《社会保障概论》课程教学资源（课后阅读资料）APSR_Volume112. Issue 4.Nov 2018_Primaries_and_Candidate_Polarization_Behavioral_Theory_and_Experimental_Evidence

American Political Science Review (2018)112.4.826-843 doi:10.1017/S0003055418000515 American Political Science Association 2018 Primaries and Candidate Polarization:Behavioral Theory and Experimental Evidence JONATHAN WOON University of Pittsburgh o primary elections cause candidates to take extreme,polarized positions?Standard equilibrium analysis predicts full convergence to the median voter's position with complete information, but behavioral game theory predicts divergence when players are policy-motivated and have out-of-equilibrium beliefs.Theoretically,I show that primary elections can cause greater extremism or moderation,depending on the beliefs candidates and voters have about their opponents.In a controlled incentivized experiment,I find that candidates diverge substantially and that primaries have little effect on average positions.Voters employ a strategy that weeds out candidates who are either too moderate or too extreme,which enhances ideological purity without increasing divergence.The analysis highlights the importance of behavioral assumptions in understanding the effects of electoral institutions. The partisan primary system,which favors more ideolog- Political scientists have tested this argument,find- ically pure candidates,has contributed to the election of ing that while there is some evidence to suggest more extreme officeholders and increased political polar- that primary elections promote extremism,the em- ization.It has become a menace to governing. pirical record is mixed.Extremists are more likely to Sen.Charles Schumer(D-NY)! win congressional primaries than moderates (Brady. Han,and Pope 2007),and legislators elected under he divergence between candidates and legisla- closed primaries take more extreme positions than tors from the two major parties is an enduring feature of the American political landscape(An- legislators elected under open primaries(Gerber and Morton 1998).But other analyses find that polariza- solabehere,Snyder,and Stewart 2001;Bonica 2013; tion is largely unrelated to the introduction of direct Poole and Rosenthal 1984,1997).and the fact that polarization is at historically high levels is a signifi- primaries (Hirano et al.2010)and to the variation in the openness of primaries across states(McGhee et al. cant concern for scholars and observers of democratic governance,representation,and public policy(Hacker 2014).At best,primaries may cause polarization un- and Pierson 2006;Mann and Ornstein 2013;McCarty, der limited circumstances(Bullock and Clinton 2011), and despite the divergence of candidate positions,gen- Poole,and Rosenthal 2006,2013).Indeed,politicians eral elections nevertheless exert nontrivial pressure on and the popular press often lay much of the blame for candidates to moderate (Hall 2015:Hirano et al.2010) this phenomenon on partisan primary elections,typ- These findings seem puzzling in light of the basic theory ically employing a simple,intuitively appealing argu- of representation at the heart of this literature that the ment:Candidates take extreme positions because they extremity of primary electorates should directly affect must appeal to partisan primary voters,whose prefer- the extremity of party candidates. ences are more extreme than those of voters in the gen- How,then,should we understand the causal relation- eral election ship between primary elections and candidate position- ing?I examine the connection,both theoretically and Jonathan Woon is a Professor,Department of Political Science,De- partment of Economics(secondary),and Pittsburgh Experimenta experimentally,by comparing elections with and with- Economics Laboratory.4437 Wesley W.Posvar Hall,Pittsburgh,PA. out primaries while holding other features of the elec- 15260(woon@pitt.edu). toral environment constant,including preferences and Thanks to Keith Dougherty,Sandy Gordon,Greg Huber,Scott information.The analysis focuses on a particular as- Moser,Charlie Plott,Danielle Thomsen,Alan Wiseman,the editor and anonymous reviewers,participants at the Yale CSAP American pect of primary elections-how the introduction of vot- Politics Conference.seminar participants at Washington University ers in the candidate selection process affects strategic in St.Louis,University of Oxford (Nuffield College CESS).IC3JM competition between parties-while abstracting away (Juan March Institute),and the Pittsburgh Experimental Economics from many other considerations that might also affect Lab for helpful comments and feedback.I am also indebted to Kris polarization.2 Kanthak for vigorous discussions during the early stages of this project.Previous versions of the paper were presented at the 2014 The contribution of this paper is to develop a more Annual Meeting of the American Political Science Association,the nuanced theoretical understanding of the relationship 2016 Public Choice Society Meeting,and the 2016 Midwest Polit- between primaries and polarization than is portrayed ical Science Association Conference.This research was supported in the existing literature.The key theoretical innova- by the National Science Foundation(SES-1154739)and was ap tion is to move beyond preference-based explanations proved by the University of Pittsburgh Institutional Review Board under protocol PRO14060001.Replication material is available on by treating beliefs as a primitive of the model in a the American Political Science Review Dataverse:https://doi.org/10. way that is ruled out by standard equilibrium analysis 7910/DVN/YUNDMQ. Received:June 27 2016;revised:September 11,2017;accepted:July 12,2018.First published online:September 10,2018. 2 Such considerations include candidate valence,turnout,activists. or campaign contributions (Adams and Merrill 2008:Callander Charles E.Schumer,"Adopt the Open Primary,"New York Times, and Wilson 2007:Hirano,Snyder,and Ting 2009;Hummel 2013: July21,2014. Meirowitz 2005:Snyder and Ting 2011). 826

American Political Science Review (2018) 112, 4, 826–843 doi:10.1017/S0003055418000515 © American Political Science Association 2018 Primaries and Candidate Polarization: Behavioral Theory and Experimental Evidence JONATHAN WOON University of Pittsburgh Do primary elections cause candidates to take extreme, polarized positions? Standard equilibrium analysis predicts full convergence to the median voter’s position with complete information, but behavioral game theory predicts divergence when players are policy-motivated and have out-of-equilibrium beliefs. Theoretically, I show that primary elections can cause greater extremism or moderation, depending on the beliefs candidates and voters have about their opponents. In a controlled incentivized experiment, I find that candidates diverge substantially and that primaries have little effect on average positions. Voters employ a strategy that weeds out candidates who are either too moderate or too extreme, which enhances ideological purity without increasing divergence. The analysis highlights the importance of behavioral assumptions in understanding the effects of electoral institutions. The partisan primary system, which favors more ideolog￾ically pure candidates, has contributed to the election of more extreme officeholders and increased political polar￾ization. It has become a menace to governing. — Sen. Charles Schumer (D-NY)1 The divergence between candidates and legisla￾tors from the two major parties is an enduring feature of the American political landscape (An￾solabehere, Snyder, and Stewart 2001; Bonica 2013; Poole and Rosenthal 1984, 1997), and the fact that polarization is at historically high levels is a signifi￾cant concern for scholars and observers of democratic governance, representation, and public policy (Hacker and Pierson 2006; Mann and Ornstein 2013; McCarty, Poole, and Rosenthal 2006, 2013). Indeed, politicians and the popular press often lay much of the blame for this phenomenon on partisan primary elections, typ￾ically employing a simple, intuitively appealing argu￾ment: Candidates take extreme positions because they must appeal to partisan primary voters, whose prefer￾ences are more extreme than those of voters in the gen￾eral election. Jonathan Woon is a Professor, Department of Political Science, De￾partment of Economics (secondary), and Pittsburgh Experimental Economics Laboratory, 4437 Wesley W. Posvar Hall, Pittsburgh, PA, 15260 (woon@pitt.edu). Thanks to Keith Dougherty, Sandy Gordon, Greg Huber, Scott Moser, Charlie Plott, Danielle Thomsen, Alan Wiseman, the editor and anonymous reviewers, participants at the Yale CSAP American Politics Conference, seminar participants at Washington University in St. Louis, University of Oxford (Nuffield College CESS), IC3JM (Juan March Institute), and the Pittsburgh Experimental Economics Lab for helpful comments and feedback. I am also indebted to Kris Kanthak for vigorous discussions during the early stages of this project. Previous versions of the paper were presented at the 2014 Annual Meeting of the American Political Science Association, the 2016 Public Choice Society Meeting, and the 2016 Midwest Polit￾ical Science Association Conference. This research was supported by the National Science Foundation (SES-1154739) and was ap￾proved by the University of Pittsburgh Institutional Review Board under protocol PRO14060001. Replication material is available on the American Political Science Review Dataverse: https://doi.org/10. 7910/DVN/YUNDMQ. Received: June 27, 2016; revised: September 11, 2017; accepted: July 12, 2018. First published online: September 10, 2018. 1 Charles E. Schumer, “Adopt the Open Primary,” New York Times, July 21, 2014. Political scientists have tested this argument, find￾ing that while there is some evidence to suggest that primary elections promote extremism, the em￾pirical record is mixed. Extremists are more likely to win congressional primaries than moderates (Brady, Han, and Pope 2007), and legislators elected under closed primaries take more extreme positions than legislators elected under open primaries (Gerber and Morton 1998). But other analyses find that polariza￾tion is largely unrelated to the introduction of direct primaries (Hirano et al. 2010) and to the variation in the openness of primaries across states (McGhee et al. 2014). At best, primaries may cause polarization un￾der limited circumstances (Bullock and Clinton 2011), and despite the divergence of candidate positions, gen￾eral elections nevertheless exert nontrivial pressure on candidates to moderate (Hall 2015; Hirano et al. 2010). These findings seem puzzling in light of the basic theory of representation at the heart of this literature that the extremity of primary electorates should directly affect the extremity of party candidates. How, then, should we understand the causal relation￾ship between primary elections and candidate position￾ing? I examine the connection, both theoretically and experimentally, by comparing elections with and with￾out primaries while holding other features of the elec￾toral environment constant, including preferences and information. The analysis focuses on a particular as￾pect of primary elections—how the introduction of vot￾ers in the candidate selection process affects strategic competition between parties—while abstracting away from many other considerations that might also affect polarization.2 The contribution of this paper is to develop a more nuanced theoretical understanding of the relationship between primaries and polarization than is portrayed in the existing literature. The key theoretical innova￾tion is to move beyond preference-based explanations by treating beliefs as a primitive of the model in a way that is ruled out by standard equilibrium analysis 2 Such considerations include candidate valence, turnout, activists, or campaign contributions (Adams and Merrill 2008; Callander and Wilson 2007; Hirano, Snyder, and Ting 2009; Hummel 2013; Meirowitz 2005; Snyder and Ting 2011). 826 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:04, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000515

