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

American Political Science Review (2018)112,4,809-825 doi:10.1017/S0003055418000503 American Political Science Association 2018 Political Competition in Legislative Elections STEFAN KRASA University of Illinois MATTIAS K.POLBORN Vanderbilt University re develop a theory of electoral competition in multidistrict legislative elections when nomina- tion decisions are made by local policy-motivated party members,and voters care about both local and national positions.We show that the asymmetry generated by different national party positions reduces or even entirely removes the competitive pressure to nominate moderate candidates The model has important implications for our understanding of policy divergence and,in particular,of the effects of gerrymandering. INTRODUCTION a position to determine the unilaterally decisive policy maker in the nation,but rather just one of many repre- n the basic model of representative democracy,vot- sentatives who interacts with other representatives in ers elect legislative representatives whose positions the determination of policy. reflect the preferences of their respective districts Our model is based on two realistic ingredients: median voters.These representatives convene in an First,the majority party in a legislature is an impor- amorphous assembly-one in which parties do not play tant power center influencing the crafting of policy,and an important role-and national policy is set to cor- so voters naturally care not only about the positions respond to the preferences of the median representa- espoused by their local candidates,but also about the tive in this assembly.Thus,the legislature is composed national positions of the parties with whom these lo- of representatives who are more moderate than the 4号元 cal candidates are affiliated.A potential microfounda- voters who elect them,and actual policy and legisla- tion for why voters care about national party positions tion reflects the most moderate position in this assem- is that no legislator is a specialist in all policy areas, bly of moderates(a prediction that appears somewhat and therefore they all have to rely sometimes on the incorrect). expertise of their fellow party members (Shepsle and There is,of course,a large body of literature model- Weingast 1987;Gilligan and Krehbiel 1989).The impor- ing interactions of representatives in a legislature and tance of the majority party for law-making creates im- the effects of legislative institutions such as the power portant spillover effects between the candidates of the of specialized committees,but this literature takes the same party who run in different districts.Second,leg- set of legislators as given.There is also a large litera islative candidates are nominated by policy-motivated ture on political competition,but that literature gener- 是 primary voters who,like the general election median ally assumes that candidates either unilaterally choose voter,care about both national party and local candi- or are exogenously endowed with policy positions that date positions,but have more extreme ideal positions. enter voters'utility functions directly and exclusively. A central question in our analysis is how national party That is,voters care only about the positions of those positions affect the competitive pressure to nominate candidates that they personally can decide between.In moderate candidates,which plays a central role both this paper,we build a model of electoral competition in the classical Downsian model,and in the policy- that combines these two strands of literature:When motivated candidates model. voting for their local representative,the voters in our model explicitly take into account that they are not in While parties play a crucial role in the legislature for shaping politics and policy,there is surprisingly lit- tle analysis of how the fact that each candidate is con- Stefan Krasa is a Professor,Department of Economics,University of nected to a party and thus,implicitly,to the positions of Illinois,1407 W.Gregory Dr.,Urbana,IL 61801(skrasa@uiuc.edu). Mattias K.Polborn is a Professor.Department of Economics and candidates of that party from other districts influences Department of Political Science,Vanderbilt University,Nashville nomination decisions,as well as election outcomes in TN,37235(mattias.polborn@vanderbilt.edu). different legislative districts. We are very grateful for the comments of three referees and the Applying the simplest Downsian model naively to editor that helped us to improve the paper.Both authors gratefully Congressional elections-which much of the empirical acknowledge financial support from National Science Foundation Grant SES-1261016.Any opinions,findings,and conclusions or rec- literature implicitly does-generates empirically incor- ommendations expressed in this paper are those of the authors and rect predictions:Since,in the Downsian model,all can- do not necessarily reflect the views of the National Science Founda- didates adopt the preferred position of their district's tion or any other organization.We are thankful for helpful comments median voter,all voters should be policywise indiffer- by seminar participants at USC,Caltech,NYU.MPI Munich.ITAM ent between the Democratic candidate and his Repub- Toulouse,Illinois.Princeton.Western Illinois,lowa.Michigan,Notre Dame,UC Irvine,Illinois State,Mannheim,ETH Zurich,Brigham lican opponent.Thus,Republicans in New England or Young,New Economic School,Higher School of Economics,Yale, Democrats in rural Western districts should have a sub- Southern Methodist and Vanderbilt,as well as Odilon Camara. stantial chance to be elected to Congress if only they Tiberiu Dragu,Bernie Grofman,Matthias Messner,and Arturas match their opponent's policy platform.Furthermore, Rozenas.Replication files are available on the American Political Science Review Dataverse:https://doi.org/10.7910/DVN/SNW8PV. Received:August 1,2017;revised:April 3,2018;accepted:July 11. See Table 1 in Winer,Kenny,and Grofman(2014)for evidence 2018.First published online:August 22,2018. that a significant share of U.S.Senate elections are noncompetitive. 809

