political parties do not holdtheir own private negotiations. Even if the head ofstate has designated formateur status to the leader ofone party, the leaders of other parties are nearly alwaysbargaining with each other in private over what aviable coalition would be. Indeed, our Israeli examplefrom earlier indicates that the leaders of Kadima andLikud both claimed victory and began simultaneouslynegotiating with potential coalition partners.

It is important to recognize in all of this thatgovernment formation is the principal and mostimportant game to be played in any parliamentarydemocracy. As a result, it is hard to imagine why anyreal-world party leader would sit by if she thoughtthat she could put together a viable government. Therecent U.K. government formation process is ofparticular interest here. Historically, it has been acustom that the incumbent British PM gets first shotat forming a government when there is a hungparliament. In February 2010 prior to the generalelection, this custom was formalized for the first timein revisions to the Cabinet Manual (Chapter 6) byGus O’Donnell, the head of the civil service. The factthat the political parties ultimately ignored thisformal rule suggests that even when they do exist,rules about formateur selection and proposal rightsare de facto nonbinding when it comes to somethingas important as government formation.

There are several insights to take away from thisdiscussion. The first is the distinct lack of structurethat characterizes the typical government-formationprocess. The second is that negotiations over poten-tial governments occur simultaneously rather thansequentially. And finally, much of the bargainingamong party leaders occurs in private with the resultthat scholars have very little information about hownegotiations actually proceed in practice.

The Outcome of theGovernment-Formation Process

What do we know about the outcomes associated withthe typical parliamentary government formation proc-ess? In what follows, we focus on the various types ofgovernment that emerge, the degree of proportionalityin portfolio allocation, and delays in the government-formation process.

Government Types. Historically, most govern-ment-formation models predict that minimalwinning coalitions will form. This prediction, though,is only partially borne out in the real world. In fact,fewer than half the governments that formed in WestEuropean parliamentary democracies between 1945and 1998 conform to this prediction: about 16% of thegovernments were single party majority governmentsand about 30% were minimal winning coalitions. Itturns out that about 37% of West European govern-ments have been minority governments and a further17% have been surplus majority governments (Clark,Golder, and Golder 2009, 419). Surplus majoritygovernments even occur 15% of the time when asingle party controls a legislative majority.

Recently, formal scholars have made great stridesin constructing models that predict governments otherthan minimal winning coalitions (Bandyopadhyay andOak 2008; Baron and Diermeier 2001; Diermeier andMerlo 2000). However, most of these models areunable to produce the full range of government typesthat we see in the real world—single party majority,single party minority, minority coalition, minimalwinning, and surplus majority. To our knowledge,Diermeier, Eraslan, and Merlo (2003) present the onlymodel capable of producing the full range of observedgovernment types. No existing model predicts thedistribution of government types.8

Allocation of Portfolios. One of the strongestregularities in all of political science—Gamson’sLaw—states that cabinet portfolios are distributedamong government parties in proportion to thenumber of seats that each party contributes to thegovernment’s legislative majority. Gamson’s Law im-plies that if we were to regress a party’s share ofportfolios against its share of the government’s legis-lative seats, then we would obtain a slope close to oneand an intercept close to zero. Empirical studies haveconsistently found support for this (Warwick andDruckman 2001, 2006).

8We should note that many of these models employ a restrictednumber of parties, policy space, or timing of offers for reasons oftractability—it is not trivial to derive comparative statics in amodel containing both policy preferences and distributive goods.For example, although Jackson and Moselle (2002) are able toprove the existence of certain classes of equilibria in anunrestricted legislative-bargaining model with distributive goodsand a one-dimensional policy space, they are forced to turn toexamples with three parties and specific parameter values todetail the comparative statics of these equilibria. A model likeours that simultaneously produces comparative statics on port-folio allocation, government type, and bargaining delay on anunrestricted domain is an advance in this respect.


Despite being one of the strongest and mostrobust empirical laws in all of political science,Gamson’s Law is not an implication of virtually anybargaining model of coalition formation. In fact,standard models have the potential to produce quitea high degree of disproportionality, depending onthings like party discount factors (Austen-Smith andBanks 1988; Baron and Diermeier 2001; Baron andFerejohn 1989; Snyder, Ting, and Ansolabehere2005). We recognize that a few models do produceGamson’s Law (Bassi 2008; Carroll and Cox 2007;Morelli 1999), but even these only predict it for someequilibria, not all equilibria.

Bargaining Delays. A characteristic of mostparliamentary systems is that elections do not typi-cally determine the identity of the government butinstead set the stage for a prolonged period ofbargaining over the composition and policy goals ofthe cabinet (Golder 2010). Consider the government-formation process following the June 2010 electionsin Belgium. As is usual, the king appointed aninformateur to gather information and report back ona suitable formateur to manage the actual government-formation process. The nonpartisan king has been keptunusually active appointing numerous informateursand formateurs as negotiations over possible coalitionsrepeatedly failed. As of September 2011—over a yearlater—Belgium still had no new duly mandatedgovernment.

Although the long duration of this particularBelgian government formation process is somewhatunusual, it is not uncommon for there to be a delayof several weeks or months while party leaders bargainover the choice of government. While it takes a fewdays on average for a cabinet to form in France,Norway, and Sweden, it takes close to three monthsfor them to form in the Netherlands. On average, ithas taken close to a month for governments to form inWestern Europe (Clark, Golder, and Golder 2009).Significantly, these delays can be quite consequential(Golder 2010). For example, the political and eco-nomic uncertainty generated by bargaining delays hasbeen shown to affect things like exchange rate markets,stock market volatility, the types of assets in whichactors invest, and government stability.