Primaries and Candidate Polarization in complete information environments.I show that The key finding from the experiment is that pri- primaries can cause polarization or moderation,de- maries appear to cause a kind of ideological purity pending on candidates'beliefs about opposing voters rather than greater extremism.Regardless of whether strategic behavior-even when preferences are held there is a primary election or not,I find that subjects constant.To generate this insight,I rely on ideas from take positions that diverge significantly from the me- behavioral game theory,which retains much of the the dian voter's position.This finding lends support for the oretical apparatus from standard game theory while al- behavioral theory.However,the extent to which pri- lowing for key departures(Camerer 2003).Specifically, maries cause polarization is limited.Greater polariza I allow players to have"incorrect"or"nonequilibrium tion only occurs without feedback such that candidates beliefs about others'actions (Crawford.Costa-Gomes. cannot learn about the behavior of others,and this po- and Iriberri 2013).but assume they are nevertheless larization happens because voters tend to select ex- strategic in the sense that they best respond to what tremists over moderates,even though candidate posi- they think other players do (Camerer.Ho.and Chong tions do not vary with the election format.More pre- 2004;Nagel 1995;Stahl and Wilson 1995).The analysis cisely,the analysis reveals that voters do not support demonstrates that changes in preferences alone are party extremists or party moderates unconditionally. not the only cause of polarization.Instead,beliefs and Instead,they select candidates with intermediate posi- expectations about the strategic behavior of others tions,consistent with their own subjective beliefs about play important roles in conditioning the effect of optimal candidate positions,approximately halfway institutions. between the median voter and their own party's ideal I then turn to the laboratory and conduct a series of point.This behavior generates a greater concentra- experiments to test the effects of primaries on candi- tion of candidate positions around an average that di- date positions and to distinguish between behavioral verges from the median voter.Hence,greater ideolog- assumptions.The chief advantage of the laboratory for ical homogeneity reinforces,rather than exacerbates, theory testing is control(Aldrich and Lupia 2011;Falk polarization 4号元 and Heckman 2009;Morton and Williams 2010),so we can be confident that the observed behavior oc- curs under the conditions specified by the theoretical RELATED LITERATURE model.Importantly,subjects face the same key trade- My analysis follows a long tradition of using spatial off in the experiment as the actors do in the theoretical voting models to understand elections.Although ex- model between increasing the favorability of winning isting spatial models predict candidate divergence in outcomes versus increasing the probability of winning. elections with primaries,they do so in isolation and In the lab,theoretically relevant quantities of interest do not compare them explicitly to elections without that are difficult to measure using observational data primaries (Aronson and Ordeshook 1972;Coleman with any accuracy or without strong assumptions (in 1972:Owen and Grofman 2006).These models also as- particular,preferences and positions)are also known sume that general election outcomes are probabilistic, exactly.Furthermore,experimental manipulations per- which is theoretically consequential because the mech- mit tests of mechanisms not possible using observa- tional data.Thus,laboratory experiments are ideal for anism they rely on to produce divergence is the com- theory testing given their high internal validity.3 bination of policy motivations and uncertainty about which candidate will win the general election-the same forces that generate incentives for candidate di- 3 The main question of interest for theory testing.as Aldrich and Lu- vergence in the absence of primaries (Calvert 1985: pia (2011.90)put it,is"Will people who are in the situations you de- Wittman 1983).Thus,it is unclear from the literature scribe in your model act as you predict?"For related discussions,see whether polarization can be traced to any distinctive Dickson(2011).Palfrey(2006).and especially.Morton and Williams features of primaries per se,as electoral institutions. (2010).While the question of external validity ("To what extent can we generalize from a particular sample?")is an enduring source of By explicitly comparing institutions,my analysis speaks controversy in political science,Falk and Heckman(2009)argue in directly to the connection between primaries and their insightful defense of the value of lab experiments in social sci- polarization. ence that "Behavior in the laboratory is reliable and real:Participants in the lab are real human beings who perceive their behavior as rel- evant,experience real emotions,and take decisions with real eco. nomic consequences"(536).Indeed,there are many precedents for testing theories of elite behavior using laboratory experiments(e.g., strategic than ordinary people (because they have more experi eys Aragones and Palfrey 2007:Frechette,Kagel,and Lehrer 2003:Mor- ence,access to advice,information,etc.),there is surprisingly little ton 1993).Moreover,Druckman and Kam(2011)note that there is evidence to support such claims.To the contrary,recent compar- nothing inherently problematic with using student samples,and there isons by Sheffer et al.(2018)demonstrate that politicians are just as is little evidence to suggest that using undergraduates as stand-ins (and sometimes more)susceptible to choice anomalies than ordinary for elites biases the results in any particular direction (see Morton citizens and Williams 2010,343-7).For example,Potters and van Winden An exception is Jackson,Mathevet,and Mattes (2007),who com- (2000)find significant,but small,differences between students and pare alternative nomination systems in a citizen-candidate frame- lobbyists:Fatas,Neugebauer,and Tamborero(2007)find elites do work.In their model,primary elections affect whose preference is not fit prospect theory as well as students,while studies by Belot decisive in nominating candidates and have no effect if party leaders Duch,and Miller (2015),Cooper et al.(1999),and Mintz,Redd,and and the median party voter have the same preferences.Other formal Vedlitz(2006)suggest that student samples provide a lower bound to models of primary elections largely focus on considerations of voter departures from rational decision-making.Despite the common as. uncertainty,incomplete information,and signaling along with issues sertion that politicians must be better decision makers and more of candidate valence and distributional concerns. 827

Primaries and Candidate Polarization in complete information environments. I show that primaries can cause polarization or moderation, de￾pending on candidates’ beliefs about opposing voters’ strategic behavior—even when preferences are held constant. To generate this insight, I rely on ideas from behavioral game theory, which retains much of the the￾oretical apparatus from standard game theory while al￾lowing for key departures (Camerer 2003). Specifically, I allow players to have “incorrect” or “nonequilibrium” beliefs about others’ actions (Crawford, Costa-Gomes, and Iriberri 2013), but assume they are nevertheless strategic in the sense that they best respond to what they think other players do (Camerer, Ho, and Chong 2004; Nagel 1995; Stahl and Wilson 1995). The analysis demonstrates that changes in preferences alone are not the only cause of polarization. Instead, beliefs and expectations about the strategic behavior of others play important roles in conditioning the effect of institutions. I then turn to the laboratory and conduct a series of experiments to test the effects of primaries on candi￾date positions and to distinguish between behavioral assumptions. The chief advantage of the laboratory for theory testing is control (Aldrich and Lupia 2011; Falk and Heckman 2009; Morton and Williams 2010), so we can be confident that the observed behavior oc￾curs under the conditions specified by the theoretical model. Importantly, subjects face the same key trade￾off in the experiment as the actors do in the theoretical model between increasing the favorability of winning outcomes versus increasing the probability of winning. In the lab, theoretically relevant quantities of interest that are difficult to measure using observational data with any accuracy or without strong assumptions (in particular, preferences and positions) are also known exactly. Furthermore, experimental manipulations per￾mit tests of mechanisms not possible using observa￾tional data. Thus, laboratory experiments are ideal for theory testing given their high internal validity.3 3 The main question of interest for theory testing, as Aldrich and Lu￾pia (2011, 90) put it, is “Will people who are in the situations you de￾scribe in your model act as you predict?” For related discussions, see Dickson (2011), Palfrey (2006), and especially, Morton and Williams (2010). While the question of external validity (“To what extent can we generalize from a particular sample?”) is an enduring source of controversy in political science, Falk and Heckman (2009) argue in their insightful defense of the value of lab experiments in social sci￾ence that “Behavior in the laboratory is reliable and real:Participants in the lab are real human beings who perceive their behavior as rel￾evant, experience real emotions, and take decisions with real eco￾nomic consequences” (536). Indeed, there are many precedents for testing theories of elite behavior using laboratory experiments (e.g., Aragones and Palfrey 2007; Frechette, Kagel, and Lehrer 2003; Mor￾ton 1993). Moreover, Druckman and Kam (2011) note that there is nothing inherently problematic with using student samples, and there is little evidence to suggest that using undergraduates as stand-ins for elites biases the results in any particular direction (see Morton and Williams 2010, 343–7). For example, Potters and van Winden (2000) find significant, but small, differences between students and lobbyists; Fatas, Neugebauer, and Tamborero (2007) find elites do not fit prospect theory as well as students, while studies by Belot, Duch, and Miller (2015), Cooper et al. (1999), and Mintz, Redd, and Vedlitz (2006) suggest that student samples provide a lower bound to departures from rational decision-making. Despite the common as￾sertion that politicians must be better decision makers and more The key finding from the experiment is that pri￾maries appear to cause a kind of ideological purity rather than greater extremism. Regardless of whether there is a primary election or not, I find that subjects take positions that diverge significantly from the me￾dian voter’s position. This finding lends support for the behavioral theory. However, the extent to which pri￾maries cause polarization is limited. Greater polariza￾tion only occurs without feedback such that candidates cannot learn about the behavior of others, and this po￾larization happens because voters tend to select ex￾tremists over moderates, even though candidate posi￾tions do not vary with the election format. More pre￾cisely, the analysis reveals that voters do not support party extremists or party moderates unconditionally. Instead, they select candidates with intermediate posi￾tions, consistent with their own subjective beliefs about optimal candidate positions, approximately halfway between the median voter and their own party’s ideal point. This behavior generates a greater concentra￾tion of candidate positions around an average that di￾verges from the median voter. Hence, greater ideolog￾ical homogeneity reinforces, rather than exacerbates, polarization. RELATED LITERATURE My analysis follows a long tradition of using spatial voting models to understand elections. Although ex￾isting spatial models predict candidate divergence in elections with primaries, they do so in isolation and do not compare them explicitly to elections without primaries (Aronson and Ordeshook 1972; Coleman 1972;Owen and Grofman 2006).4 These models also as￾sume that general election outcomes are probabilistic, which is theoretically consequential because the mech￾anism they rely on to produce divergence is the com￾bination of policy motivations and uncertainty about which candidate will win the general election—the same forces that generate incentives for candidate di￾vergence in the absence of primaries (Calvert 1985; Wittman 1983). Thus, it is unclear from the literature whether polarization can be traced to any distinctive features of primaries per se, as electoral institutions. By explicitly comparing institutions,my analysis speaks directly to the connection between primaries and polarization. strategic than ordinary people (because they have more experi￾ence, access to advice, information, etc.), there is surprisingly little evidence to support such claims. To the contrary, recent compar￾isons by Sheffer et al. (2018) demonstrate that politicians are just as (and sometimes more) susceptible to choice anomalies than ordinary citizens. 4 An exception is Jackson, Mathevet, and Mattes (2007), who com￾pare alternative nomination systems in a citizen-candidate frame￾work. In their model, primary elections affect whose preference is decisive in nominating candidates and have no effect if party leaders and the median party voter have the same preferences. Other formal models of primary elections largely focus on considerations of voter uncertainty, incomplete information, and signaling along with issues of candidate valence and distributional concerns. 827 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:04, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000515