American Political Science Review (2018) 112, 4, 809–825 doi:10.1017/S0003055418000503 © American Political Science Association 2018 Political Competition in Legislative Elections STEFAN KRASA University of Illinois MATTIAS K. POLBORN Vanderbilt University We develop a theory of electoral competition in multidistrict legislative elections when nomina￾tion decisions are made by local policy-motivated party members, and voters care about both local and national positions. We show that the asymmetry generated by different national party positions reduces or even entirely removes the competitive pressure to nominate moderate candidates. The model has important implications for our understanding of policy divergence and, in particular, of the effects of gerrymandering. INTRODUCTION I n the basic model of representative democracy, vot￾ers elect legislative representatives whose positions reflect the preferences of their respective districts’ median voters. These representatives convene in an amorphous assembly—one in which parties do not play an important role—and national policy is set to cor￾respond to the preferences of the median representa￾tive in this assembly. Thus, the legislature is composed of representatives who are more moderate than the voters who elect them, and actual policy and legisla￾tion reflects the most moderate position in this assem￾bly of moderates (a prediction that appears somewhat incorrect). There is, of course, a large body of literature model￾ing interactions of representatives in a legislature and the effects of legislative institutions such as the power of specialized committees, but this literature takes the set of legislators as given. There is also a large litera￾ture on political competition, but that literature gener￾ally assumes that candidates either unilaterally choose or are exogenously endowed with policy positions that enter voters’ utility functions directly and exclusively. That is, voters care only about the positions of those candidates that they personally can decide between. In this paper, we build a model of electoral competition that combines these two strands of literature: When voting for their local representative, the voters in our model explicitly take into account that they are not in Stefan Krasa is a Professor, Department of Economics, University of Illinois, 1407 W. Gregory Dr., Urbana, IL 61801 (skrasa@uiuc.edu). Mattias K. Polborn is a Professor, Department of Economics and Department of Political Science, Vanderbilt University, Nashville, TN, 37235 (mattias.polborn@vanderbilt.edu). We are very grateful for the comments of three referees and the editor that helped us to improve the paper. Both authors gratefully acknowledge financial support from National Science Foundation Grant SES-1261016. Any opinions, findings, and conclusions or rec￾ommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Founda￾tion or any other organization.We are thankful for helpful comments by seminar participants at USC, Caltech, NYU, MPI Munich, ITAM, Toulouse, Illinois, Princeton, Western Illinois, Iowa, Michigan, Notre Dame, UC Irvine, Illinois State, Mannheim, ETH Zurich, Brigham Young, New Economic School, Higher School of Economics, Yale, Southern Methodist and Vanderbilt, as well as Odilon Camara, Tiberiu Dragu, Bernie Grofman, Matthias Messner, and Arturas Rozenas. Replication files are available on the American Political Science Review Dataverse: https://doi.org/10.7910/DVN/SNW8PV. Received: August 1, 2017; revised: April 3, 2018; accepted: July 11, 2018. First published online: August 22, 2018. a position to determine the unilaterally decisive policy maker in the nation, but rather just one of many repre￾sentatives who interacts with other representatives in the determination of policy. Our model is based on two realistic ingredients: First, the majority party in a legislature is an impor￾tant power center influencing the crafting of policy, and so voters naturally care not only about the positions espoused by their local candidates, but also about the national positions of the parties with whom these lo￾cal candidates are affiliated. A potential microfounda￾tion for why voters care about national party positions is that no legislator is a specialist in all policy areas, and therefore they all have to rely sometimes on the expertise of their fellow party members (Shepsle and Weingast 1987;Gilligan and Krehbiel 1989).The impor￾tance of the majority party for law-making creates im￾portant spillover effects between the candidates of the same party who run in different districts. Second, leg￾islative candidates are nominated by policy-motivated primary voters who, like the general election median voter, care about both national party and local candi￾date positions, but have more extreme ideal positions. A central question in our analysis is how national party positions affect the competitive pressure to nominate moderate candidates, which plays a central role both in the classical Downsian model, and in the policy￾motivated candidates model. While parties play a crucial role in the legislature for shaping politics and policy, there is surprisingly lit￾tle analysis of how the fact that each candidate is con￾nected to a party and thus, implicitly, to the positions of candidates of that party from other districts influences nomination decisions, as well as election outcomes in different legislative districts. Applying the simplest Downsian model naively to Congressional elections—which much of the empirical literature implicitly does—generates empirically incor￾rect predictions: Since, in the Downsian model, all can￾didates adopt the preferred position of their district’s median voter, all voters should be policywise indiffer￾ent between the Democratic candidate and his Repub￾lican opponent. Thus, Republicans in New England or Democrats in rural Western districts should have a sub￾stantial chance to be elected to Congress if only they match their opponent’s policy platform.1 Furthermore, 1 See Table 1 in Winer, Kenny, and Grofman (2014) for evidence that a significant share of U.S. Senate elections are noncompetitive. 809 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000503

Stefan Krasa and Mattias K.Polborn in this framework,gerrymandering districts affects only lican candidate as a 'supporter'of the 'Bush agenda'or candidate positions in the gerrymandered districts but as a 'rubberstamp,'Democrats believe the President's does not help a party to increase their expected rep- low approval ratings are a stone they can use to sink resentation in Congress.These predictions are cer- their opponents [...Democratic Sen.Hillary Clinton tainly empirically incorrect,but understanding why is of New York got the most mentions in Republican ads challenging. holding forth the supposed horrors of a Democratic- In our model,voters'utility depends on both their controlled Senate [...The runner-up is'San Francisco local representative's position,and the position of the Liberal Nancy Pelosi,'who is mentioned in at least 6 majority party.In the general election,voters take into GOP ads as a reason not to vote for a Democrat who account the two local candidates'positions,as well as would in turn vote to make her Speaker of the House."5 the chance that the election outcome in their district In contrast to the classical one-district spatial model, may change which party is the majority party in the the ideological composition of districts in our model legislature. does not only influence the ideological position of The latter effect implies that,in most districts,the elected candidates,but also the chances of parties to median voter cares not just about the local candidates' win,thus increasing partisan incentives for gerryman- positions when deciding whom to vote for,but also dering.Gerrymandering or,more generally,the intensi- about their party labels,as they are associated with fication of the median ideological preferences in some different national positions.The favored party's pri- districts,affects the political equilibrium even in those mary voter can exploit this situation by nominating a districts where the median voter preferences remain 元 more extreme candidate than the general election me- the same as before.Our results