Although the evidence indicates that there can bea considerable delay in the government-formationprocess and that these delays can have serious con-sequences, many models predict that governmentsform immediately. Furthermore, those models thatallow for multiple formateurs and hence delays(Austen-Smith and Banks 1988; Baron and Diermeier2001; Diermeier, Eraslan and Merlo 2003) do not

predict the actual length of delay and, in fact, typicallymake use of the rationality of parties to limit thelength of time over which negotiations take place.

A Zero-Intelligence Model ofGovernment Formation

In this section, we present a zero-intelligence modelof government formation. Our single-district modelconsists of a series of elections, each containing twostages: an election stage and a government-formationstage. In the election stage, m parties, where m is aparameter of the model, are assigned platforms in atwo-dimensional Euclidean policy space X 4 R

2.9

The N voters, who are evenly spaced in the policyspace, are all proximity voters; that is, they vote forthe closest party in the policy space, deciding ties viaa fair die. The election stage thus determines the voteshare that each party receives, which is translateddirectly into a legislative seat share via a perfectlyproportional rule. Note that the election stage in-volves no choices by actors; it simply takes policylocations for m parties as parameter inputs andproduces seat shares as outputs. The election stageis deliberately simple and nonstrategic since ourprimary goal is to examine the government-formationprocess from the point at which legislative seats havebeen allocated.

The election stage in our model defines a ‘‘partysystem’’ consisting of a set of parties, policy positions,and seat shares. Once the election stage is complete,the government-formation process begins. Thegovernment-formation stage takes as an input theparty system as well as an endogenous status quogovernment and its policy position. The utilityfunctions of the parties are linear combinations oftheir cabinet shares in the eventual government and aquadratic loss term that results from policy diver-gences between their ideal points and the eventualgovernment policy.10 Let csi be party i’s proportionof cabinet seats; it takes the value 0 when a party isnot in government. Similarly, we assume that x isthe government policy in two dimensions, and zi

is party i’s ideal point, which is also its platform.We assume that cabinet portfolios are infinitely

9Analysis using a one-dimensional policy space yields qualita-tively similar results to those that we present.

10As we have no priors on the true functional form of this policyloss, we also analyzed the model using a piecewise-linear lossterm. Results were qualitatively similar.


divisible. With these assumptions, party i’s utility isui 5 csi 2 b(x 2 zi)

2. b is the utility weight, relativeto a normalized value of 1 for the cabinet share, thatparties place on policy concerns.

The government-formation stage consists of thefollowing five steps, which define the transitionprobabilities of a Markov process, with the statusquo governments as states:

1. Each party simultaneously chooses a potentialcoalition, always including itself, at random. Allpossible coalitions, including the one with noother members but itself, are equally likely.

2. Each party chooses a random distribution ofcabinet portfolios and a policy position for thispotential coalition. All distributions and policieswithin X are equally likely.11

3. Each party then compares the utilities associatedwith each of the proposed coalitions to the utilityassociated with the status quo. With the exceptionof the first election, the status quo is always theprevious election’s government, which serves asthe caretaker government just after the election.The initial status quo before any election hasoccurred consists of the median voter’s policywith cabinet shares equal to zero for all parties.Any proposed government that strictly beatsthe status quo for all potential members of thegoverning coalition and additionally for a numberof parties controlling a simple majority of legis-lative seats draws the attention of the head of state.

4. If only one proposed government has drawn thehead of state’s attention, then this is installed asthe duly mandated government and becomes thenew status quo for the next election. If more thanone proposed government fits the bill, then thehead of state chooses one randomly and installs it

as the new government and status quo.12 Theendogenously determined successful formateur isthe proposer of the government alternative thattakes office. If no proposed government has thesupport of its coalition and a majority of thelegislature, then all proposed governments arediscarded and all parties start from scratch in step 1.

5. This process continues until either a governmentis installed or 100 periods pass. In the latter case,the caretaker government is reinstalled. This maybe interpreted as the need for a functioninggovernment taking precedence over continuedbickering. This cutoff is typically invoked in themodel when a particular arrangement of partiesand policies favors a narrow range of proposals,leading to the failure of parties to find anythingbetter in subsequent elections.13

In our analysis, we model a repeated government-formation process for a given party system, i.e., for afixed set of parties, policy positions, and seat shares.With the exception of the initial status quo, govern-ments emerge endogenously and the choice of gov-ernment responds dynamically to the previous statusquo government. We then repeat this process fordifferent party systems.

Results

With more than three parties, random coalitionchoice, and majority rule voting, no tractable analyticsolution exists from which to draw insight. Wetherefore turn to simulation methods (Bendor et al.2011; Laver and Sergenti 2011; Miller and Page 2007).

11One might argue that assuming a uniform distribution overproposals is a rather strong assumption. However, we believe thatassuming a uniform distribution over proposals is, in a veryspecific sense, the weakest assumption one can make in a modelwhere proposals must be made. Note that any model thatrequires the production of proposals is necessarily equivalent toa model that delineates some distribution, possibly degenerate,over possible proposals. Given this, the uniform distribution isthe least informative distribution available to us. Indeed this isprecisely why it is employed in zero-intelligence models and whya ‘‘flat’’ prior is so often used in Bayesian statistics. We shouldnote, though, that we replicated our analysis with a variant modelin which parties cannot make proposals that include a policy ineither dimension that is more extreme than the proposedcoalition’s most extreme party’s ideal point in that dimension.Other than a decrease in the mean duration of bargaining delay,results were qualitatively similar.