Jonathan Woon Existing theoretical models of two-stage elections fice motivations.Parties are completely homogeneous also typically maintain the assumption that all politi- as candidates and voters belonging to the same party cal actors,candidates as well as voters,are strategic and both care about policy and have the same ideal point. forward-looking (e.g..Owen and Grofman 2006).Sev- Thus,there are three ideal points in the model:0,for eral models consider the issue of raiding and crossover members of Party L,Og for members of Party R,and voting in open primaries (Cho and Kang 2014;Chen eM for the electorate's median voter,where 0.Preferences are also common knowledge,so the divergence,but in their model candidates are office- election takes place under conditions of complete in- motivated and vary in their campaign skills.In contrast formation. to the preponderance of existing formal models,I take There are two types of elections.In one-stage elec- a behavioral (i.e.,bounded rationality)approach advo- tions(1S),each party has one candidate and their posi- cated by Simon (1955).Ostrom(1998).Bendor (2010). tions are cL and cR.respectively,and there is one round and others.I do so by explicitly allowing for sincere of majority rule voting to select the winning candidate (myopic)voting as well as subjective beliefs that are In two-stage elections (2S),each party has two candi- inconsistent with observed behavior. dates (denoted cLi and cL2 for Party L,cRI and cR2 This paper is also related to two distinct literatures for Party R)who first compete in intraparty elections in experimental political science.The experimental lit- (the primaries).The candidates who win their respec- erature on candidate positioning in two-party elections tive party primaries then compete in a second-round finds a strong tendency for candidates and election out- election (the general election)to select the winning comes to converge to the median voter's position and, policy w.In other words,the parties hold simultaneous more generally,to the Condorcet winner under a va- "closed"primaries in which the voter with ideal point riety of conditions,including incomplete information eL chooses cL E [CLI,CL2)for Party L while the voter (Collier et al.1987:McKelvey and Ordeshook 1982 with ideal point OR chooses cR E[CR1,cR2 for Party R.In 1985).An exception is Morton (1993),in which can- the general election,the median voter with ideal point didates are ideological and voting is probabilistic.The ey chooses the election outcome from the two candi- other related literature,on strategic voting,generally dates selected by the parties'respective median voters finds little (at best,mixed)evidence for voter sophisti- w∈{CL,CR}. cation in the early stages of a multistage voting agenda To generate predictions about candidate positioning or election contest (Cherry and Kroll 2003;Eckel and and to identify the effects of the election format,I con- Holt 1989;Herzberg and Wilson 1988;McCuen and sider a variety of alternative behavioral assumptions.I Morton 2010:Plott and Levine 1978:Van der Straeten begin with standard game theoretic analysis,applying et al.2010).5 Taken together,these previous studies Nash equilibrium as the solution concept.Since I am raise doubts that voters will be highly strategic (even interested in making behavioral predictions,the inter- if candidates are),calling into question theories predi- pretation of Nash equilibrium is worth a brief discus- cated on voter rationality and strategic sophistication. sion.One way to interpret Nash equilibrium is to think of it as an idealized set of assumptions such that actors THEORETICAL FRAMEWORK AND are not only fully rational but also that their rationality ANALYSIS is common knowledge(Aumann and Brandenburger 1995).In this interpretation,we can think of political I consider an environment with two parties,Party L and actors as forming beliefs about others'current and fu- Party R,competing to win a single office.Candidates ture behavior (as well as beliefs about beliefs and ra- choose positions in a one-dimensional policy space, tionality,and so on)that are fully consistent with play- and the winning candidate's position is implemented ers'actual strategies and behavior.Alternatively,Nash as the policy outcome.In the electorate,there are an equilibrium can be interpreted as merely representing equal number of voters in each party and a set of inde- a stable outcome in which strategies are mutual best pendent,nonpartisan "swing"voters.Candidates and responses,without necessarily invoking an epistemic or voters alike are entirely policy-motivated,caring only belief-based justification of how individuals make deci- about the location of the policy outcome we R.The in- sions in games.The latter approach,however,does not centive to win office is therefore purely instrumental in make clear cut predictions about how games are played this model,which departs from the usual Downsian of- before an equilibrium state is reached.Nevertheless under a wide variety of learning models,experience can lead play to converge to Nash equilibrium(Fudenberg Smirnov (2009),who studies endogenous agendas and finds behav- and Levine 1998).and the role of experience can be ior consistent with sophisticated expected utility maximization,is an investigated experimentally. exception.There is stronger experimental evidence for other kinds Relaxing the Nash assumption of the mutual con- strategic voting.however,such as coordinating on a less-preferred candidate in multicandidate contests (Rietz 2008),and in incom sistency of beliefs and actions generates an interest- plete information pivotal voter settings(e.g.,Battaglini,Morton,and ing variety of behavioral possibilities.In my analysis Palfrey 2010). I first explore the implications of voter sophistication 828

Jonathan Woon Existing theoretical models of two-stage elections also typically maintain the assumption that all politi￾cal actors, candidates as well as voters, are strategic and forward-looking (e.g., Owen and Grofman 2006). Sev￾eral models consider the issue of raiding and crossover voting in open primaries (Cho and Kang 2014; Chen and Yang 2002; Oak 2006), which requires a fairly high degree of strategic sophistication, but this kind of be￾havior is outside the scope of my analysis. My results also differ from Adams and Merrill (2014), who find that strategic versus expressive voting both generate divergence, but in their model candidates are office￾motivated and vary in their campaign skills. In contrast to the preponderance of existing formal models, I take a behavioral (i.e., bounded rationality) approach advo￾cated by Simon (1955), Ostrom (1998), Bendor (2010), and others. I do so by explicitly allowing for sincere (myopic) voting as well as subjective beliefs that are inconsistent with observed behavior. This paper is also related to two distinct literatures in experimental political science. The experimental lit￾erature on candidate positioning in two-party elections finds a strong tendency for candidates and election out￾comes to converge to the median voter’s position and, more generally, to the Condorcet winner under a va￾riety of conditions, including incomplete information (Collier et al. 1987; McKelvey and Ordeshook 1982, 1985). An exception is Morton (1993), in which can￾didates are ideological and voting is probabilistic. The other related literature, on strategic voting, generally finds little (at best, mixed) evidence for voter sophisti￾cation in the early stages of a multistage voting agenda or election contest (Cherry and Kroll 2003; Eckel and Holt 1989; Herzberg and Wilson 1988; McCuen and Morton 2010; Plott and Levine 1978; Van der Straeten et al. 2010).5 Taken together, these previous studies raise doubts that voters will be highly strategic (even if candidates are), calling into question theories predi￾cated on voter rationality and strategic sophistication. THEORETICAL FRAMEWORK AND ANALYSIS I consider an environment with two parties,Party L and Party R, competing to win a single office. Candidates choose positions in a one-dimensional policy space, and the winning candidate’s position is implemented as the policy outcome. In the electorate, there are an equal number of voters in each party and a set of inde￾pendent, nonpartisan “swing” voters. Candidates and voters alike are entirely policy-motivated, caring only about the location of the policy outcome w ∈ R. The in￾centive to win office is therefore purely instrumental in this model, which departs from the usual Downsian of- 5 Smirnov (2009), who studies endogenous agendas and finds behav￾ior consistent with sophisticated expected utility maximization, is an exception. There is stronger experimental evidence for other kinds strategic voting, however, such as coordinating on a less-preferred candidate in multicandidate contests (Rietz 2008), and in incom￾plete information pivotal voter settings (e.g., Battaglini, Morton, and Palfrey 2010). fice motivations. Parties are completely homogeneous, as candidates and voters belonging to the same party both care about policy and have the same ideal point. Thus, there are three ideal points in the model: θL for members of Party L, θR for members of Party R, and θM for the electorate’s median voter, where θL 0. Preferences are also common knowledge, so the election takes place under conditions of complete in￾formation. There are two types of elections. In one-stage elec￾tions (1S), each party has one candidate and their posi￾tions are cL and cR, respectively, and there is one round of majority rule voting to select the winning candidate. In two-stage elections (2S), each party has two candi￾dates (denoted cL1 and cL2 for Party L, cR1 and cR2 for Party R) who first compete in intraparty elections (the primaries). The candidates who win their respec￾tive party primaries then compete in a second-round election (the general election) to select the winning policy w. In other words, the parties hold simultaneous “closed” primaries in which the voter with ideal point θL chooses cL ∈ {cL1, cL2} for Party L while the voter with ideal point θR chooses cR ∈ {cR1, cR2} for Party R. In the general election, the median voter with ideal point θM chooses the election outcome from the two candi￾dates selected by the parties’ respective median voters, w ∈ {cL, cR}. To generate predictions about candidate positioning and to identify the effects of the election format, I con￾sider a variety of alternative behavioral assumptions. I begin with standard game theoretic analysis, applying Nash equilibrium as the solution concept. Since I am interested in making behavioral predictions, the inter￾pretation of Nash equilibrium is worth a brief discus￾sion. One way to interpret Nash equilibrium is to think of it as an idealized set of assumptions such that actors are not only fully rational but also that their rationality is common knowledge (Aumann and Brandenburger 1995). In this interpretation, we can think of political actors as forming beliefs about others’ current and fu￾ture behavior (as well as beliefs about beliefs and ra￾tionality, and so on) that are fully consistent with play￾ers’ actual strategies and behavior. Alternatively, Nash equilibrium can be interpreted as merely representing a stable outcome in which strategies are mutual best responses, without necessarily invoking an epistemic or belief-based justification of how individuals make deci￾sions in games. The latter approach, however, does not make clear cut predictions about how games are played before an equilibrium state is reached. Nevertheless, under a wide variety of learning models, experience can lead play to converge to Nash equilibrium (Fudenberg and Levine 1998), and the role of experience can be investigated experimentally. Relaxing the Nash assumption of the mutual con￾sistency of beliefs and actions generates an interest￾ing variety of behavioral possibilities. In my analysis, I first explore the implications of voter sophistication 828 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:04, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000515