imply that testing for dian voter would prefer.In particular,if voters care the causal effect of gerrymandering on polarization in sufficiently strongly about national positions relative Congress is more complicated than the existing litera- to local candidate positions,then the favored party's ture has recognized. primary voter can simply nominate his own preferred 4 candidate and still win,generally even with a strict su- permajority of votes. RELATED LITERATURE The local general election loses some of its disci- Ever since Downs's(1957)seminal work,candidates' plining force because the voters'national preference position choice is a central topic in political economy factors in their vote choice.The electoral prospects While the classical median voter framework identi- of candidates in a given district are influenced by the fies reasons for platform convergence,many subse- expected ideological position of their parties'winning quent electoral competition models develop different candidates elsewhere.The association with a party that reasons for policy divergence,including policy moti- is not attuned with a district's ideological leanings may vation (Wittman 1983:Calvert 1985:Londregan and be poisonous for a candidate,even if his own policy po- Romer 1993:Osborne and Slivinski 1996:Besley and 是 sitions are tailor-made for his district. Coate 1997:Martinelli 2001:Gul and Pesendorfer Consider,for example,Lincoln Chafee,the former 2009);entry deterrence (Palfrey 1984;Callander 2005); Republican U.S.senator from Rhode Island,who had agency problems(Van Weelden 2013);incomplete in- taken a number of moderate and liberal positions that formation among voters or candidates (Castanheira 5.501g brought him in line with voters in his state.2 As the New 2003;Bernhardt,Duggan,and Squintani 2007;Callan- York Times reported,in the 2006 election,"exit polls der 2008):and differential candidate valence (Bern- gave Senator Lincoln Chafee a 62 percent approval hardt and Ingberman 1985;Groseclose 2001;Krasa and rating.But before they exited the polls,most voters re- Polborn 2010b,2012:Bierbrauer and Bover 2013). jected him,many feeling it was more important to give Most of the literature looks at isolated one-district the Democrats a chance at controlling the Senate."3 elections.Exceptions are Austen-Smith(1984);Snyder His Democratic challenger Whitehouse "succeeded (1994);Ansolabehere,Leblanc,and Snyder(2012)and by attacking the instances in which Chafee supported subsequent work by Polborn and Snyder (2017).In his party's conservative congressional leadership Austen-Smith(1984),the party that wins the majority (whose personalities and policies were very unpopular, of n districts implements an aggregate of its candidates' state-wide).'4 positions.Each district candidate chooses his position In a review of 2006 campaign ads,factcheck.org sum- to maximize his chance of winning.If an equilibrium marized:"President Bush was far and away the most exists,then both party positions fully converge to the frequent supporting actor in Democratic ads [...The median voter in the median district,even though indi- strategy is clear:whether they're referring to a Repub- vidual candidates'positions differ.In contrast,in our model,positions are chosen by policy-motivated pri- In 29.4%of U.S.Senate elections between 1922 and 2004 without an mary voters,and voters care about both national party incumbent running,the winner received a vote share that was at least positions and local candidates.In our equilibrium,na- 20 percentage points larger than the loser's vote share. tional party positions diverge,and we can analyze the 2 For example,Chafee was pro-choice,anti-death-penalty,supported effects of gerrymandering and of more or less radical gay marriage,and voted against the Irag war (see http://en.wikipedia primary voters. org/wiki/Lincoln_Chafee). 3"A GOP Breed loses its place in New England,",New York Times, November 27 2006. See http://en.wikipedia.org/wiki/Lincoln_Chafee See https://www.factcheck.org/2006/11/our-2006-awards. 810

Stefan Krasa and Mattias K. Polborn in this framework, gerrymandering districts affects only candidate positions in the gerrymandered districts but does not help a party to increase their expected rep￾resentation in Congress. These predictions are cer￾tainly empirically incorrect, but understanding why is challenging. In our model, voters’ utility depends on both their local representative’s position, and the position of the majority party. In the general election, voters take into account the two local candidates’ positions, as well as the chance that the election outcome in their district may change which party is the majority party in the legislature. The latter effect implies that, in most districts, the median voter cares not just about the local candidates’ positions when deciding whom to vote for, but also about their party labels, as they are associated with different national positions. The favored party’s pri￾mary voter can exploit this situation by nominating a more extreme candidate than the general election me￾dian voter would prefer. In particular, if voters care sufficiently strongly about national positions relative to local candidate positions, then the favored party’s primary voter can simply nominate his own preferred candidate and still win, generally even with a strict su￾permajority of votes. The local general election loses some of its disci￾plining force because the voters’ national preference factors in their vote choice. The electoral prospects of candidates in a given district are influenced by the expected ideological position of their parties’ winning candidates elsewhere. The association with a party that is not attuned with a district’s ideological leanings may be poisonous for a candidate, even if his own policy po￾sitions are tailor-made for his district. Consider, for example, Lincoln Chafee, the former Republican U.S. senator from Rhode Island, who had taken a number of moderate and liberal positions that brought him in line with voters in his state.2 As the New York Times reported, in the 2006 election, “exit polls gave Senator Lincoln Chafee a 62 percent approval rating. But before they exited the polls, most voters re￾jected him, many feeling it was more important to give the Democrats a chance at controlling the Senate.”3 His Democratic challenger Whitehouse “succeeded by attacking the instances in which Chafee supported his party’s conservative congressional leadership (whose personalities and policies were very unpopular, state-wide).”4 In a review of 2006 campaign ads, factcheck.org sum￾marized: “President Bush was far and away the most frequent supporting actor in Democratic ads [...] The strategy is clear: whether they’re referring to a Repub￾In 29.4% of U.S. Senate elections between 1922 and 2004 without an incumbent running, the winner received a vote share that was at least 20 percentage points larger than the loser’s vote share. 2 For example, Chafee was pro-choice, anti-death-penalty, supported gay marriage, and voted against the Iraq war (see http://en.wikipedia. org/wiki/Lincoln_Chafee). 3 “A GOP Breed loses its place in New England,”, New York Times, November 27, 2006. 