12We explored two variations to this rule. In one, we had the headof state choose the proposal with the policy closest to the medianvoter. In the other, we had the head of state take a straw poll of allparties and choose the plurality winning proposal. These differentrules did not yield appreciably different results. We also analyzeda variant of our model in which all parties had the chance tomake some number of additional proposals in an attempt to beateach new status quo before it was installed as the next govern-ment. Although we obtained qualitatively similar results for thedistribution of government types and the allocation of portfolios,we obtained somewhat different results for bargaining delay. Thereason for this is that in this variant of the model easily beatenstatus quos lead to longer delays, not shorter ones, as newwinning proposals are introduced again and again. Given a lackof empirical knowledge as to exactly how the bargaining processunfolds, we chose to stick with the simpler modeling assumption.

13We also examined the situation in which the government-formation process could continue for 1,000 periods before thecaretaker government was reinstalled; our results were qualita-tively similar.


The Markov process defined in the previous section isergodic when discretized in the simulation, implyingthat for any set of parameters, all simulated outputs(government types, Gamson’s law regression param-eters, and delay lengths) will be draws from uniquelimiting distributions.14 Our process is thus welldefined. In this case, the Markov process will con-verge to its unique limiting distribution from allinitial state vectors, so we do not have to worry thatour results are dependent on the initial conditions,specifically the arbitrary initial status quo. The benefitof this is that the model can be thought to havesubstantial predictive power (Bendor, Diermeier, andTing 2003, 271).15

Our simulation procedure is as follows. First, wechoose a set of 2 3 m + 2 parameters correspondingto the number of parties (m), the value parties placeon policy relative to holding cabinet ministries (b),and the two-dimensional ideal points for each party(zi). For simplicity and to make interpretation easier,we assume the same value of b for all parties. Eachparameter is drawn from a corresponding uniformdistribution. The number of parties ranges from threeto ten, covering a wide range of real-world partysystems. Ideal points are drawn from X 5 [23, 3] 3

[23, 3], and b is drawn from the set [0, 1] torepresent parties’ policy interests. As described in theprevious section, the initial status quo sets all cabinetshares to zero, and the government policy to that ofthe median voter, which here is located at (0, 0).

Second, we execute an election followed by aseries of 2,500 government formations; we call thisa ‘‘run.’’ Each run represents a simulated data set froma single ‘‘party system’’ about which we collect variousquantities of interest relating to formation outcomes.Although the initial parameters describing the partysystem are fixed during a given run, the proposals madeby the parties vary from one formation process to thenext. Governments emerge endogenously in accordancewith the model outlined previously. As a result, govern-ment choice in each formation process respondsdynamically to the previous status quo government.

As an illustration, Figure 1 plots the cumulativeestimated slope and intercept coefficients from mod-els in which we regress the share of cabinet portfoliosheld by governmental parties against the share of thegovernment’s legislative seats that these parties con-trol for one set of parameter values (party system)over the course of many government formations.16

The vertical dashed line in each panel indicates theend of our normal run of 2,500 government for-mations and the estimated coefficients that we obtainat this point. As one can see, both the slope and theintercept coefficients have settled down to theirsteady-state values of approximately 0.86 and 0.06,respectively, by this point, and do not subsequentlyvary much over time. The settling down processillustrated in Figure 1 obtains for all sets of parametervalues. Further, for a particular set of parametervalues, these results reproduce across runs.17

During the government formations, and at theirend, we record a variety of outcome measures.The value of each of these outcome measures takenat the 2,500th government formation produces anestimate of the mean of the limiting distribution for

14Though the theoretical model may have an infinite state space,instantiation on a finite-state machine (i.e., a computer) impliesthat the simulation is a finite-state Markov process. Define aproposal formally as (cs, x) 2 A, and A9 4 A as the top cycle of A.There is then a nonzero probability that a status quo in A9 maycarry over to the next government formation. Further, bydefinition, it is possible to construct a series of status quos thatreach any other status quo in finite time. Accordingly, the processis aperiodic and all states in A9 communicate. Again by definition,all proposals not in A9 must be beatable by those in A9; thus allsuch states are transient, and the set A9 absorbing. Accordingly,the process is ergodic and produces a unique limiting distribu-tion on A9 to which it converges from all initial conditions. SeeBendor et al. (2011) for a discussion of the importance ofergodicity for simulated results.

15We can now see why there is no tractable analytic solution tothis problem. An analytic solution would entail, at a minimum,determining the limiting distribution of the Markov chain, whichwould require specifying the transition matrix between (veryhigh-dimensional) state vectors. While we can specify theprobability that any particular proposal is made during anygovernment formation attempt, the use of majority rule todetermine which proposals might be enacted introduces compli-cations. For nearly all initial conditions, for any proposal thereexist other proposals that a majority would prefer, given a two-dimensional policy space and an m 2 1 simplex of possiblecabinet share distributions. To specify the transition matrix, onemust determine the set of proposals preferred by a majority toevery status quo proposal; this set need not be convex. While thisis theoretically possible for a finite proposal space, it is nottractable. Thus, much as we turn to (Monte Carlo) simulations tounderstand the properties of estimators in quantitative analyses,we do so here to understand the dynamics of our model.

16The run used five randomly chosen parties located at (20.0058,2.3), (2.5, 22.4), (21.1, 1.5), (0.25, 0.66), and (20.47, 21.0),with b 5 0.25. By cumulative, we mean that the slope andintercept coefficients are reestimated after new data points areadded following each new government formation.

17While the steady-state value for each run is only a draw fromthe well-defined limiting distribution corresponding to that set ofparameter values, we have found that these steady-state valuesvary comparatively little across runs. For example, the standarddeviations of the means of the output measures across only 10runs was between just 5% and 10% of their mean values.Accordingly, to conserve computational time we use only onerun per set of parameter values in the results below; this allows usto explore more of the parameter space.


each measure, and thus a meaningful result on thenature of government formation for a particular setof parameter values (party system). Focusing on theoutcome measures from the final government for-mation minimizes any effects in early governmentformations that might be driven by the exogenouslydetermined initial status quo (Laver and Sergenti2011). In other words, we utilize a ‘‘burn-in period’’sufficient to carry us into the limiting distribution(Laver 2005, 269).18

Because empirical regularities occur across partysystems, and so across parameter values, we simulate50,000 party systems, each with randomly chosenparameters. We use random parameters rather thanparameterizing our model in such a way as to best fitreal-world data in order to avoid biasing our results.While we could, of course, guarantee empirical con-gruence of our model with the real world by carefullychoosing parameters, any subsequent comparisons ofour model’s outcomes to real-world data would not bea fair test of our model.