Primaries and Candidate Polarization for candidate positioning while holding candidate ra- be specified.Given a set of candidate positions and vot- tionality constant.If voting is "sincere,"then primary ers'expectations that the general election median voter elections produce more polarized candidates than vot- will choose the more moderate of the parties'candi ing that follows an equilibrium strategy.I then consider dates,a primary voter's strategy is to choose the can- another departure from standard assumptions:beliefs didate closest to her ideal point as long as she believes that some players make mistakes in choosing their po- the candidate will also win the general election (and sitions.They might do so for any number of reasons, in equilibrium,the voter's beliefs about which candi- such as miscalculating the optimal position.misjudg date will win are correct).Because candidates and vot- ing or underestimating the rationality of others,or hav- ers have the same preferences,the incentives guiding ing preferences over outcomes of the game that are optimal candidate strategies in the one-stage election not fully captured by their material payoffs.Strategi- are similar to those that guide rational voting behav- cally sophisticated players,recognizing that there are ior in two-stage elections:if offered the same choices. other players who make mistakes,will then choose po- candidates and voters would choose the same position sitions that differ from the Nash predictions-in the di- (the only difference is that candidates can choose any rection of their parties'ideal points-but that are op- position while primary voters'choices are constrained). timal given their own beliefs about the distribution of In any equilibrium of the two-stage election game, opponents'positions.Introducing noise or the possibil- there must be at least one candidate from each party ity of mistakes generates divergence in both one-stage located at eM,so primary voters will always be ob- and two-stage elections,despite complete information served choosing the moderate candidate along the path about preferences. of play.If so,both parties'primary voters will select a With noise,the effect of introducing a primary elec- candidate at the median voter's ideal point and the pol- tion is more nuanced.Similar to the case in which can- icy outcome is therefore w=0M.Ruling out other pos- didates do not make mistakes,the optimal positions sible outcomes then follows from the same logic as in depend critically on the behavior of primary voters.If the nonprimary election.Assuming fully strategic be- 4r元 voters choose moderate primary candidates,then two- havior from voters therefore predicts full convergence stage elections will generate greater convergence of to the median voter's position in both one-stage and candidate positions than in one-stage elections.How- two-stage elections. ever,if voters choose extreme primary candidates,then candidates in two-stage elections will be more polar- Prediction 1.If voters and candidates are rational, ized than candidates in one-stage elections.There is forward-looking agents and form correct beliefs about also a third possibility:If voters form their own be- others'behavior,then (a)the moderate candidates from liefs about the position most likely to maximize their each party will adopt the median voter's position and expected utility and vote for candidates closest to this (b)primaries will have no effect on the polarization of position.then the degree of candidate divergence in candidates in the general election. two-stage elections is increasing in what we might call voters'belief-induced ideal points.Behavioral game Candidate Equilibrium with Sincere Voters theory thus establishes a critical link between candi- dates'beliefs about opponents'primary voting behav- I next consider the possibility that primary voters are ior and the effect of primaries. myopic and vote"sincerely."6 I assume that sincere vot- ers simply vote for the candidate closest to their ideal points,so they are myopic in the sense that they fail to recognize that the candidate's chances of winning the Candidate Equilibrium with Fully Strategic general election affect the policy outcome(and hence Voters their payoffs).With myopic voters,the two-stage elec- Standard equilibrium analysis leads to identical predic- tion game has multiple equilibria in which candidates tions for both one-stage and two-stage elections.This take divergent positions while the equilibrium of the is because,in any equilibrium,the winning candidate's one-stage election game remains the same(full conver- position is the median voter's ideal point.In one-stage gence,since there are no primary voters) elections,the logic is straightforward.The median voter In any equilibrium of the two-stage election game chooses the party candidate closest to his or her ideal with sincere voters,candidates within each party must point as the winning candidate,so if one candidate adopt the same position,and opposing party can- didates must be equidistant from the median voter. 四 adopts 0w as a campaign position,no other position can defeat it.In the unique equilibrium of the one-stage Specifically,an equilibrium is characterized by the election game,both parties'candidates must choose condition that cLI CL2 =0M-8 and CRI CR2 cL=CR =0M.If not,either the winning party's candi- e+8,where 8>0 denotes some amount of diver- date could do better by finding a position closer to her gence between candidates.The median voter's strategy ideal point while still winning the election or the los ing candidate can find a position that wins the election While the overall level of voter "rationality"remains an ongoing thereby obtaining a better policy outcome for herself. subject of debate,the assumption that voters are myopic is consistent Thus,w=6M is the unique equilibrium policy outcome. with recent observational and experimental research on accountabil- ity (e.g..Healy and Malhotra 2009;Huber,Hill,and Lenz 2012;Woon In two-stage elections,the outcome is the same,but 2012a).A theory of elections with boundedly rational,behavioral the equilibrium strategies of the primary voters must voters is also worked out by Bendor et al.(2011). 829

Primaries and Candidate Polarization for candidate positioning while holding candidate ra￾tionality constant. If voting is “sincere,” then primary elections produce more polarized candidates than vot￾ing that follows an equilibrium strategy. I then consider another departure from standard assumptions: beliefs that some players make mistakes in choosing their po￾sitions. They might do so for any number of reasons, such as miscalculating the optimal position, misjudg￾ing or underestimating the rationality of others, or hav￾ing preferences over outcomes of the game that are not fully captured by their material payoffs. Strategi￾cally sophisticated players, recognizing that there are other players who make mistakes, will then choose po￾sitions that differ from the Nash predictions—in the di￾rection of their parties’ ideal points—but that are op￾timal given their own beliefs about the distribution of opponents’ positions. Introducing noise or the possibil￾ity of mistakes generates divergence in both one-stage and two-stage elections, despite complete information about preferences. With noise, the effect of introducing a primary elec￾tion is more nuanced. Similar to the case in which can￾didates do not make mistakes, the optimal positions depend critically on the behavior of primary voters. If voters choose moderate primary candidates, then two￾stage elections will generate greater convergence of candidate positions than in one-stage elections. How￾ever, if voters choose extreme primary candidates, then candidates in two-stage elections will be more polar￾ized than candidates in one-stage elections. There is also a third possibility: If voters form their own be￾liefs about the position most likely to maximize their expected utility and vote for candidates closest to this position, then the degree of candidate divergence in two-stage elections is increasing in what we might call voters’ belief-induced ideal points. Behavioral game theory thus establishes a critical link between candi￾dates’ beliefs about opponents’ primary voting behav￾ior and the effect of primaries. Candidate Equilibrium with Fully Strategic Voters Standard equilibrium analysis leads to identical predic￾tions for both one-stage and two-stage elections. This is because, in any equilibrium, the winning candidate’s position is the median voter’s ideal point. In one-stage elections, the logic is straightforward.The median voter chooses the party candidate closest to his or her ideal point as the winning candidate, so if one candidate adopts θM as a campaign position, no other position can defeat it. In the unique equilibrium of the one-stage election game, both parties’ candidates must choose cL = cR = θM. If not, either the winning party’s candi￾date could do better by finding a position closer to her ideal point while still winning the election or the los￾ing candidate can find a position that wins the election, thereby obtaining a better policy outcome for herself. Thus,w = θM is the unique equilibrium policy outcome. In two-stage elections, the outcome is the same, but the equilibrium strategies of the primary voters must be specified.Given a set of candidate positions and vot￾ers’ expectations that the general election median voter will choose the more moderate of the parties’ candi￾dates, a primary voter’s strategy is to choose the can￾didate closest to her ideal point as long as she believes the candidate will also win the general election (and in equilibrium, the voter’s beliefs about which candi￾date will win are correct). Because candidates and vot￾ers have the same preferences, the incentives guiding optimal candidate strategies in the one-stage election are similar to those that guide rational voting behav￾ior in two-stage elections: if offered the same choices, candidates and voters would choose the same position (the only difference is that candidates can choose any position while primary voters’ choices are constrained). In any equilibrium of the two-stage election game, there must be at least one candidate from each party located at θM, so primary voters will always be ob￾served choosing the moderate candidate along the path of play. If so, both parties’ primary voters will select a candidate at the median voter’s ideal point and the pol￾icy outcome is therefore w = θM. Ruling out other pos￾sible outcomes then follows from the same logic as in the nonprimary election. Assuming fully strategic be￾havior from voters therefore predicts full convergence to the median voter’s position in both one-stage and two-stage elections. Prediction 1. If voters and candidates are rational, forward-looking agents and form correct beliefs about others’ behavior, then (a) the moderate candidates from each party will adopt the median voter’s position and (b) primaries will have no effect on the polarization of candidates in the general election. Candidate Equilibrium with Sincere Voters I next consider the possibility that primary voters are myopic and vote “sincerely.”6 I assume that sincere vot￾ers simply vote for the candidate closest to their ideal points, so they are myopic in the sense that they fail to recognize that the candidate’s chances of winning the general election affect the policy outcome (and hence their payoffs). With myopic voters, the two-stage elec￾tion game has multiple equilibria in which candidates take divergent positions while the equilibrium of the one-stage election game remains the same (full conver￾gence, since there are no primary voters). In any equilibrium of the two-stage election game with sincere voters, candidates within each party must adopt the same position, and opposing party can￾didates must be equidistant from the median voter. Specifically, an equilibrium is characterized by the condition that cL1 = cL2 = θM − δ and cR1 = cR2 = θM + δ, where δ ≥ 0 denotes some amount of diver￾gence between candidates. The median voter’s strategy 6 While the overall level of voter “rationality” remains an ongoing subject of debate, the assumption that voters are myopic is consistent with recent observational and experimental research on accountabil￾ity (e.g.,Healy and Malhotra 2009;Huber,Hill, and Lenz 2012;Woon 2012a). A theory of elections with boundedly rational, behavioral voters is also worked out by Bendor et al. (2011). 829 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:04, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000515