4 See http://en.wikipedia.org/wiki/Lincoln_Chafee. lican candidate as a ‘supporter’ of the ‘Bush agenda’ or as a ‘rubberstamp,’ Democrats believe the President’s low approval ratings are a stone they can use to sink their opponents [...] Democratic Sen. Hillary Clinton of New York got the most mentions in Republican ads holding forth the supposed horrors of a Democratic￾controlled Senate [...] The runner-up is ‘San Francisco Liberal Nancy Pelosi,’ who is mentioned in at least 6 GOP ads as a reason not to vote for a Democrat who would in turn vote to make her Speaker of the House.”5 In contrast to the classical one-district spatial model, the ideological composition of districts in our model does not only influence the ideological position of elected candidates, but also the chances of parties to win, thus increasing partisan incentives for gerryman￾dering.Gerrymandering or,more generally, the intensi￾fication of the median ideological preferences in some districts, affects the political equilibrium even in those districts where the median voter preferences remain the same as before. Our results imply that testing for the causal effect of gerrymandering on polarization in Congress is more complicated than the existing litera￾ture has recognized. RELATED LITERATURE Ever since Downs’s (1957) seminal work, candidates’ position choice is a central topic in political economy. While the classical median voter framework identi￾fies reasons for platform convergence, many subse￾quent electoral competition models develop different reasons for policy divergence, including policy moti￾vation (Wittman 1983; Calvert 1985; Londregan and Romer 1993; Osborne and Slivinski 1996; Besley and Coate 1997; Martinelli 2001; Gul and Pesendorfer 2009); entry deterrence (Palfrey 1984; Callander 2005); agency problems (Van Weelden 2013); incomplete in￾formation among voters or candidates (Castanheira 2003; Bernhardt, Duggan, and Squintani 2007; Callan￾der 2008); and differential candidate valence (Bern￾hardt and Ingberman 1985;Groseclose 2001;Krasa and Polborn 2010b, 2012; Bierbrauer and Boyer 2013). Most of the literature looks at isolated one-district elections. Exceptions are Austen-Smith (1984); Snyder (1994); Ansolabehere, Leblanc, and Snyder (2012) and subsequent work by Polborn and Snyder (2017). In Austen-Smith (1984), the party that wins the majority of n districts implements an aggregate of its candidates’ positions. Each district candidate chooses his position to maximize his chance of winning. If an equilibrium exists, then both party positions fully converge to the median voter in the median district, even though indi￾vidual candidates’ positions differ. In contrast, in our model, positions are chosen by policy-motivated pri￾mary voters, and voters care about both national party positions and local candidates. In our equilibrium, na￾tional party positions diverge, and we can analyze the effects of gerrymandering and of more or less radical primary voters. 5 See https://www.factcheck.org/2006/11/our-2006-awards. 810 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000503

Political Competition in Legislative Elections Snyder (1994)considers a dynamic setting in which heira and Crutzen (2010),Eguia (2011a,2011b)and voters care only about national party positions tha Diermeier and Vlaicu(2011)provide theories of en- are chosen by the party's representatives in the pre- dogenous institution choice leading to powerful par- election legislature to maximize their individual reelec- ties.All these models of the importance of parties in tion chances.In Ansolabehere,Leblanc,and Snyder Congress take the distribution of legislator preferences (2012),a special version of this model,the left and the as exogenously given,while our model provides for right party locate at the 25th and 75th percentile of an electoral model and thus endogenizes the types of the district median distribution.Polborn and Snyder elected legislators. (2017)analyze a model of legislative competition in which only the two parties'national positions matter MODEL for voters and are determined by the median caucus member.Their main focus is on deriving comparative A polity is divided into a set of districts /where #is static predictions about the effects of idiosyncratic (i.e. odd.Each district i contains three strategic agents:a lo- candidate-specific)valence uncertainty and systematic cal Democratic leader.a local Republican leader,and 4 electoral shifts (as in wave elections,where one party a general election median voter. does better in most districts than in previous elections) In the first stage,in each district i,the local leader of on polarization,and testing them empirically.To focus each party P=D,R chooses the position xiP ER of 4 on these comparative static predictions,their model of party P's candidate in district i.The local party lead- candidate competition is much simpler than ours,es- ers can be thought of as a shorthand for the decisive sentially assuming that the local candidates perfectly voter in the respective party's primary election that de- represent the median voter in their respective districts. cides which candidate to nominate.We therefore as- In contrast.our focus is on the effect of the nomina- sume that these local party leaders are not interested in tion process in which candidates are chosen by policy- winning per se,but rather,like any other voter,derive motivated primary voters,who,as we show,generally utility from policy(with details explained below). 4号元 select nominees who are more extreme than the gen- In the second stage,there is a general election in all eral election median voter of the district would prefer districts.In addition to their local candidates'positions. In the influential models of Erikson and Romero each party has a national policy Xp that it can imple- (1990)and Adams and Merrill (2003),voters receive, ment if it receives a majority in the legislature.The na- in addition to the payoff from the elected candidate's tional policy position is not a strategic choice by any position,a "partisan"payoff from his party affiliation, particular player,but rather some aggregate of the po- which,however,is exogenous and orthogonal to his sitions of a party's legislators,discussed further below. policy position.Our model provides a microfoundation The utility of a voter with ideal position 0 from for these partisan payoffs,and shows how they depend district i is on the equilibrium polarization between the parties' candidates in other districts.and how they,in turn,af- g(Xp,x.Q)=-(1-y)Xp-9)2-y(c.o-8)2, fect the candidates'equilibrium positions Probabilistic voting models (e.g.,Lindbeck and (1) Weibull 1987;Dixit and Londregan 1995),as well as differentiated candidates models (DCMs;Aragones where y e(0,1)is the voter's weight on the local rep- and Palfrey 2002:Soubeyran 2009:Krasa and Polborn resentative's position,the policy of the district's elected 2010a,2010b,2012,2014;Camara2012),often con- representative is xi.o,where O[D,R]is the represen- 8 sider an exogenous valence dimension.In the spirit tative's party,and the policy of the majority party P in of the DCM,one can interpret party affiliation in our the legislature is Xp. model as a fixed characteristic,but