As one can imagine, though, our simulationprocedure yields a large space of possible partysystems, some of which may not occur with great

frequency in the real world. Because of this, we reporttwo different sets of simulation outcomes in theresults below. The first set of outcomes is obtainedby averaging across all 50,000 sets of runs, treatingeach as having an equal probability of occurring. Thesecond set is designed to better reflect the types ofparty systems we actually observe in the real world. Inthis second set of outcomes, we weight each run bythe relative frequency with which the effective num-ber of legislative parties in that run appears inreal-world data (1945–98) from 17 West Europeancountries (Strøm, Muller, and Bergman 2003). Ob-viously, we would like to do more to better approx-imate the frequency with which different partysystems occur in the real world. However, this wouldrequire knowing things like the weight that partiesplace on policy relative to office and how this isdistributed across different party systems. Unfortu-nately, this type of information does not exist.

We now turn to our results regarding (1) theproportions of each type of government observed;(2) the proportionality of portfolio allocation; and(3) bargaining delays in the formation process.

Government Types

In addition to producing the full variety of observedgovernment types—single party majority, single party

FIGURE 1 Cumulative Estimated Slope and Intercept Coefficients Across Government Formations forOne Set of Parameter Values

18We also performed analyses in which we included all simulateddata and not just those from the final period. Results werequalitatively similar.


minority, minimal winning, minority coalitions, andsurplus majority—our model also produces an em-pirically realistic distribution of these governmenttypes. In Table 1, we provide information on theproportion of governments that fall into each govern-ment type category. In the first column, we show theproportion of governments comprised by each govern-ment type using real-world data from 17 West Europeancountries (1945–98). In the next two columns, we reportthe average proportion of governments comprised bythese different types from our simulated elections,showing both unweighted and weighted results.

On the whole, our model does well at approach-ing the real-world distribution of government types.Of course, this, in and of itself, is not a sufficient testof our model’s predictive power. Even though thedistributions we obtain are similar to those in the realworld, it is possible that substantial differences mayexist between the distribution of governments weobtain for a particular configuration of party locationsand policy weights and that which would obtain giventhe identical scenario in an actual government for-mation opportunity. So to better understand ourmodel’s behavior and to make a start at discountingsuch possibilities, we proceed as in any formal modelby deriving comparative statics on our aggregate resultsas a function of our parameters. If the aggregate resultsvary with the parameters in a reasonable manner—matching real-world results whenever available—thenwe can start to have more confidence that our model,despite its simplicity, captures an element of whathappens in real government-formation processes.

To see how this works, note that the only con-sistent deviations in the weighted simulation results area bias toward producing minority governments and a

bias against producing surplus majority governmentsrelative to what we observe in the real world. We knowthe existence of minority governments in all models,including ours, requires parties to value policy suffi-ciently highly compared to office, otherwise minoritygovernments would not obtain the necessary majoritylegislative support to come to power.19 Further, weexpect surplus majority governments to become lesscommon as policy becomes more important and itbecomes more difficult to find common groundamong larger coalitions. It stands to reason, therefore,that at least some of the bias we find may be arisingdue to the wide range of policy weights that weconsider in our simulations (b varies from 0 to 1).Although we do not have any empirical support forchoosing more realistic values of b, we can examinehow the distribution of government types in ourweighted simulated data varies with b. Our expectationis that minority governments should become morelikely, and majority governments less likely, as therelative weight placed on policy, b, increases.

To examine this expectation, we employ a seriesof generalized additive models using the weightedsimulated data to examine the (possibly nonlinear)relationship between the proportion of each govern-ment type and b (Beck and Jackman 1998). InFigure 2, we plot the predicted relationship betweengovernment type and b for four of our five govern-ment types along with 95% pointwise confidenceintervals. Specifically, we plot the predicted change inthe proportion of each government type against b.Thus, positive values indicate a higher proportion of

TABLE 1 Types of Parliamentary Governments

Government Type

Proportion Occurring:

Real-World DataWestern Europe

Simulated Data

Unweighted Weighted

Single Party Majority .130 .086 .157Minimal Winning Coalition .307 .196 .257Minority Coalition .118 .461 .254Single Party Minority .229 .150 .230Surplus Majority .216 .107 .102

Note: The real-world data in the first column are for 17 West European countries—Austria, Belgium, Denmark, Finland, France (5th

Republic), Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, and the UnitedKingdom—and cover the period from 1945 to 1998 (Strøm, Muller, and Bergman 2003). The unweighted simulated data in the secondcolumn represent the proportion of each government type in the last election of 50,000 simulated party systems. The weighted simulateddata in the third column come from the same simulated party systems, but now each system is weighted by the frequency with which itseffective number of parties occurs in the observational data from Western Europe.

19A separate analysis with b 5 0, so that parties have no interestin policy, yielded no minority governments.


a particular government type for a given b andnegative values indicate a lower proportion. We donot provide a plot for single party majorities becausethe proportion of this government type was unaf-fected by the weight that parties place on policy.