Jonathan Woon is to select the candidate closest to her own ideal point. To model this,let candidate i's beliefs about the po- breaking ties in favor of each party with equal proba- sitions of candidates from the opposing party ji be bility.The result of the general election is therefore a given by the cumulative distribution F(ci).Importantly, lottery over w [eM-8,eM+8),and the expected these beliefs need not be accurate.For instance,if i's value of the outcome is the median voter's position true position is ci=0,candidate i might believe that E[w]=0M.Any candidate who adopts a more extreme c;is uniformly distributed between-1 and 1.We can position would,at best,be able to win their own pri- think of the distribution F(ci)as representing subjec- mary but then would lose the general election with cer- tive beliefs that will typically not satisfy the equilibrium tainty.Moving to a more moderate position would not consistency requirement. change the result of the primary and thus would not By relaxing the standard equilibrium assumption of change the general election result either.Since no can- belief consistency,an otherwise expected utility max- didate can obtain a better policy outcome by unilater- imizing candidate will choose a position that diverges ally adopting a different position,campaign promises from the median voter's ideal point.The reasoning is as characterized by intraparty convergence and interparty follows.If a candidate believes there is some possibil- symmetric divergence constitute an equilibrium of the ity that the opposing candidate's position diverges from primary election game with sincere voters.The basic the median voter,then it cannot be optimal for a policy- intuition underlying this result is that due to the myopic motivated candidate to choose a platform exactly at behavior of sincere primary voters,intraparty compe- the median voter's ideal point.Instead,the candidate tition limits any one candidate's ability to moderate will choose a position that trades off some probabil- 元 their party's position in the general election.Thus,in ity of winning against potential policy gains obtained contrast to full convergence in one-stage elections,any from choosing a position closer to his or her own ideal amount of divergence can be supported in two-stage point.To illustrate this concretely,suppose that oR= elections. 1,the left party's ideal point is L=-1,the median is 令 eM =0,and F(cL)is a uniform random variable,cL~ 4号元 Prediction 2.If candidates are rational and forward- UI-1,0].With linear loss utility,the optimal position looking but primary voters "sincerely"select candidates closest to their own ideal points,then (a)candidates from that balances this tradeoff is c=.This is illustrated each party will take positions that diverge from the me- by the solid line showing the expected utility function dian voter by the same amount in two-stage elections, EU(cR)in Figure 1.10 While this logic is similar to the and(b)winning candidates will be weakly more polar- tradeoff found in Calvert (1985)and Wittman(1983), ized in two-stage elections than in one-stage elections, the important distinction is that the source of uncer- while candidates in the latter will converge to the median tainty in this model is entirely about opponents'behav- voter. ior rather than about voters or preferences.Moreover, candidate positions are responsive to beliefs such that when a candidate is more likely to expect her oppo- Candidate Best Responses to nent to be extreme (i.e.,when F(c)puts more weight Out-of-Equilibrium Beliefs on extreme positions),then she herself will take a posi- The previous sections assumed that candidates cor- tion with greater divergence from the median voter in rectly anticipate whether voters use either Nash or sin- response cere voting strategies and that their beliefs about other Next,I consider how these beliefs about opposing candidates are consistent with those candidates'actual candidates'positions interact with the type of elec- behavior.That is,if candidate j chooses the platform tion.The main result is that the effect of primaries will cj,then candidate i must believe with certainty that ci depend on the candidates'beliefs about the opposing party's primary voters.The baseline for comparison is a must really be i's position.However,this mutual con- sistency of candidates'beliefs and actions might break one-stage election with opponents drawn from the be- down in a number of ways.Candidates are likely to lief distribution F(ci).For the purposes of exposition, face cognitive constraints,they may engage in incom- suppose that F(cj)is uniform as in the example just plete strategic reasoning,or they may doubt the ratio- given and as shown in the left side of Figure 2,so the nality of other candidates.In this section,I apply the notion of limited strategic sophistication motivated by level-k models in behavioral game theory (Crawford levels of sophistication or reasoning as modeled explicitly in the level-k framework. 2003;Nagel 1995;Stahl and Wilson 1995),positing that 9 I assume that the density f(ci)has full support over the interval candidates have some(possibly arbitrary)beliefs and between median voter M and the opposing party 0j.The distribution analyze the best response to such beliefs.s F(cj) can also be interpreted as an objective probability distribution if candidates'choices are noisy and F(c)reflects the true distribution of candidate positions. 7 Note that it is also possible to construct equilibria in which the me- 10 Formally,given beliefs with density f(cL),the expected utility func- dian voter has a bias for one of the parties (i.e.,breaks ties in fa L vor of one party rather than randomizing),but this would not affect N-CR the equilibrium positions of the candidates.Thus,even though the EU(CR) u(CR)f(CL)dcL+ u(cL)f(CL)dcL, random tie-breaking rule matches the experimental setup,it is not 28M-ER necessary for the results. where the integral on the left is the expected utility if cR is closer s While level-k models are a subset of the class of models that as- to the median voter and wins while the integral on the right is the sume out-of-equilibrium beliefs,my theory does not rely on different expected utility if the opposing candidate cL is closer to the median. 830

Jonathan Woon is to select the candidate closest to her own ideal point, breaking ties in favor of each party with equal proba￾bility.7 The result of the general election is therefore a lottery over w ∈ {θM − δ, θM + δ}, and the expected value of the outcome is the median voter’s position, E[w] = θM. Any candidate who adopts a more extreme position would, at best, be able to win their own pri￾mary but then would lose the general election with cer￾tainty. Moving to a more moderate position would not change the result of the primary and thus would not change the general election result either. Since no can￾didate can obtain a better policy outcome by unilater￾ally adopting a different position, campaign promises characterized by intraparty convergence and interparty symmetric divergence constitute an equilibrium of the primary election game with sincere voters. The basic intuition underlying this result is that due to the myopic behavior of sincere primary voters, intraparty compe￾tition limits any one candidate’s ability to moderate their party’s position in the general election. Thus, in contrast to full convergence in one-stage elections, any amount of divergence can be supported in two-stage elections. Prediction 2. If candidates are rational and forward￾looking but primary voters “sincerely” select candidates closest to their own ideal points,then (a) candidates from each party will take positions that diverge from the me￾dian voter by the same amount in two-stage elections, and (b) winning candidates will be weakly more polar￾ized in two-stage elections than in one-stage elections, while candidates in the latter will converge to the median voter. Candidate Best Responses to Out-of-Equilibrium Beliefs The previous sections assumed that candidates cor￾rectly anticipate whether voters use either Nash or sin￾cere voting strategies and that their beliefs about other candidates are consistent with those candidates’ actual behavior. That is, if candidate j chooses the platform cj, then candidate i must believe with certainty that cj must really be j’s position. However, this mutual con￾sistency of candidates’ beliefs and actions might break down in a number of ways. Candidates are likely to face cognitive constraints, they may engage in incom￾plete strategic reasoning, or they may doubt the ratio￾nality of other candidates. In this section, I apply the notion of limited strategic sophistication motivated by level-k models in behavioral game theory (Crawford 2003; Nagel 1995; Stahl and Wilson 1995), positing that candidates have some (possibly arbitrary) beliefs and analyze the best response to such beliefs.8 7 Note that it is also possible to construct equilibria in which the me￾dian voter has a bias for one of the parties (i.e., breaks ties in fa￾vor of one party rather than randomizing), but this would not affect the equilibrium positions of the candidates. Thus, even though the random tie-breaking rule matches the experimental setup, it is not necessary for the results. 8 While level-k models are a subset of the class of models that as￾sume out-of-equilibrium beliefs, my theory does not rely on different To model this, let candidate i’s beliefs about the po￾sitions of candidates from the opposing party j = i be given by the cumulative distribution F(cj). Importantly, these beliefs need not be accurate. For instance, if j’s true position is cj = 0, candidate i might believe that cj is uniformly distributed between −1 and 1. We can think of the distribution F(cj) as representing subjec￾tive beliefs that will typically not satisfy the equilibrium consistency requirement.9 By relaxing the standard equilibrium assumption of belief consistency, an otherwise expected utility max￾imizing candidate will choose a position that diverges from the median voter’s ideal point. The reasoning is as follows. If a candidate believes there is some possibil￾ity that the opposing candidate’s position diverges from the median voter, then it cannot be optimal for a policy￾motivated candidate to choose a platform exactly at the median voter’s ideal point. Instead, the candidate will choose a position that trades off some probabil￾ity of winning against potential policy gains obtained from choosing a position closer to his or her own ideal point. To illustrate this concretely, suppose that θR = 1, the left party’s ideal point is θL = −1, the median is θM = 0, and F(cL) is a uniform random variable, cL ∼ U[ − 1, 0]. With linear loss utility, the optimal position that balances this tradeoff is c∗ R = 1 3 . This is illustrated by the solid line showing the expected utility function EU(cR) in Figure 1. 10 While this logic is similar to the tradeoff found in Calvert (1985) and Wittman (1983), the important distinction is that the source of uncer￾tainty in this model is entirely about opponents’ behav￾ior rather than about voters or preferences. Moreover, candidate positions are responsive to beliefs such that when a candidate is more likely to expect her oppo￾nent to be extreme (i.e., when F(cj) puts more weight on extreme positions), then she herself will take a posi￾tion with greater divergence from the median voter in response. Next, I consider how these beliefs about opposing candidates’ positions interact with the type of elec￾tion. The main result is that the effect of primaries will depend on the candidates’ beliefs about the opposing party’s primary voters.The baseline for comparison is a one-stage election with opponents drawn from the be￾lief distribution F(cj). For the purposes of exposition, suppose that F(cj) is uniform as in the example just given and as shown in the left side of Figure 2, so the levels of sophistication or reasoning as modeled explicitly in the level-k framework. 9 I assume that the density f(cj) has full support over the interval between median voter θM and the opposing party θj.The distribution F(cj) can also be interpreted as an objective probability distribution if candidates’ choices are noisy and F(cj) reflects the true distribution of candidate positions. 10 Formally, given beliefs with density f(cL), the expected utility func￾tion is given by EU(cR) = 2θM−cR θL u(cR)f(cL)dcL + θM 2θM−cR u(cL)f(cL)dcL, where the integral on the left is the expected utility if cR is closer to the median voter and wins while the integral on the right is the expected utility if the opposing candidate cL is closer to the median. 830 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:04, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000515

Primaries and Candidate Polarization FIGURE 1.Comparison of Candidate Expected Utility in One-Stage and Two-Stage Elections as a Function of Out-of-Equilibrium Beliefs and Opponents'Primary Voting Behavior EUe(CR) EU(CR) I EUm(CR) M Positions Note:EU(CR)corresponds to 1S elections,EU(CR)corresponds to 2S elections against moderates,and EU(CA)corresponds to 2S elections against extremists. FIGURE 2.Comparison of Beliefs in One-Stage and Two-Stage Elections as a Function of Opponents'Primary Voting Behavior Distribution of candidates in second stage after selection by primary voters candidate closest to OL If voters select OL 0M Distribution of candidates in first stage and one-stage elections If voters select candidate closest to 9L+0M 2 OL If voters select candidate closest to OM OL 0M 831

Primaries and Candidate Polarization FIGURE 1. Comparison of Candidate Expected Utility in One-Stage and Two-Stage Elections as a Function of Out-of-Equilibrium Beliefs and Opponents’ Primary Voting Behavior Note: EU(cR) corresponds to 1S elections, EUm(cR) corresponds to 2S elections against moderates, and EUe(cR) corresponds to 2S elections against extremists. FIGURE 2. Comparison of Beliefs in One-Stage and Two-Stage Elections as a Function of Opponents’ Primary Voting Behavior 831 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:04, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000515