in contrast to exist- If voters only care about the policy implemented by ing DCMs,voters'preferences over characteristics(i.e., the legislature,then the value of y is zero.There are the candidates'party affiliations)depend on national at least two conceptually distinct reasons why y might party positions and therefore,ultimately,on positions be positive.First,voters may attach an expressive value of candidates in other districts. to their actual vote;that is,a voter may derive utility Our model assumes that national party positions from voting for a local candidate whose position he matter for voters,and a significant number of mod- likes (or opposing one that he dislikes)even if he rec- els explains why this is so.Conditional party govern- ognizes that national policy is determined by national ment theory (Rohde 2010;Aldrich 1995)and endoge- party positions.Second,representatives may have spe- nous party government theory (Volden and Bergman cial influence on policy that is particularly relevant for 2006;Patty 2008)argue that party leaders can use in- their district,for example,through funding projects in centives and resources to ensure cohesiveness of their their district whose payoffs depend on ideology.Note party.Procedural cartel theory (Cox and McCubbins that the case where each election is completely inde- 2005)argues that party leadership can at least en- pendent of what happens in the rest of the country(i.e., force voting discipline over procedural issues.Castan- where literally "all politics is local"and nobody cares about national legislation)corresponds to y =1. Halberstam and Montagnes(2015)provide empirical evidence of spillovers from national presidential campaigns on Senate elections 7 In principle,we could also allow for y to vary between districts, and the positions of candidates in those elections. and all of our results would generalize(with y being replaced by yi 811

Political Competition in Legislative Elections Snyder (1994) considers a dynamic setting in which voters care only about national party positions that are chosen by the party’s representatives in the pre￾election legislature to maximize their individual reelec￾tion chances. In Ansolabehere, Leblanc, and Snyder (2012), a special version of this model, the left and the right party locate at the 25th and 75th percentile of the district median distribution. Polborn and Snyder (2017) analyze a model of legislative competition in which only the two parties’ national positions matter for voters and are determined by the median caucus member. Their main focus is on deriving comparative static predictions about the effects of idiosyncratic (i.e., candidate-specific) valence uncertainty and systematic electoral shifts (as in wave elections, where one party does better in most districts than in previous elections) on polarization, and testing them empirically. To focus on these comparative static predictions, their model of candidate competition is much simpler than ours, es￾sentially assuming that the local candidates perfectly represent the median voter in their respective districts. In contrast, our focus is on the effect of the nomina￾tion process in which candidates are chosen by policy￾motivated primary voters, who, as we show, generally select nominees who are more extreme than the gen￾eral election median voter of the district would prefer. In the influential models of Erikson and Romero (1990) and Adams and Merrill (2003), voters receive, in addition to the payoff from the elected candidate’s position, a “partisan” payoff from his party affiliation, which, however, is exogenous and orthogonal to his policy position.Our model provides a microfoundation for these partisan payoffs, and shows how they depend on the equilibrium polarization between the parties’ candidates in other districts, and how they, in turn, af￾fect the candidates’ equilibrium positions. Probabilistic voting models (e.g., Lindbeck and Weibull 1987; Dixit and Londregan 1995), as well as differentiated candidates models (DCMs; Aragones and Palfrey 2002; Soubeyran 2009; Krasa and Polborn 2010a, 2010b, 2012, 2014; Camara 2012), often con￾sider an exogenous valence dimension. In the spirit of the DCM, one can interpret party affiliation in our model as a fixed characteristic, but in contrast to exist￾ing DCMs, voters’ preferences over characteristics (i.e., the candidates’ party affiliations) depend on national party positions and therefore, ultimately, on positions of candidates in other districts. Our model assumes that national party positions matter for voters,6 and a significant number of mod￾els explains why this is so. Conditional party govern￾ment theory (Rohde 2010; Aldrich 1995) and endoge￾nous party government theory (Volden and Bergman 2006; Patty 2008) argue that party leaders can use in￾centives and resources to ensure cohesiveness of their party. Procedural cartel theory (Cox and McCubbins 2005) argues that party leadership can at least en￾force voting discipline over procedural issues. Castan- 6 Halberstam and Montagnes (2015) provide empirical evidence of spillovers from national presidential campaigns on Senate elections and the positions of candidates in those elections. heira and Crutzen (2010), Eguia (2011a, 2011b) and Diermeier and Vlaicu (2011) provide theories of en￾dogenous institution choice leading to powerful par￾ties. All these models of the importance of parties in Congress take the distribution of legislator preferences as exogenously given, while our model provides for an electoral model and thus endogenizes the types of elected legislators. MODEL A polity is divided into a set of districts I, where #I is odd. Each district i contains three strategic agents: a lo￾cal Democratic leader, a local Republican leader, and a general election median voter. In the first stage, in each district i, the local leader of each party P = D, R chooses the position xi,P ∈ R of party P’s candidate in district i. The local party lead￾ers can be thought of as a shorthand for the decisive voter in the respective party’s primary election that de￾cides which candidate to nominate. We therefore as￾sume that these local party leaders are not interested in winning per se, but rather, like any other voter, derive utility from policy (with details explained below). In the second stage, there is a general election in all districts. In addition to their local candidates’ positions, each party has a national policy XP that it can imple￾ment if it receives a majority in the legislature. The na￾tional policy position is not a strategic choice by any particular player, but rather some aggregate of the po￾sitions of a party’s legislators, discussed further below. The utility of a voter with ideal position θ from district i is uθ (XP, xi,Q) = −(1 − γ )(XP − θ ) 2 − γ (xi,Q − θ ) 2 , (1) where γ ∈ (0, 1) is the voter’s weight on the local rep￾resentative’s position, the policy of the district’s elected representative is xi, Q, where Q ∈ {D, R} is the represen￾tative’s party, and the policy of the majority party P in the legislature is XP. If voters only care about the policy implemented by the legislature, then the value of γ is zero. There are at least two conceptually distinct reasons why γ might be positive. First, voters may attach an expressive value to their actual vote; that is, a voter may derive utility from voting for a local candidate whose position he likes (or opposing one that he dislikes) even if he rec￾ognizes that national policy is determined by national party positions. Second, representatives may have spe￾cial influence on policy that is particularly relevant for their district, for example, through funding projects in their district whose payoffs depend on ideology. Note that the case where each election is completely inde￾pendent of what happens in the rest of the country (i.e., where literally “all politics is local” and nobody cares about national legislation) corresponds to γ = 1.7 7 In principle, we could also allow for γ to vary between districts, and all of our results would generalize (with γ being replaced by γ i 811 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000503