Two things are apparent in Figure 2. The first isthat minority governments of both types (single partyminority and minority coalition) become more com-mon as the weight on policy increases, whereasmajority governments of both types (minimal winningcoalitions and surplus majority) become less common.This is exactly as expected. The second is that nearly allof the action occurs for low values of b. Above aboutb 5 0.2, the effect of any additional weight on policy ismarginal. Placing enough weight on policy so that itcompetes with cabinet shares in the utility of partiesopens up the bargaining space to allow for minoritygovernments, a fact to which we will return later;further increasing the policy weight has little effect.

In effect, our zero-intelligence model not onlyproduces an empirically plausible distribution of allgovernment types, but it also produces a distributionof government types that varies with parameters suchas the weight that parties place on policy in atheoretically intuitive manner.

Allocation of Portfolios

Numerous studies have sought to determine whetherportfolios are allocated among governmental partiesin proportion to the percentage of legislative seatsthat these parties contribute to the government. Onthe whole, these studies evaluate the proportionalityof portfolio allocation by regressing a governmentalparty’s share of portfolios against its share of thegovernment’s legislative seats. According to Gamson’sLaw, such regressions should produce a slope coef-ficient close to one and an intercept coefficient close to

FIGURE 2 Relative Importance of Policy (b) and the Distribution of Government Types


zero. Almost every empirical study has reportedregression results that approximate these predictions.Although the slope coefficient is always slightly lessthan one in these studies, indicating that smallerparties are overcompensated and larger parties under-compensated, the overall picture is that portfolios areallocated in a strongly proportional manner. The nexttest of our model is to see how we fare in thisimportant regard.

In Table 2, we provide information about theslope and intercept coefficients from analyses em-ploying both real-world and simulated data. The firstcolumn reports the estimated slope and interceptcoefficients from an analysis using observational datafrom 14 West European countries. These data consistof portfolio allocations to 917 parties that partici-pated in 378 West European governments. In thesecond column, we report the slope and interceptcoefficients using unweighted data from the lastelections of 50,000 simulated party systems. In thethird column, we report the same results, but eachparty system is weighted according to the frequencywith which its effective number of parties occurs inour observational data. In each of the analyses, weinclude all government types in recognition of thefact that the determination of government type andthe allocation of portfolios occur simultaneously bothin our model and in the real world.

Although neither the simulated data nor the real-world data generate an intercept of exactly zero or aslope of exactly one, they come reasonably close andare in line with results from previous empiricalanalyses (Warwick and Druckman 2001, 2006). Asbefore, appropriately weighting the frequency of oursimulated data to approximate the distribution of

party systems in the observational data brings oursimulated results even closer to the ones based on realWest European governments. Although not oftenreported, there is some heterogeneity across countriesin the slope (and intercept) coefficients that areobtained from regression models similar to the oneemployed here (Buttard and Golder 2011; Indri+ason2010). It turns out that the slope coefficient based onour weighted simulation data is very close to theslope coefficients obtained when using real-worlddata from Germany, Italy, and Denmark. Overall,we believe that the degree of concurrence betweenour simulation and real-world data is quite remark-able, particularly considering that party leaders in ourmodel can propose any allocation of portfolios.

We now explore things further to see whatfeatures of our model influence the proportionalityof portfolio allocation. As all subsequent results arequalitatively similar using both unweighted andweighted data, we report only analyses using weighteddata in what follows.

What Affects the Proportionality of PortfolioAllocation? We can use our simulated results bothto better understand our model and to generate newhypotheses. As a first example, consider the thornyissue of whether there is a formateur bonus inportfolio allocation. While most models do not makepredictions on the degree of proportionality ofportfolio allocation across all input parameters, allbut a few (Bassi 2008; Morelli 1999; Penn 2009)predict that the formateur will receive more thanher fair share of the cabinet posts. The empiricalevidence for this prediction is mixed at best, though.While Ansolabehere et al. (2005) find evidence fora formateur advantage when it comes to portfolio

TABLE 2 Portfolio Allocation

Dependent Variable: Cabinet Portfolio Share

Independent Variables Real-World Data: Western Europe

Simulated Data

Unweighted Weighted

Seat Share 0.891*** (0.009) 0.744*** (0.002) 0.771*** (0.002)Intercept 0.045*** (0.003) 0.102*** (0.001) 0.117*** (0.001)N 917 125,996 125,996

Note: Cells show coefficients with standard errors clustered on the government in parentheses. The real-world data in the first columnare for 14 West European countries—Austria, Belgium, Denmark, Finland, France (5th Republic), Germany, Iceland, Ireland, Italy,Luxembourg, Netherlands, Norway, Portugal, and Sweden—from 1945 to 2000 (Strøm, Muller, and Bergman 2003; Warwick andDruckman 2006). The unweighted simulated data in the second column represent coefficients and standard errors using data from thelast elections of 50,000 simulated party systems. The weighted simulated data in the third column come from the same simulated data,but now each party system is weighted by the frequency with which its effective number of parties occurs in the observational data fromWestern Europe. * p , 0.10; ** p , 0.05; *** p , 0.01 (two-tailed).


allocation, Warwick and Druckman (2006) find evi-dence of a formateur disadvantage.