Jonathan Woon candidate's best position is the one that maximizes the point and the median voter,G(c)will be the symmetric same expected utility function EU(cR)mentioned pre- triangular distribution in the middle-right of Figure 2. viously in Figure 1. Note that while the mean of this distribution is the In a two-stage election,it is not the original distribu- same as the original distribution F(ci),it has lower vari- tion of candidates F(ci)that matters,but beliefs about ance.13 Primary elections may therefore also have the which candidate will emerge from the primary election. effect of reinforcing ideological purity (i.e.,increasing Let G(ci)denote this latter set of beliefs about the can- homogeneity)within parties even when there is no dis- didate selected by the opposing party's primary-the cernible effect on average candidate positions (i.e.,ab- candidate that i expects to face in the general election. sent changes in polarization). We can think of the primary election as a selection In contrast to standard equilibrium analysis.which mechanism or filtering process that affects whether a predicts full convergence,a simple model with out- party's candidate is systematically more or less extreme of-equilibrium beliefs generates divergence in candi- than the party's initial set of candidates. date positions,even in the absence of primaries and More precisely,suppose that both of the opposing with complete information about preferences.More- party's candidates are independently drawn from F(c). over,the effect of primaries varies with candidates'ex- Now consider how primary voting behavior affects pectations about the opposing party's voting behavior G(c)and,in turn,candidates'positions.If i's primary Primaries can indeed cause greater polarization (but voters unconditionally select the more extreme candi- only if primary voters select sufficiently extreme can- date(as they would if they voted sincerely),then party didates),cause greater moderation (if primary voters i's candidate in the general election will be the more ex- select moderates),or cause increased intraparty ho- treme of two independent draws from F(ci).This results mogeneity (if voters select on the basis of intermedi in a distribution G(ci)that is skewed more toward i's ate belief-induced ideal points).Thus,the behavioral own ideal point than F(ci),as shown by the triangular theory identifies how the effect of primaries depends distribution in the upper-right of Figure 2 when F(ci) on the connection between beliefs and behavior rather 4号元 is uniform.When voters choose extremists,primaries than on preferences alone. generate incentives for greater extremism than in one- stage elections,as illustrated by the upper-dashed ex- Prediction 3.If candidates have out-of-equilibrium be- pected utility function EU(cR)in Figure 1. liefs about the distribution of opposing candidates,then The flip-side of this is that if i's primary voters select (a)candidate positions will diverge from the median the more moderate candidate (as they would in equi- voter's ideal point in both one-stage and two-stage elec- librium),they generate incentives for greater modera- tions,(b)the direction of the effect of primary elec- tion than in one-stage elections.This is because party tions on candidate polarization depends on expectations i's general election candidate will be the more mod- about voting behavior,and (c)polarization in two-stage erate of two independent draws from F(ci),resulting elections is increasing in the expected extremity of can- in a distribution of beliefs G(ci)that is skewed more didates selected by the opposing party's primary voters. toward the median voter than F(ci).This is shown in Figure 2 by the triangular distribution in the bottom right.2 When the probability of facing an extremist op- EXPERIMENTAL ANALYSIS ponent is lower,a candidate must moderate their posi- The theoretical analysis generated a set of competing tion in response,which is shown by the lower-dashed predictions about the effect of primaries as a function expected utility function EU(cR)in Figure 1. of alternative behavioral assumptions.If all players are These are not the only possibilities,as primary voters fully strategic,then we should observe full convergence might also behave in other ways.For example,a fairly to the median voter's position and primaries should sophisticated voter might reason in the same way as a have no effect (Prediction 1).If candidates are strate- candidate and form the same beliefs G(c;)based on ex- gic but voters are not,then we should observe can- pectations about opposing primary voters.To general- didate divergence only in two-stage elections but not ize this idea,suppose that a voter has a belief-induced in one-stage elections(Prediction 2).If the behavioral ideal point c and always votes for the candidate in theory has merit and candidates have subjective be- the primary whose position is closest to c(sometimes liefs about their opponents'positions,then polariza- this will be the moderate and sometimes the extremist). tion,moderation,or increased homogeneity are possi- The result is a distribution of primary candidates G(ci) ble depending on voter behavior(Prediction 3).Which that has greater mass closer to c than F(c)does.If c set of assumptions is a better reflection of how humans happens to be the midpoint between the voter's ideal behave is ultimately an empirical question,and thus,I 1 If Lparty voters select the extremist,then cL-min (cLi.cL2 and Ge(cL)is first order stochastically dominated by F(cL).If cL and cL2 13 The best response,however.is not exactly the same in the 2S elec- are independently drawn from 0-1,0,then G(cL)has density tion for the symmetric triangular distribution as it is for the uniform selecting the moderate=maand s)first distribution in the 1S election.Nevertheless,there does exist a belief. induced ideal point(via an intermediate value theorem argument order stochastically dominates F(cL).In the example where the uni- which generates an asymmetric distribution)such that candidates form distribution is Ul-1,0],G"(cL)has density g"(cL)=2cL+2 optimal positions diverge from the median voter by the same amount for CL∈[-1,0 (i.e.,the best responses are identical)in both 1S and 2S elections. 832

Jonathan Woon candidate’s best position is the one that maximizes the same expected utility function EU(cR) mentioned pre￾viously in Figure 1. In a two-stage election, it is not the original distribu￾tion of candidates F(cj) that matters, but beliefs about which candidate will emerge from the primary election. Let G(cj) denote this latter set of beliefs about the can￾didate selected by the opposing party’s primary—the candidate that i expects to face in the general election. We can think of the primary election as a selection mechanism or filtering process that affects whether a party’s candidate is systematically more or less extreme than the party’s initial set of candidates. More precisely, suppose that both of the opposing party’s candidates are independently drawn from F(cj). Now consider how primary voting behavior affects G(cj) and, in turn, candidates’ positions. If j’s primary voters unconditionally select the more extreme candi￾date (as they would if they voted sincerely), then party j’s candidate in the general election will be the more ex￾treme of two independent draws from F(cj).This results in a distribution G(cj) that is skewed more toward j’s own ideal point than F(cj), as shown by the triangular distribution in the upper-right of Figure 2 when F(cj) is uniform.11 When voters choose extremists, primaries generate incentives for greater extremism than in one￾stage elections, as illustrated by the upper-dashed ex￾pected utility function EUe (cR) in Figure 1. The flip-side of this is that if j’s primary voters select the more moderate candidate (as they would in equi￾librium), they generate incentives for greater modera￾tion than in one-stage elections. This is because party j’s general election candidate will be the more mod￾erate of two independent draws from F(cj), resulting in a distribution of beliefs G(cj) that is skewed more toward the median voter than F(cj). This is shown in Figure 2 by the triangular distribution in the bottom right.12 When the probability of facing an extremist op￾ponent is lower, a candidate must moderate their posi￾tion in response, which is shown by the lower-dashed expected utility function EUm(cR) in Figure 1. These are not the only possibilities, as primary voters might also behave in other ways. For example, a fairly sophisticated voter might reason in the same way as a candidate and form the same beliefs G(ci) based on ex￾pectations about opposing primary voters. To general￾ize this idea, suppose that a voter has a belief-induced ideal point c∗ j and always votes for the candidate in the primary whose position is closest to c∗ j (sometimes this will be the moderate and sometimes the extremist). The result is a distribution of primary candidates G(cj) that has greater mass closer to c∗ j than F(cj) does. If c∗ j happens to be the midpoint between the voter’s ideal 11 If L party voters select the extremist, then cL = min {cL1, cL2} and Ge(cL) is first order stochastically dominated by F(cL). If cL1 and cL2 are independently drawn from U[ − 1, 0], then Ge(cL) has density ge(cL) = −2cL for cL ∈ [ − 1, 0]. 12 In selecting the moderate, cL = max {cL1, cL2} and so Gm(cL) first order stochastically dominates F(cL). In the example where the uni￾form distribution is U[ − 1, 0], Gm(cL) has density gm(cL) = 2cL + 2 for cL ∈ [ − 1, 0]. point and the median voter,G(cj) will be the symmetric triangular distribution in the middle-right of Figure 2. Note that while the mean of this distribution is the same as the original distribution F(cj), it has lower vari￾ance.13 Primary elections may therefore also have the effect of reinforcing ideological purity (i.e., increasing homogeneity) within parties even when there is no dis￾cernible effect on average candidate positions (i.e., ab￾sent changes in polarization). In contrast to standard equilibrium analysis, which predicts full convergence, a simple model with out￾of-equilibrium beliefs generates divergence in candi￾date positions, even in the absence of primaries and with complete information about preferences. More￾over, the effect of primaries varies with candidates’ ex￾pectations about the opposing party’s voting behavior. Primaries can indeed cause greater polarization (but only if primary voters select sufficiently extreme can￾didates), cause greater moderation (if primary voters select moderates), or cause increased intraparty ho￾mogeneity (if voters select on the basis of intermedi￾ate belief-induced ideal points). Thus, the behavioral theory identifies how the effect of primaries depends on the connection between beliefs and behavior rather than on preferences alone. Prediction 3. If candidates have out-of-equilibrium be￾liefs about the distribution of opposing candidates, then (a) candidate positions will diverge from the median voter’s ideal point in both one-stage and two-stage elec￾tions, (b) the direction of the effect of primary elec￾tions on candidate polarization depends on expectations about voting behavior, and (c) polarization in two-stage elections is increasing in the expected extremity of can￾didates selected by the opposing party’s primary voters. EXPERIMENTAL ANALYSIS The theoretical analysis generated a set of competing predictions about the effect of primaries as a function of alternative behavioral assumptions. If all players are fully strategic, then we should observe full convergence to the median voter’s position and primaries should have no effect (Prediction 1). If candidates are strate￾gic but voters are not, then we should observe can￾didate divergence only in two-stage elections but not in one-stage elections (Prediction 2). If the behavioral theory has merit and candidates have subjective be￾liefs about their opponents’ positions, then polariza￾tion, moderation, or increased homogeneity are possi￾ble depending on voter behavior (Prediction 3).Which set of assumptions is a better reflection of how humans behave is ultimately an empirical question, and thus, I 13 The best response, however, is not exactly the same in the 2S elec￾tion for the symmetric triangular distribution as it is for the uniform distribution in the 1S election. Nevertheless, there does exist a belief￾induced ideal point (via an intermediate value theorem argument, which generates an asymmetric distribution) such that candidates’ optimal positions diverge from the median voter by the same amount (i.e., the best responses are identical) in both 1S and 2S elections. 832 Downloaded from https://www.cambridge.org/core. 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Primaries and Candidate Polarization turn to the lab to distinguish between the competing were denominated in "points"and converted to cash theories.14 by dividing by 10 and rounding to the nearest quarter. -00081140 Given this conversion rate,the range of possible mone- Procedures tary payoffs for each election was between $0 and $20. The final payment was determined by randomly select- The experiment was conducted at the Pittsburgh Ex- ing one election to count from the entire session and perimental Economics Laboratory and involved a to- then adding the show-up fee. tal of 182 participants drawn primarily from the uni- At the beginning of each election period,subjects versity's undergraduate population.Each session in- first learned the position of every player's ideal point. volved 14 participants,and each subject participated Every subject then chose a policy position (referred in one session of either the 1S election treatment (six to as their "campaign promise"),and they were in- sessions)or the 2S election treatment(seven sessions) formed that if their campaign promise was selected At the beginning of each session,following standard as the winning position,it would affect every other laboratory procedures,subjects gave informed consent, subject's payoff.After subjects chose their campaign the instructions were read out loud to induce public promise,the computer then randomly selected candi- knowledge,and subjects answered a set of questions dates from each group:one candidate from each group about the rules on their computers to ensure compre- in the 1S election and two candidates from each group 4 hension.15 The interface was computerized and pro- in the 2S election,with each group member equally like grammed using the software z-Tree (Fischbacher 2007) to be selected and the selection of candidates indepen- Each session took about an hour and a half to complete, dent across election periods.The rest of the subjects and subjects earned an average of $21.05(including a were assigned to the role of a voter in that election $7 show-up fee). Thus,at the beginning of each election,every subject Subjects participated in a total of 40 elections,and was a potential candidate and did not know whether the instructions emphasized that each election was to he or she was a candidate until after submitting a cam- 4号 be treated as a"separate decision task."For each elec- paign promise.19 tion,subjects were divided into two groups of seven Once the candidates were selected,the game pro- 'asn participants,and every member of a group had the ceeded to the voting stages.In the 2S election,voters same payoff function and ideal point.6 Throughout the first chose between one of their group's two candidates experiment,the policy space was the set of integers by majority rule.Each primary(first stage)vote is held from 1 to 200.and payoffs were given by the linear loss simultaneously,and neither party knew the positions function 200-w6:.17 The parties'ideal points were of the other group's candidates while voting.Absten- located symmetrically from the median voter's ideal tions were not allowed.After each group selected its point em such that 0L=0M-d,0R =0M d,and nominee,a second round of voting took place to choose d (50,75).The numerical value of eM varied from the winning policy from the two groups'nominees.All election to election,while the exact sequence of values voters participated in this second round,which was ef- was identical across sessions and treatments.18 Payoffs fectively the "general election."20 In contrast to the 2S election treatment,the 1S election treatment fea- tured only one round of voting in which every voter 14 See Woon(2012b)for an extended discussion of why laboratory participated. experiments are well-suited for behavioral inference in the context The median voter in the general election in both the is See the Supplementary Material for the full text of the experi- IS and 2S election treatments was a computer voter mental instructions.Comprehension of the instructions was high.The who had a distinct ideal point and,as the instructions percentage of correct responses for individual questions ranged from explained to subjects,similar to Morton (1993),was 81%to 94%,and 69%answered all four questions correctly while "like a robot programmed to always vote for the candi- only 8%missed more than one question. These figures likely un date whose campaign promise gives it the higher payoff derestimate the overall degree of comprehension since subjects read of the otwers before playing thegame value."In the case of ties,the computer voted for each We can think of each group as a party,although I was careful to candidate with equal probability.The subjects were in- avoid using the term "party"when describing the game to subjects formed of the computer voter's ideal point before ev- Groups were randomly reassigned between rounds in two sessions of ery election each treatment,while the remaining sessions involved fixed groups The 40 elections within each session were divided The method of group assignment did not qualitatively affect the re- sults,so I ignore the distinction and pool the data in the analysis. into two parts,where each part varied the type of 17 Note that with a linear loss function(in contrast to quadratic loss) every possible policy outcome between the parties'ideal points gen- erates an equal amount of total social welfare,making it unlikely that and between 76 and 125 when d=75.I varied the numerical values risk neutral,altruistic subjects will want to choose the midpoint be. to encourage subjects to pay attention and think about their relative tween parties to maximize the total social monetary payoffs of both rather than absolute,positions. groups.However,to the extent that subjects'preferences for money 1This method of role assignment is similar in spirit to the strategy exhibit risk aversion(and they expect this of other subjects),tota method and maximized the number of observed positions in the ex- social welfare will be maximized at the midpoint between parties periment given that one of the primary goals of the experiment is to which would bias the results toward median convergence.Similarly. measure and test candidate positioning behavior. inequity aversion would also bias choices toward convergence to the 20 To avoid priming subjects'political attitudes regarding primaries,I Todetermine the sequence of values.I randomly selected the m avoid referring to the two rounds of voting as a"primary"and"gen eral"election but instead refer to them as the "first voting stage"and dian's position,M,from the integers between 51 and 150 for d=50 the "second voting stage." 833