Stefan Krasa and Mattias K.Polborn Ex ante,there is uncertainty about the ideal position Let the indifferent voter type for whom Equation(2) 马 of district i's median voter,described by a cdf ()that holds as equality be denoted by is symmetric about ui.Let pi denote the probability that district i is decisive in determining which party has a majority in the legislature(i.e.,pi is the probability 1(1-y)p:(X3-X3)+y(xR-D) that both parties win the same number of representa- 0(xL.D.*R)=(1-Y)p:(XR-Xp)+y(iR-x tives in all other districts ji).Note that pi can either (3) be derived by the equilibrium played in other districts Then Mi prefers to vote for the Democrat if and only or can simply be thought of as reflecting the(not neces- if Mis(xi.D,xi.R).The probability that the Democrat sarily rational)perception of the voters in district i that wins in district i is therefore (xiD,xi.R)). their district is pivotal. For example,if the district cannot be pivotal(pi=0) In summary,the game proceeds as follows: then Equation (3)implies that 0()=(xi.R +x.D)/2 that is,the median voter chooses the candidate whose 1.In each district i.the local Democratic leader with platform is closest to Mi.The probability that the ideal point di selects the Democratic candidate's Democrat wins is thereforeΦ，(ktD). position to maximize his expected utility,taking as Now consider the first stage of the game.The Demo- given the probability that the district is decisive,pi, cratic leader with ideal point di chooses xi.p to maxi- and the party policies,Xp and XR.Similarly,the lo- mize his expected payoff,that is, cal Republican leader with ideal point ri selects xi.R, with an analogous objective. 2.In each district i,the median voter Mi is realized,and max-Φ，(e(cD,.R)(1-y) votes for his preferred candidate,if any.If M;is indif- ferent between Democrat and Republican,he votes ×p(Xn-d2+yxD-d)2） 4号 for the candidate of the party whose national posi- tion he prefers(if any),or otherwise randomizes.10 -(（1-,(6(cD,xR(1-y) EQUILIBRIUM ×p(XR-d)2+ycR-d)P） Our analysis starts with stage 2 of the game.The local -(1-p)1-y)Erl(Xp-d)2] (4) median voter Mi has expected utility piuM,(XR,xi.R)+ (1-pi)Ep[uM,(Xp,xi.R)]if the Republican candidate Similarly,the Republican primary voter solves wins,where Ep[.is the expectation over which party wins a majority,given that district i is not pivotal.Sim- ilarly,if the Democrat wins,Mi's expected payoff is max-,(8.D,R)1-y） PiuM(XD.xi.D)+(1-Pi)Ep[uM (Xp,xi.D)].Using the utility function in Equation(1),it follows that median voter Mi prefers the Democrat to the Republican if x pi(Xp-n)2+y(xi.D-n)2) -(1-Φ，(e(x.D,xR)(1-y) -pi(1-y)(Xp Mi)2-y(xD.i-Mi)2 -P:(1-Y)(XR-M)2-y(xR.i-M)}2.(2) ×p:(XR-n)2+Y(x.R-r)） -(1-p)1-y)E[(Xp-r)2] (5) Definition 1 Policies xi.p and xi.R are an equilibrium in in most formulas).We refrain from doing so explicitly to keep the notation simpler. district i if and only if xi.D solves Equation (4)and xi R If citizens vote only because of the probability that their vote makes solves Equation (5). a difference for the election outcome,actual participation levels in large elections can,with any positive cost of voting.only be rational- If pi=0,then all terms that reflect the parties'na- ized if voters mistakenly believe that the pivot probability is much tional positions drop out and the optimization problem higher than it actually is.For example,in the entire history of U.S. reduces to that of a standard Calvert-Wittman model. elections,no single voter has ever been pivotal for the outcome in a Congressional race.In a similar vein,voters may also overestimate As mentioned above,in this case (xi.D,xi.R)=(xi.D the pivot probability of their own district.(Of course,participation +xi.R)/2.Thus,after substituting pi=0,dropping the in elections can also be rationalized through a sufficiently large civic third(constant)term in Equation(5),and dividing by benefit from the act of voting,or a rule utilitarian paradigm (Coate y,the Republican primary voter's problem is equiva- and Conlin 2004;Feddersen and Sandroni 2006).) lent to After the main analysis,we will endogenize the party policies XD and XR as aggregations of a party's successful candidates'policies. 10 We will point out below where we use this tie-breaking assumption that,in case of indifference,the median voter votes for the candidate 2D-)2 /:sony of the party whose national position he prefers.Other tie-breaking assumptions would be slightly more cumbersome to work with,but not lead to qualitatively different results. (-( .R-n)2; 812

Stefan Krasa and Mattias K. Polborn Ex ante, there is uncertainty about the ideal position of district i’s median voter, described by a cdf i(·) that is symmetric about μi. Let pi denote the probability that district i is decisive in determining which party has a majority in the legislature (i.e., pi is the probability that both parties win the same number of representa￾tives in all other districts j = i). Note that pi can either be derived by the equilibrium played in other districts or can simply be thought of as reflecting the (not neces￾sarily rational) perception of the voters in district i that their district is pivotal.8 In summary, the game proceeds as follows: 1. In each district i, the local Democratic leader with ideal point di selects the Democratic candidate’s position to maximize his expected utility, taking as given the probability that the district is decisive, pi, and the party policies, XD and XR. 9 Similarly, the lo￾cal Republican leader with ideal point ri selects xi, R, with an analogous objective. 2. In each district i, the median voter Mi is realized, and votes for his preferred candidate,if any. If Mi is indif￾ferent between Democrat and Republican, he votes for the candidate of the party whose national posi￾tion he prefers (if any), or otherwise randomizes.10 EQUILIBRIUM Our analysis starts with stage 2 of the game. The local median voter Mi has expected utility piuMi(XR, xi,R) + (1 − pi)EP[uMi(XP, xi,R)] if the Republican candidate wins, where EP[ · ] is the expectation over which party wins a majority, given that district i is not pivotal. Sim￾ilarly, if the Democrat wins, Mi’s expected payoff is piuMi(XD, xi,D) + (1 − pi)EP[uMi(XP, xi,D)]. Using the utility function in Equation (1), it follows that median voter Mi prefers the Democrat to the Republican if −pi(1 − γ )(XD − Mi) 2 − γ (xD,i − Mi) 2 ≥ − pi(1 − γ )(XR − Mi) 2 − γ (xR,i − Mi) 2 . (2) in most formulas). We refrain from doing so explicitly to keep the notation simpler. 