Given the empirical uncertainty that surrounds thisissue and our prior success in matching real-worldbehavior, we now examine whether our model produ-ces a formateur advantage by adding a dichotomousvariable for formateur status to the model specificationshown in Table 2. The results from this new regressionare shown in the first column of Table 3. The formateuris endogenously defined as the maker of the proposalthat the head of state chooses to enact as the newgovernment. As one can see, our model produces asmall formateur bonus—formateurs receive a largershare of portfolios than one would predict from simplylooking at their contribution to the government’slegislative majority. This formateur bonus occurs dueto a lack of foresight on the part of our parties. Whileactors in Penn’s (2009) model, for example, reasonforward to assess the probability that future proposalsmight be made that would overturn a status quogovernment that overly benefited a proposer, leadingto a smoother distribution of benefits to each party, nosuch smoothing mechanism exists for our myopicparties. Lacking foresight, the parties in our modelmake proposals purely at random, and this proposalmechanism produces a formateur advantage.20

In addition to considering extant questions suchas whether a formateur bonus exists, we can also usethe model to develop new hypotheses. As an example,we now explore the impact of varying our model’sinput parameters on the slope coefficient indicatingthe relationship between a party’s share of thegovernment’s legislative seats and its share of theportfolios.21 Recall that we have 2 3 m + 2parameters: b, which indicates how much policy isweighted relative to office; the number of parties, m;and m two-dimensional policy positions for eachparty. The first two—b and m—are easily varied andhave clear substantive interpretations. As a result, weinclude them directly in our analysis. However, eachof the 2 3 m party locations have no obvious

independent meaning; rather, combined they dictatethe size and ideological diversity of the party system,both of which are of substantive import. We measurethese two substantively important concepts via twodeterministic functions of our parameters.

The first is the effective number of legislativeparties, which measures the size of our simulatedparty systems. The second captures the ideologicaldiversity of the party systems and is the inverse ofAlvarez and Nagler’s (2004) weighted party systemcompactness measure. It measures the weighteddistance of all parties from the ideological center ofthe party system relative to the dispersion of voter

preferences, and is calculated as+ sj zj��zð Þj j

sc, where �z is

the seat share weighted mean of all the parties’positions, and sc is the standard deviation of citizenpreferences.

TABLE 3 Portfolio Allocation, Formateurs, andParameter Settings

Dependent Variable: Cabinet Portfolio Share

IndependentVariables

FormateurAdvantage

Effect ofParameters

Seat Share 0.714***(0.002)

1.099***(0.011)

Intercept 0.107***(0.001)

0.084***(0.006)

Formateur Status 0.076***(0.002)

Parameters:Seat Share 3 Number

of Parties (m)-0.098***(0.002)

Seat Share 3 EffectiveNumber of Parties

0.046***(0.005)

Seat Share 3 IdeologicalDiversity

-0.130***(0.009)

Seat Share 3 PolicyWeight (b)

0.040***(0.006)

Number of Parties (m) 0.027***(0.001)

Effective Numberof Parties

-0.030***(0.002)

Ideological Diversity 0.058***(0.005)

Policy Weight (b) -0.010**(0.003)

N 125,996 125,996R2 0.56 0.57

Note: Cells show coefficients with standard errors clustered onthe government in parentheses. All models use the weightedsimulation data. * p , 0.10; ** p , 0.05; *** p , 0.01(two-tailed).

20As we demonstrate shortly, the proportionality of portfolioallocation declines with the number of cabinet parties due to therandom proposal mechanism in our model. It is the fact thatformateur parties, by virtue of being in all governments, arerelatively more likely to be in smaller cabinets than nonformateurparties that produces the formateur bonus. Note that theformateur bonus is not caused by the two constitutionalconstraints in our model—a model with no constitutionalconstraints produces a similar formateur bonus.

21The intercept tends to decrease as the slope increases, and so wedo not examine it separately.


In the second column of Table 3, we report theresults from a model in which we add variablescapturing the raw number of parties, the effectivenumber of parties, the ideological diversity in theparty system, and the relative weight that partiesplace on policy to those variables already included inthe regression presented in the last column of Table 2.In addition, we also include interaction terms be-tween each of these new covariates and the share oflegislative seats contributed by each party. Thecoefficients of interest here are those on the inter-action terms, as these coefficients indicate how thesize and shape of the party system, as well as theweight that parties place on policy, affect the pro-portionality of portfolio allocation. In effect, theinteraction term coefficients indicate if and how thenew covariates affect the slope of the relationshipbetween the share of seats a party contributes to thegovernment’s legislative majority and its share ofportfolios. For example, a positive coefficient on SeatShare 3 Policy Weight indicates that the slope of thisrelationship increases, and hence that portfolios areallocated more proportionally, as parties place moreweight on policy relative to office.

Given our large sample size, it is not surprisingthat the coefficients on the interaction terms are allstatistically significant. More interesting, though, isthat these coefficients are substantively significant,and robust to weighting the simulation data andaltering the parties’ utility functions. This means thatwe can make clear statements about how our model’sinput parameters influence the slope of the relation-ship between the share of seats a party contributes tothe government’s majority and its share of cabinetportfolios.

First, consider the variables that relate to partysystem complexity and size. As the negative coeffi-cient on Seat Share 3 Number of Parties indicates, themarginal effect of Seat Share is decreasing in the rawnumber of parties, m, implying that more complexparty systems exhibit less support for Gamson’s Law.This occurs due to the nature of proposal making inour model. The more parties there are, the less likelyit is that a random draw of cabinet shares will mirrorthe contributed seat shares.22 In contrast, the positivecoefficient on Seat Share 3 Effective Number ofParties indicates that the marginal effect of Seat Shareis increasing in the effective number of parties

(controlling for ideological diversity and the rawnumber of parties). This indicates that once onecontrols for party system complexity, more equalparty sizes, as indicated by a larger effective numberof parties, imply a more proportional allocation ofportfolios.23 This too occurs due to our randomproposal mechanism. The more equal the seat shares,the more likely that the average random proposal forthe distribution of portfolios will match the seatshares contributed by each governmental party.Interestingly, the random proposal mechanism pro-duces outcomes that mimic what would be expectedintuitively: the fairness of portfolio distributions isincreasing in the need for proposers to be fair (moreevenly sized parties), but decreasing in party systemcomplexity because complexity opens up additionalless-fair options of which to partake. These twoeffects—party system complexity and size—are byfar the strongest in our analysis and account for mostof the explained variance in the slope of the relation-ship between a party’s share of the government’slegislative majority and its share of portfolios.