Primaries and Candidate Polarization turn to the lab to distinguish between the competing theories.14 Procedures The experiment was conducted at the Pittsburgh Ex￾perimental Economics Laboratory and involved a to￾tal of 182 participants drawn primarily from the uni￾versity’s undergraduate population. Each session in￾volved 14 participants, and each subject participated in one session of either the 1S election treatment (six sessions) or the 2S election treatment (seven sessions). At the beginning of each session, following standard laboratory procedures, subjects gave informed consent, the instructions were read out loud to induce public knowledge, and subjects answered a set of questions about the rules on their computers to ensure compre￾hension.15 The interface was computerized and pro￾grammed using the software z-Tree (Fischbacher 2007). Each session took about an hour and a half to complete, and subjects earned an average of $21.05 (including a $7 show-up fee). Subjects participated in a total of 40 elections, and the instructions emphasized that each election was to be treated as a “separate decision task.” For each elec￾tion, subjects were divided into two groups of seven participants, and every member of a group had the same payoff function and ideal point.16 Throughout the experiment, the policy space was the set of integers from 1 to 200, and payoffs were given by the linear loss function 200 − |w − θi|.17 The parties’ ideal points were located symmetrically from the median voter’s ideal point θM such that θL = θM − d, θR = θM + d, and d ∈ {50, 75}. The numerical value of θM varied from election to election, while the exact sequence of values was identical across sessions and treatments.18 Payoffs 14 See Woon (2012b) for an extended discussion of why laboratory experiments are well-suited for behavioral inference in the context of formal models. 15 See the Supplementary Material for the full text of the experi￾mental instructions. Comprehension of the instructions was high.The percentage of correct responses for individual questions ranged from 81% to 94%, and 69% answered all four questions correctly while only 8% missed more than one question. These figures likely un￾derestimate the overall degree of comprehension since subjects read explanations of the correct answers before playing the game. 16 We can think of each group as a party, although I was careful to avoid using the term “party” when describing the game to subjects. Groups were randomly reassigned between rounds in two sessions of each treatment, while the remaining sessions involved fixed groups. The method of group assignment did not qualitatively affect the re￾sults, so I ignore the distinction and pool the data in the analysis. 17 Note that with a linear loss function (in contrast to quadratic loss), every possible policy outcome between the parties’ ideal points gen￾erates an equal amount of total social welfare,making it unlikely that risk neutral, altruistic subjects will want to choose the midpoint be￾tween parties to maximize the total social monetary payoffs of both groups. However, to the extent that subjects’ preferences for money exhibit risk aversion (and they expect this of other subjects), total social welfare will be maximized at the midpoint between parties, which would bias the results toward median convergence. Similarly, inequity aversion would also bias choices toward convergence to the median. 18 To determine the sequence of values, I randomly selected the me￾dian’s position, θM, from the integers between 51 and 150 for d = 50 were denominated in “points” and converted to cash by dividing by 10 and rounding to the nearest quarter. Given this conversion rate, the range of possible mone￾tary payoffs for each election was between $0 and $20. The final payment was determined by randomly select￾ing one election to count from the entire session and then adding the show-up fee. At the beginning of each election period, subjects first learned the position of every player’s ideal point. Every subject then chose a policy position (referred to as their “campaign promise”), and they were in￾formed that if their campaign promise was selected as the winning position, it would affect every other subject’s payoff. After subjects chose their campaign promise, the computer then randomly selected candi￾dates from each group: one candidate from each group in the 1S election and two candidates from each group in the 2S election, with each group member equally like to be selected and the selection of candidates indepen￾dent across election periods. The rest of the subjects were assigned to the role of a voter in that election. Thus, at the beginning of each election, every subject was a potential candidate and did not know whether he or she was a candidate until after submitting a cam￾paign promise.19 Once the candidates were selected, the game pro￾ceeded to the voting stages. In the 2S election, voters first chose between one of their group’s two candidates by majority rule. Each primary (first stage) vote is held simultaneously, and neither party knew the positions of the other group’s candidates while voting. Absten￾tions were not allowed. After each group selected its nominee, a second round of voting took place to choose the winning policy from the two groups’ nominees. All voters participated in this second round, which was ef￾fectively the “general election.”20 In contrast to the 2S election treatment, the 1S election treatment fea￾tured only one round of voting in which every voter participated. The median voter in the general election in both the 1S and 2S election treatments was a computer voter who had a distinct ideal point and, as the instructions explained to subjects, similar to Morton (1993), was “like a robot programmed to always vote for the candi￾date whose campaign promise gives it the higher payoff value.” In the case of ties, the computer voted for each candidate with equal probability. The subjects were in￾formed of the computer voter’s ideal point before ev￾ery election. The 40 elections within each session were divided into two parts, where each part varied the type of and between 76 and 125 when d = 75. I varied the numerical values to encourage subjects to pay attention and think about their relative, rather than absolute, positions. 19 This method of role assignment is similar in spirit to the strategy method and maximized the number of observed positions in the ex￾periment given that one of the primary goals of the experiment is to measure and test candidate positioning behavior. 20 To avoid priming subjects’ political attitudes regarding primaries, I avoid referring to the two rounds of voting as a “primary” and “gen￾eral” election but instead refer to them as the “first voting stage” and the “second voting stage.” 833 Downloaded from https://www.cambridge.org/core. 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Jonathan Woon feedback subiects received.Part 1 consisted of ten elec- Second,while the general election candidate closer tions without any feedback.21 Part 2 consisted of 30 to the median voter's position generally wins,it is rare elections with feedback provided to subjects after each for the winning candidate to be located exactly at election.The information subjects received included the predicted equilibrium position.Even in session 4 the positions of the subjects who were selected as can- (1S),in which the electoral outcome appears most fre- didates,the number of votes for each candidate,the quently near the median voter's position,the winning winning position,and the payoff from the final out- candidate is located at the median's position in only come.Within each part,I varied the distance between three elections (in another eight elections,the winning the groups'ideal points by dividing each set of elec- candidate is +1 from the median voter's position).In tions into two halves.In the first half,the left and right session ten,the winning candidate usually appears to groups'ideal points were 100 units apart(d=50),while be just barely closer to the median voter than the losing in the second half,they were 150 units apart(d =75). candidate. Note that both of these within-subjects manipulations Third,primary voters are inconsistent in selecting ei- varied ancillary assumptions (feedback and distance ther extreme or moderate candidates.Notably,there between ideal points)and therefore serve as robust- are several candidates in two-stage elections who lo- ness checks.The experimental manipulation of theo- cate at exactly the median voter's position yet lose the retical interest is the between-subjects manipulation of primary.In session one,there were 12 out of 14 such the electoral institution. candidates,and in session six,there were six out of ten.While this could suggest that primary voters prefer Electoral Dynamics extremists,there are also many elections in which the more moderate candidate wins.For example,in elec- To get a sense of the kinds of promises candidates make tion 11 of session six,the left party candidate at-30 and whether moderates or extremists win elections defeated the candidate at-45,and the right party can- Figure 3 presents the sequence of candidate positions didate at 20 defeated the candidate located at 50.with and outcomes for selected sessions (two 1S sessions the right party candidate (who is closer to the median and two 2S sessions).The horizontal axis indicates the voter)winning the general election.Indeed,Figure 3 election,and the vertical axis indicates the promises of depicts losing candidates in primary elections on either the subjects selected as the candidates.These positions side of the parties'winning candidates (indicated by are adjusted(centered)so that the general election me- the fact that the hollow candidate markers appear both dian voter's position is zero.The vertical lines indicate above and below the solid ones) when the electoral conditions change in terms of feed- These sample dynamics suggest that standard game back and the distance between the parties'ideal points. theoretic analysis poorly predicts candidate positions General election candidates are depicted using solid and voting behavior in the experiment.Whereas equi- shapes(candidates in 1S elections and the primary win- librium predicts complete candidate convergence in ners in 2S elections)while primary candidates who lost both 1S and 2S elections,I find that candidates'po- the first stage election are depicted with hollow shapes. sitions instead diverge.The considerable heterogene- The winning position of the general election is shown ity in candidate positions and the selection of extreme by the solid line.Although the dynamics of each session candidates by primary voters indicate that behavioral differ,these plots reveal several noteworthy patterns. game theory and nonequilibrium analysis may be use- First,the positions of candidates from the two par- ful tools for understanding the consequences of elec- ties clearly diverge from the median voter's position toral institutions.Of course,Figure 3 only provides a This is true for both 1S and 2S elections,and it ap- snapshot of experimental behavior.The remainder of pears to persist over the course of the experiment even the analysis demonstrates that many of the patterns de- after subjects gain considerable experience.In session scribed above generalize across subjects and sessions. ten (1S),for example,the candidates from each party choose positions close to their own ideal points,and po- Candidate Positions larization between the candidates'positions increases when the underlying preference polarization increases. Figure 4 shows the average positions over time and by Along with divergence,there also appears to be sub- election format for all candidates (top panel)and for stantial heterogeneity and fluctuation in candidate winning candidates (bottom panel).In the remainder positions.22 of the analysis.I measure the extremity of a candi- date's position (vertical axis)by normalizing positions 21 The fact that the game is sequential means that it would be impos- so that a subject's own ideal point is one and the me- sible to prevent learning across elections if subjects completed each dian voter's ideal point is zero(so the opposing party's election game before proceeding to the next.I solved this problem by implementing a procedure similar in spirit to the strategy method ideal point is-1 on this transformed scale).The top whereby the game was divided into stages and subjects made their panel of Figure 4 shows that candidate positions clearly decisions for all elections in one stage before moving to the next diverge from the median voter's position throughout stage.That is,subjects first chose their positions for all ten elections the experiment regardless of the election format.This in Part 1,subjects in the 2S treatment then voted for their party's can- didates in all ten primary elections,and then subjects in both treat. The figures also reveal that candidates and voters sometimes make dates are located to the left of the median voter,with the party R mistakes.For example,in election 1 in session 4,both parties'candi- candidate located at leftmost position in the policy space. 834