8 If citizens vote only because of the probability that their vote makes a difference for the election outcome, actual participation levels in large elections can, with any positive cost of voting, only be rational￾ized if voters mistakenly believe that the pivot probability is much higher than it actually is. For example, in the entire history of U.S. elections, no single voter has ever been pivotal for the outcome in a Congressional race. In a similar vein, voters may also overestimate the pivot probability of their own district. (Of course, participation in elections can also be rationalized through a sufficiently large civic benefit from the act of voting, or a rule utilitarian paradigm (Coate and Conlin 2004; Feddersen and Sandroni 2006).) 9 After the main analysis, we will endogenize the party policies XD and XR as aggregations of a party’s successful candidates’ policies. 10 We will point out below where we use this tie-breaking assumption that, in case of indifference, the median voter votes for the candidate of the party whose national position he prefers. Other tie-breaking assumptions would be slightly more cumbersome to work with, but not lead to qualitatively different results. Let the indifferent voter type for whom Equation (2) holds as equality be denoted by θ (xi,D, xi,R) = 1 2 (1 − γ )pi(X2 R − X2 D) + γ (x2 i,R − x2 i,D) (1 − γ )pi(XR − XD) + γ (xi,R − xi,D) . (3) Then Mi prefers to vote for the Democrat if and only if Mi θ(xi, D, xi, R). The probability that the Democrat wins in district i is therefore i(θ(xi, D, xi, R)). For example, if the district cannot be pivotal (pi = 0), then Equation (3) implies that θ(·) = (xi, R + xi, D)/2, that is, the median voter chooses the candidate whose platform is closest to Mi. The probability that the Democrat wins is therefore i xi,R+xi,D 2 . Now consider the first stage of the game. The Demo￾cratic leader with ideal point di chooses xi, D to maxi￾mize his expected payoff, that is, max xi,D − i(θ (xi,D, xi,R)) (1 − γ ) × pi(XD − di) 2 + γ (xi,D − di) 2  −  1 − i(θ (xi,D, xi,R))(1 − γ ) × pi(XR − di) 2 + γ (xi,R − di) 2  − (1 − pi)(1 − γ )EP  (XP − di) 2 . (4) Similarly, the Republican primary voter solves max xi,R − i(θ (xi,D, xi,R)) (1 − γ ) × pi(XD − ri) 2 + γ (xi,D − ri) 2  −  1 − i(θ (xi,D, xi,R))(1 − γ ) × pi(XR − ri) 2 + γ (xi,R − ri) 2  − (1 − pi)(1 − γ )EP  (XP − ri) 2 . (5) Definition 1 Policies xi, D and xi, R are an equilibrium in district i if and only if xi, D solves Equation (4) and xi, R solves Equation (5). If pi = 0, then all terms that reflect the parties’ na￾tional positions drop out and the optimization problem reduces to that of a standard Calvert-Wittman model. As mentioned above, in this case θ(xi, D, xi, R) = (xi, D + xi, R)/2. Thus, after substituting pi = 0, dropping the third (constant) term in Equation (5), and dividing by γ , the Republican primary voter’s problem is equiva￾lent to max xi,R − xi,D + xi,R 2 (xi,D − ri) 2 −  1 −  xi,D + xi,R 2 (xi,R − ri) 2 ; (6) 812 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000503

Political Competition in Legislative Elections and similar for the Democrat.Formally,this is equiva- didate positions xi.D,then a Republican candidate at lent to the standard problem of policy motivated candi- Xi R =i wins. dates with ideal points ri and di,respectively,who trade It is useful to define the average party policy,that off the probability of winning and selecting a policy is,the voter type who is indifferent between the two that is closer to their ideal point.1 national party positions,as=.If x is suffi- If,instead,pi>0,there is no closed form solution ciently far from the possible location of district i's me- for the equilibrium in this case.2 To learn something dian voter,then the candidate choice of the disadvan- about the structure of equilibrium,we proceed with our taged party does not constrain the advantaged party,so analysis by varying the importance of national and lo- that electoral competition has no moderating effect.In cal issues for voters,y.Note that this importance can the remainder of this section,we now turn to the other plausibly vary over time and between different cham- case.We say that candidates face effective competition bers.3 In the first of the following subsections,we deal if a Democrat located at di or a Republican located at with the case that the uncertainty about the median r;would lose with positive probability voter's position is described by a uniform distribution with sufficiently small range.In the second and third Assumption 1 There exist xi.D,xi.R ER such that ui- subsection,we analyze the limit cases of y0(i.e. c<0(di,xiR),0(xi.D,ri)<ui+c. voters care mostly about national party positions)and y1 (the Calvert-Wittman benchmark);we can do Proposition 1 characterizes the equilibria. this without imposing any assumptions on the uncer- Proposition 1 Suppose that i is uniformly distributed tainty about the median voter positions. N on [ui-c,ui cl,where di<ui-c<ui+c<ri. Let0<y <1.and suppose that Assumption I holds in Intermediate Weights on Local vs.National district i.Then there exists s>0 such that,if c <8,the Positions following holds for all pure strategy equilibria: 4号元 We start with the general case that voters care about 1.If X ui then the Republican wins with prob- both local candidate positions and national party po- ability one in any pure strategy equilibrium, sitions in a way that both components have a non- and the equilibrium candidate positions in negligible weight in their utility function(i.e.,y takes district i are an intermediate value).Tractability requires us to focus on the case where the distribution of the median voter Xi.D=ui-C,xi.R=ui-c is uniform on some interval [ui-c,ui+c],with c small. Given that the uniform distribution has bounded 1-y support,in sufficiently extreme districts,the favored 2pi(XR-XD)(ui-c-X). party's advantage is so large that they can win in dis- 2 trict i even if they choose a candidate who is located () at the respective leader's ideal point.For example,if (di,xi.R)>ui+c for all possible positions xi.R of the Republican candidate,4 then the Democrats can win 2.If X>ui then the Democrat wins with prob- for sure in district i by nominating a candidate with po- ability one in any pure strategy equilibrium, and the equilibrium candidate positions in sition xi D =di(which,clearly,is optimal in this case). Similarly,if (xi.D,r)<ui-c for all Democratic can- district i are xi.D=i十C 11 There is a minor interpretative difference:In the existing literature on policy-motivated candidates,the policy-motivated agent is the candidate himself who is assumed to be able to commit to a platform 1-Y2p,(XR-Xn)(X-4-c) different from his ideal point.In contrast,here,the party's members choose the position,by picking a candidate.This is consistent with either office-motivated candidates(who,then,choose a position such xi,R=i十C. (8) that they can win the nomination of their party)or policy-motivated candidates who cannot commit (in which case the primary voters 3.If X ui and ri-ui ui di then simply pick the candidate whose ideal position corresponds to the solution of Equation(6)for Republicans or the analogous problem xR=-xiD=山+rc/r:+c，以and both can- for the Democrats). didates win with equal probability. 