Now consider the variables that relate to ideo-logical diversity and policy significance. As thenegative coefficient on Seat Share 3 IdeologicalDiversity indicates, the marginal effect of Seat Sharedecreases in the degree to which the parties aredispersed in the policy space. This is because increaseddiversity facilitates trade-offs between office and pol-icy, thereby allowing parties to trade off a bettergovernment policy in return for a less proportionalallocation of portfolios. The positive coefficient onSeat Share 3 Policy Weight indicates that Gamson’sLaw receives increasing support the more that partiesvalue policy. It turns out, though, that the weight thatparties place on policy actually has two opposingeffects on the slope of the relationship between aparty’s share of the government’s seats and its share ofportfolios. The first is negative and arises from the factthat parties are more likely to trade off office for policywhen they place greater weight on policy. The secondis positive and arises from the fact that the size ofgovernments becomes smaller as the weight thatparties place on policy increases. Recall from Figure 2that high b produces more minority governments,which have fewer parties in them. As discussedpreviously, our random proposal mechanism producesa more proportional allocation of portfolios the

22One can see this simply by drawing two random, normalizedvectors of length m and then computing their correlation; it isdecreasing in m.

23Note that by controlling for the raw number of parties, theeffective number of parties essentially captures the extent towhich legislative parties are of roughly equal size.


fewer governmental parties there are. As the results inTable 3 indicate, this positive effect appears to out-weigh the negative effect, i.e., the coefficient on SeatShare 3 Policy Weight is positive.

In sum, support for Gamson’s Law increases inthe weight that parties place on policy and in theextent to which parties are of roughly equal size; itdecreases in the number of parties and in theideological diversity of the party system. To ourknowledge, the existing literature says nothing aboutthe likely relationship between Gamson’s Law andparty system size, ideological diversity, or the weightthat parties place on policy. Thus, our model gen-erates new hypotheses that scholars might test withreal-world data.

Bargaining Delays

As we noted earlier, most existing models that rely onBaron-Ferejohn-style bargaining predict little delay inthe government formation process, and none predictthe distribution of delay observed in the real world.In contrast, our model, like the real world, exhibitsconsiderable variation in the length of time that ittakes governments to form. We measure bargainingdelays in terms of the number of periods in whichparties get to propose potential governments before anew government is installed by the head of state.Though a period in our model is an arbitrary lengthof time, potentially encompassing a great deal of backand forth between parties, more periods do implylonger delay, and so the number of periods shouldbehave similarly to real-world bargaining delays. Inour weighted simulation data, the mean bargainingdelay is 29.84 (29.13 for the unweighted data), anddelays range anywhere from 1 to the maximum of100.

More interesting than these simple descriptivestatistics, though, is the shape of the distribution ofbargaining delays. In Figure 3, we display two kerneldensity plots of delay distributions. The left onecorresponds to real-world data taken from 17 WestEuropean democracies. The right one displays ourweighted simulation data (the plot for unweighteddata is similar), scaled by 2.08 so that the largest delayin our model corresponds to the largest delay (208days) in our observational data. Other than the humpat 208, which is entirely caused by our decision toartificially censor formation attempts after 100 peri-ods and which generally corresponds to cases inwhich the arrangement of parties is such that thereexists a set of proposals sufficiently attractive so as tobe rarely beatable should one become the status quo,

the two distributions look very similar.24 Thus, themodel does a good job not only of predicting varyinglevels of delay, but also in replicating the distributionof delays observed in the real world.

What causes delays in the government-formationprocess? In general, there are few empirical studies ofbargaining delays in the real world (Diermeier andvan Roozendaal 1998; Golder 2010; Martin andVanberg 2003). Most of the studies that exist, though,focus on explaining delays in terms of either un-certainty or bargaining complexity. ‘‘Uncertainty’’refers to not knowing the preferences over policyand office of all the actors whose agreement might benecessary to form a government. ‘‘Bargaining com-plexity’’ refers to things such as the number of differ-ent potential government proposals, both in terms ofportfolio allocation and in terms of future govern-mental policy, as well as the number of politicallyrelevant actors who have to agree on the proposedgovernment. To some extent, scholars have tried todetermine whether it is uncertainty or bargainingcomplexity that is the cause of delays in the formationprocess. For example, Diermeier and van Roozendaal(1998) argue that delays are caused by uncertainty,whereas Martin and Vanberg (2003) side primarilywith bargaining complexity. More recently, Golder(2010) finds that both uncertainty and bargainingcomplexity matter but in a conditional way.

Our model can provide some light on this debate.Although we do not vary the level of uncertainty, wedo vary the level of bargaining complexity in thesense that existing scholars measure bargaining com-plexity in terms of the number of parties and theideological diversity of the party system. In Table 4,we examine how policy weight b, the raw number ofparties m, the effective number of parties, andideological diversity affect bargaining delays. The firstcolumn presents results from a model in which weuse ordinary least squares (OLS) to regress bargainingdelays on our covariates using the weighted simu-lation data. OLS may be problematic in this context,though, because the distribution of delays is notnormally distributed (see Figure 3,) delays have tobe positive, and some delays are right-censored. As aresult, the next column in Table 4 provides resultsfrom a Cox proportional hazards model that is

24In the real world, we would expect situations in which anattractive proposal is the status quo to resolve quickly, and notresult in a series of failed attempts to find something better whennothing better is forthcoming.


specifically designed to deal with these issues. Onething to note is that a positive coefficient in the OLSmodel is equivalent to a negative coefficient in theCox model and vice versa. This is because we aremodeling bargaining delay in the OLS setup but thehazard rate of completing the bargaining in the Coxsetup.