Jonathan Woon feedback subjects received. Part 1 consisted of ten elec￾tions without any feedback.21 Part 2 consisted of 30 elections with feedback provided to subjects after each election. The information subjects received included the positions of the subjects who were selected as can￾didates, the number of votes for each candidate, the winning position, and the payoff from the final out￾come. Within each part, I varied the distance between the groups’ ideal points by dividing each set of elec￾tions into two halves. In the first half, the left and right groups’ ideal points were 100 units apart (d = 50), while in the second half, they were 150 units apart (d = 75). Note that both of these within-subjects manipulations varied ancillary assumptions (feedback and distance between ideal points) and therefore serve as robust￾ness checks. The experimental manipulation of theo￾retical interest is the between-subjects manipulation of the electoral institution. Electoral Dynamics To get a sense of the kinds of promises candidates make and whether moderates or extremists win elections, Figure 3 presents the sequence of candidate positions and outcomes for selected sessions (two 1S sessions and two 2S sessions). The horizontal axis indicates the election, and the vertical axis indicates the promises of the subjects selected as the candidates. These positions are adjusted (centered) so that the general election me￾dian voter’s position is zero. The vertical lines indicate when the electoral conditions change in terms of feed￾back and the distance between the parties’ ideal points. General election candidates are depicted using solid shapes (candidates in 1S elections and the primary win￾ners in 2S elections) while primary candidates who lost the first stage election are depicted with hollow shapes. The winning position of the general election is shown by the solid line.Although the dynamics of each session differ, these plots reveal several noteworthy patterns. First, the positions of candidates from the two par￾ties clearly diverge from the median voter’s position. This is true for both 1S and 2S elections, and it ap￾pears to persist over the course of the experiment even after subjects gain considerable experience. In session ten (1S), for example, the candidates from each party choose positions close to their own ideal points, and po￾larization between the candidates’ positions increases when the underlying preference polarization increases. Along with divergence, there also appears to be sub￾stantial heterogeneity and fluctuation in candidate positions.22 21 The fact that the game is sequential means that it would be impos￾sible to prevent learning across elections if subjects completed each election game before proceeding to the next. I solved this problem by implementing a procedure similar in spirit to the strategy method whereby the game was divided into stages and subjects made their decisions for all elections in one stage before moving to the next stage. That is, subjects first chose their positions for all ten elections in Part 1, subjects in the 2S treatment then voted for their party’s can￾didates in all ten primary elections, and then subjects in both treat￾ments voted in all ten general elections. 22 The figures also reveal that candidates and voters sometimes make mistakes. For example, in election 1 in session 4, both parties’ candi￾Second, while the general election candidate closer to the median voter’s position generally wins, it is rare for the winning candidate to be located exactly at the predicted equilibrium position. Even in session 4 (1S), in which the electoral outcome appears most fre￾quently near the median voter’s position, the winning candidate is located at the median’s position in only three elections (in another eight elections, the winning candidate is ±1 from the median voter’s position). In session ten, the winning candidate usually appears to be just barely closer to the median voter than the losing candidate. Third, primary voters are inconsistent in selecting ei￾ther extreme or moderate candidates. Notably, there are several candidates in two-stage elections who lo￾cate at exactly the median voter’s position yet lose the primary. In session one, there were 12 out of 14 such candidates, and in session six, there were six out of ten.While this could suggest that primary voters prefer extremists, there are also many elections in which the more moderate candidate wins. For example, in elec￾tion 11 of session six, the left party candidate at −30 defeated the candidate at −45, and the right party can￾didate at 20 defeated the candidate located at 50, with the right party candidate (who is closer to the median voter) winning the general election. Indeed, Figure 3 depicts losing candidates in primary elections on either side of the parties’ winning candidates (indicated by the fact that the hollow candidate markers appear both above and below the solid ones). These sample dynamics suggest that standard game theoretic analysis poorly predicts candidate positions and voting behavior in the experiment. Whereas equi￾librium predicts complete candidate convergence in both 1S and 2S elections, I find that candidates’ po￾sitions instead diverge. The considerable heterogene￾ity in candidate positions and the selection of extreme candidates by primary voters indicate that behavioral game theory and nonequilibrium analysis may be use￾ful tools for understanding the consequences of elec￾toral institutions. Of course, Figure 3 only provides a snapshot of experimental behavior. The remainder of the analysis demonstrates that many of the patterns de￾scribed above generalize across subjects and sessions. Candidate Positions Figure 4 shows the average positions over time and by election format for all candidates (top panel) and for winning candidates (bottom panel). In the remainder of the analysis, I measure the extremity of a candi￾date’s position (vertical axis) by normalizing positions so that a subject’s own ideal point is one and the me￾dian voter’s ideal point is zero (so the opposing party’s ideal point is −1 on this transformed scale). The top panel of Figure 4 shows that candidate positions clearly diverge from the median voter’s position throughout the experiment regardless of the election format. This dates are located to the left of the median voter, with the party R candidate located at leftmost position in the policy space. 834 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:04, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000515

FIGURE 3.Sample Session Dynamics One Stage-Session 4 One Stage-Session 10 8· 10 20 30 40 20 30 40 Election Election ●Left Right Winner Let▲Right Winner Two Stage-Session 1 Two Stage-Session 6 8 Primaries 00· 0 0 20 30 0 20 30 40 目lection Election ●LWin o LLose▲R Win R Lose -Winner ●LWin o LLose▲R Win RLose Winner and Candidate Polarization

Primaries and Candidate Polarization FIGURE 3. Sample Session Dynamics -100 -50 0 50 100 Position 0 10 20 30 40 Election Left Right Winner One Stage - Session 4 -100 -50 0 50 100 Position 0 10 20 30 40 Election Left Right Winner One Stage - Session 10 -100 -50 0 50 100 Position 0 10 20 30 40 Election L Win L Lose R Win R Lose Winner Two Stage - Session 1 -100 -50 0 50 100 Position 0 10 20 30 40 Election L Win L Lose R Win R Lose Winner Two Stage - Session 6 835 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:04, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000515