12 However,numerical solutions can be easily found by solving Equations(4)and (5)for the best-response =rp(xi.R) Note first that,if national party positions differ and if &a2ne8aacpeacm no two districts have the same expected median voter justices might retire in the near future(and if this topic is important positions,then either all or almost all districts are in for voters),then it is plausible that 1-y is higher in Senate elections cases 1 or 2.Consider the case that X<ui,so that type than in House elections,and in the present election relative to other ui strictly prefers the Republican national platform elections where no Supreme Court vacancies are expected.It could M/:sonu also be the case that the importance of national issues relative to local over the Democratic one.In equilibrium,voter type 发6,the voter who is indifferent between the two candidates must be located at ui-c,the lowest possible median voter po- type who is indifferent between the candidates. sition.Otherwise,if >ui-c and c is small,then the 813

Political Competition in Legislative Elections and similar for the Democrat. Formally, this is equiva￾lent to the standard problem of policy motivated candi￾dates with ideal points ri and di, respectively, who trade off the probability of winning and selecting a policy that is closer to their ideal point.11 If, instead, pi > 0, there is no closed form solution for the equilibrium in this case.12 To learn something about the structure of equilibrium,we proceed with our analysis by varying the importance of national and lo￾cal issues for voters, γ . Note that this importance can plausibly vary over time and between different cham￾bers.13 In the first of the following subsections, we deal with the case that the uncertainty about the median voter’s position is described by a uniform distribution with sufficiently small range. In the second and third subsection, we analyze the limit cases of γ ≈ 0 (i.e., voters care mostly about national party positions) and γ ≈ 1 (the Calvert-Wittman benchmark); we can do this without imposing any assumptions on the uncer￾tainty about the median voter positions. Intermediate Weights on Local vs. National Positions We start with the general case that voters care about both local candidate positions and national party po￾sitions in a way that both components have a non￾negligible weight in their utility function (i.e., γ takes an intermediate value).Tractability requires us to focus on the case where the distribution of the median voter is uniform on some interval [μi − c,μi + c], with c small. Given that the uniform distribution has bounded support, in sufficiently extreme districts, the favored party’s advantage is so large that they can win in dis￾trict i even if they choose a candidate who is located at the respective leader’s ideal point. For example, if θ(di, xi, R) > μi + c for all possible positions xi, R of the Republican candidate,14 then the Democrats can win for sure in district i by nominating a candidate with po￾sition xi, D = di (which, clearly, is optimal in this case). Similarly, if θ(xi, D, ri) < μi − c for all Democratic can- 11 There is a minor interpretative difference: In the existing literature on policy-motivated candidates, the policy-motivated agent is the candidate himself who is assumed to be able to commit to a platform different from his ideal point. In contrast, here, the party’s members choose the position, by picking a candidate. This is consistent with either office-motivated candidates (who, then, choose a position such that they can win the nomination of their party) or policy-motivated candidates who cannot commit (in which case the primary voters simply pick the candidate whose ideal position corresponds to the solution of Equation (6) for Republicans or the analogous problem for the Democrats). 12 However, numerical solutions can be easily found by solving Equations (4) and (5) for the best-response functions xi, D = rD(xi, R) and xi, R = rR(xi, D), and finding a fixed point of the function (rD,rR). 13 For example, if it is expected that a number of Supreme Court justices might retire in the near future (and if this topic is important for voters), then it is plausible that 1 − γ is higher in Senate elections than in House elections, and in the present election relative to other elections where no Supreme Court vacancies are expected. It could also be the case that the importance of national issues relative to local ones is higher in Presidential election years. 14 Remember that θ(di, xi, R), defined by Equation (3), is the voter type who is indifferent between the candidates. didate positions xi, D, then a Republican candidate at xi, R = ri wins. It is useful to define the average party policy, that is, the voter type who is indifferent between the two national party positions, as X = XD+XR 2 . If X is suffi￾ciently far from the possible location of district i’s me￾dian voter, then the candidate choice of the disadvan￾taged party does not constrain the advantaged party, so that electoral competition has no moderating effect. In the remainder of this section, we now turn to the other case. We say that candidates face effective competition if a Democrat located at di or a Republican located at ri would lose with positive probability. Assumption 1 There exist xi,D, xi,R ∈ R such that μi − c < θ(di, xi, R), θ(xi, D, ri) < μi + c. Proposition 1 characterizes the equilibria. Proposition 1 Suppose that i is uniformly distributed on [μi − c, μi + c], where di < μi − c < μi + c < ri. Let 0 <γ < 1. and suppose that Assumption 1 holds in district i. Then there exists ε > 0 such that, if c < ε, the following holds for all pure strategy equilibria: 1. If X < μi then the Republican wins with prob￾ability one in any pure strategy equilibrium, and the equilibrium candidate positions in district i are xi,D = μi − c, xi,R = μi − c + 1 − γ γ 2pi(XR − XD)(μi − c − X ). (7) 2. If X > μi then the Democrat wins with prob￾ability one in any pure strategy equilibrium, and the equilibrium candidate positions in district i are xi,D = μi + c − 1 − γ γ 2pi(XR − XD)(X − μi − c), xi,R = μi + c. (8) 3. If X = μi and ri − μi = μi − di then xi, R = −xi, D = μi + ric/(ri + c), and both can￾didates win with equal probability. Note first that,if national party positions differ and if no two districts have the same expected median voter positions, then either all or almost all districts are in cases 1 or 2. Consider the case that X < μi, so that type μi strictly prefers the Republican national platform over the Democratic one. In equilibrium, voter type θ who is indifferent between the two candidates must be located at μi − c, the lowest possible median voter po￾sition. Otherwise, if θ>μi − c and c is small, then the 813 Downloaded from https://www.cambridge.org/core. Shanghai JiaoTong University, on 26 Oct 2018 at 03:53:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0003055418000503