The results from the OLS and Cox modelseffectively match each other. In other words, bothestimation strategies indicate that an increase in thenumber of parties or the weight that parties place onpolicy lead to longer bargaining delays, whereas anincrease in the effective number of parties or partysystem diversity lead to shorter bargaining delays.Each of these results can be explained quite simply.More parties leads to more complexity in the partysystem and more wasted proposals due to the factthat obtaining a legislative majority becomes harder.This result matches the claim in the existing literaturethat bargaining complexity leads to longer bargaining

FIGURE 3 The Distribution of Bargaining Delays

TABLE 4 Bargaining Delays and ParameterSettings

Independent Variables OLS Cox Model

Policy Weight (b) 19.5***(0.52)

-0.82***(0.05)

Number of Parties (m) 8.82***(0.18)

-0.27***(0.02)

Effective Numberof Parties

-20.3***(0.27)

0.53***(0.02)

Ideological Diversity -40.7***(0.86)

1.42***(0.07)

Constant 84.8***(0.79)

R2 0.21N 50,000 50,000

Note: Cells represent coefficients; standard errors are shown inparentheses. The first column presents results from an ordinaryleast squares regression, whereas the second column presentsresults from a Cox proportional hazards model. The Efronmethod was used to handle ties in the Cox model. * p , 0.10;** p , 0.05; *** p , 0.01 (two-tailed).


delays. More weight on policy implies that randomlychosen policy proposals are likely to significantlydecrease parties’ utilities, leading to wasted proposalsand hence bargaining delay. In contrast, greaterparity in party size and more ideological diversityin the party system both imply a greater likelihoodthat a random proposal will beat the status quo formore parties, leading to fewer wasted proposals andtherefore shorter bargaining delays. To our knowl-edge, several of these findings are new and have notpreviously been evaluated in the empirical literature.

Conclusion

The government formation literature is one of thelargest in all of political science. Despite significantadvances in recent years, there remains a gap betweenthe predictions produced by standard models ofgovernment formation that are built on Baron-Ferejohn-style bargaining and what scholars repeat-edly observe in the real world. In response to this,there have been calls to rethink our theoreticalapproach to modeling government formation fromthe ground up. This is precisely what we do in thisarticle. Specifically, we present a zero-intelligencemodel in which three or more parties that care aboutoffice and policy make random government pro-posals. The parties in our model are simple—they donot maximize, adapt, or learn; they do not evenexhibit bounded rationality. The only constraints thatwe impose on government formation correspond tothe two constitutional constraints that exist in allparliamentary democracies, namely that an incum-bent government always exists and that all govern-ments must enjoy majority legislative support.

Despite its deliberately limited structure, ourmodel predicts distributions over portfolio alloca-tion, government types, and bargaining delays thatapproach those observed in the real world. Whileexisting game-theoretic models of government for-mation generally seek to explain the consequences ofthe (assumed) strategic behavior of actors involved inthe government formation process, most also seek topredict formation outcomes. Indeed, extant modelsare often evaluated in terms of whether they canproduce particular formation outcomes such asminority governments or proportional portfolio al-location. Although our model makes no pretense toexplain the actual bargaining behavior of partyleaders as they try to form a government, it isnoteworthy that it does better at simultaneously

predicting a variety of observed formation outcomesthan existing models do. Significantly, we were alsoable to demonstrate that the distributions of portfolioallocation, government types, and bargaining delayproduced by our model vary in theoretically intuitiveways as model parameters change. Overall, the resultsfrom our model indicate that the two constitutionalconstraints that bind in any parliamentary govern-ment formation process are sufficient to approximatemany of our most robust empirical regularities,independent of the strategic behavior of party leadersand their bargaining protocols. This suggests thatstructure, not behavior, may be the most importantthing when it comes to explaining government for-mation outcomes.

We conclude by raising a potentially provocativepoint about the empirical value of formal models,particularly those used to provide insight into pro-cesses generating aggregate data. Using institutionallyspecific rules that are not supported empirically, suchas an alternating offers bargaining protocol, to saysomething substantive across different settings maynot be the best way to conduct empirically relevantformal work. An alternative approach is to encompassas much institutional reality as possible into a model,and when this is not possible, make no additionalassumptions. It is not that one should believe that thegovernment formation process is ‘‘zero intelligence’’;rather, it is that the randomization in our modelenables us to feel more confident that the outcomes weobserve are truly a function of the institutional detailsthat we know to exist.

Acknowledgments

We thank Siddhartha Bandyopadhyay, JonathanBendor, Ken Benoit, Royce Carroll, Jamie Druckman,Sean Ehrlich, Jens Grosser, Michael Laver, WilliamMinozzi, John Patty, Maggie Penn, Bing Powell,Chris Reenock, Norman Schofield, John Scholz,Michael Ting, Paul Warwick, and three anonymousreviewers for their helpful comments on this project.We also thank audiences at the 2010 annual meetingof the Southern Political Science Association, thePolitical Economy Seminar at Washington Universityin St. Louis, the Complexity Seminar in the Depart-ment of Mathematics at Florida State University, the2009 annual meeting of the Midwest Political ScienceAssociation, Chicago, and the 2008 annual meeting ofthe American Political Science Association, Boston.In addition, we are grateful to High Performance


Computing at Florida State University for allowing usto use their supercomputer to run our theoreticalmodel.

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Matt Golder is Associate Professor at The Penn-sylvania State University, University Park, PA16802.

Sona N. Golder is Associate Professor at ThePennsylvania State University, University Park, PA16802.

David A. Siegel is Assistant Professor at FloridaState University, Tallahassee, FL 32306.


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Modeling the Institutional Foundation of Parliamentary Government Formationmattgolder.com/files/research/jop1.pdf · 2015-05-28 · Modeling the Institutional Foundation of Parliamentary