Stefan Krasa and Mattias K.Polborn <0=XR,that is,the expected district median voter is farther away from the leader's preferred position.The more conservative than the national Republican posi- two candidates'equilibrium positions are symmetric tion.As XR increases,the Republican advantage in dis- about the position of the expected median voter,and trict iincreases,and that allows local Republicans(who the Democrat wins if and only if the realized median have ri>ui)to nominate a more extreme candidate. voter is to the left of the expected median voter,hence As Xg increases further beyond ui,the Republican ad- with probability 1/2. vantage in district i decreases which generally (for s not What happens when y is now slightly decreased? too small)makes a somewhat more moderate candi- For concreteness,suppose that the expected median date optimal for Republicans.When Xg becomes large, voter in district i prefers the Democratic national po- district i starts to favor the Democratic national posi- sition.If y<1 and the realized median voter is equal tion (which will move xi.D toward di),and this forces to the expected one,then the Democrat wins,so that the Republican candidate toward(Xp +XR)/2. the indifferent voter type is now more conservative than in the case of y=1.The effect on the strate- Equilibrium when Local Concerns are gic location incentives of both local leaders is as fol- Dominant(y≈1) lows:For the same extent of moderation,the indiffer- ent voter type is more responsive to movements in the We finally turn to the other polar case,namely that vot- Democratic candidate's position than to that of the Re- ers care primarily about the two local candidates'posi- publican because the indifferent voter is farther away tions(y-1).The limit case ofy =1 is the well-known from the Democrat's position than from the Republi- Calvert-Wittman model,so the main point of interest can's position.15 Thus,the Democrat's marginal benefit in this section is how a minimal voter concern about from moderation increases,and the Republican's bene- national party positions affects the parties'strategic lo- fit from moderation decreases.Since the marginal cost cation incentives,relative to the Calvert-Wittman case. of moderation is unchanged for both,this means that Superficially,and from the results derived so far,it the Democratic equilibrium position will become more 4 may seem as if voters'national concerns should al- moderate,and the Republican one less so. ways lead to more polarization,relative to a standard This intuition is similar to the one in Groseclose Calvert-Wittman model in which each party trades off (2001).who analyzes the effect of a candidate's va more distance from their bliss point against some gain lence advantage on the positions chosen by the (policy- in the probability of winning.As y decreases from 1,the motivated)candidates and finds that a small valence median voter's responsiveness to local positions is low- advantage induces the favored candidate to move to- ered,and consequently nominating a candidate closer ward the expected median voter,and the disadvan- to the party's ideal point becomes less costly taged candidate to move away,with the latter move- However,nominating a more extremist candidate ment being bigger so that polarization,as measured by also becomes less attractive for the local leader because the distance between the candidates,increases.How- his utility also increasingly derives from national posi- ever,there is an interesting difference:While valence tions,and winning the local race may determine which in Groseclose's model is uniformly appreciated by all party has the majority in the legislature.From this per- voter types,the extent and even the sign of the Demo- spective,nominating a more moderate candidate ap- crat's net advantage varies with the preference type pears more attractive,and the net effect of y on polar- of the realized median voter in our model.This is the ization close to y =1 is therefore unclear.Proposition 3 reason why the polarization result is different in our analyzes this case. model.that is,for small changes of y away from 1,the distance between the equilibrium Democratic and Re- Proposition 3 Consider a district where the positions of publican position is unchanged(to the first order). the local party leaders are symmetric around the median voter's expected position (i.e.,ri-ui=ui-di).Suppose that,starting from a situation in which all voters only A CLOSER LOOK AT THE EFFECTS OF care about local candidates'positions (i.e.,y =1),y de- GERRYMANDERING creases slightly.Then,the position of the candidate of the advantaged party (i.e,the one whose national position In this section.we analyze how a change in the distri- the expected median voter prefers)moves toward ui,and bution of district median voters affects the equilibrium the opponent's position moves away from ui.Moreover, degree of polarization,in particular in those districts the first-order change in local polarization is zero,i.e., that are not directly affected by the preference change 品(cR-.D川y=1=0. For our model,it does not matter whether the change in the district median distribution was brought about Proof.See Appendix. ■ intentionally,through gerrymandering,or unintention- ally through voter sorting (say,conservatives moving With the symmetry assumption with respect to to conservative states,and liberals to liberal states).In the two local leaders,it is easy to characterize the the next subsection,we focus on the effect that works L equilibrium of the Calvert-Wittman model.Leaders choose positions to trade off the benefit of choos- ing a more moderate position-an increased winning probability-with the cost of a more moderate posi- 1s Remember that,with astrictly concave utility function,the median voter appreciates the same amount of policy moderation the more, tion,namely that the policy,if the candidate wins,is the farther away a candidate is. 816Stefan Krasa and Mattias K. Polborn < 0 = XR, that is, the expected district median voter is more conservative than the national Republican posi￾tion. As XR increases, the Republican advantage in dis￾trict i increases, and that allows local Republicans (who have ri > μi) to nominate a more extreme candidate. As XR increases further beyond μi, the Republican ad￾vantage in district i decreases which generally (fors not too small) makes a somewhat more moderate candi￾date optimal for Republicans.When XR becomes large, district i starts to favor the Democratic national posi￾tion (which will move xi, D toward di), and this forces the Republican candidate toward (XD + XR)/2. Equilibrium when Local Concerns are Dominant (γ ≈ 1) We finally turn to the other polar case, namely that vot￾ers care primarily about the two local candidates’ posi￾tions (γ → 1). The limit case of γ = 1 is the well-known Calvert-Wittman model, so the main point of interest in this section is how a minimal voter concern about national party positions affects the parties’ strategic lo￾cation incentives, relative to the Calvert-Wittman case. Superficially, and from the results derived so far, it may seem as if voters’ national concerns should al￾ways lead to more polarization, relative to a standard Calvert-Wittman model in which each party trades off more distance from their bliss point against some gain in the probability of winning.As γ decreases from 1, the median voter’s responsiveness to local positions is low￾ered, and consequently nominating a candidate closer to the party’s ideal point becomes less costly. However, nominating a more extremist candidate also becomes less attractive for the local leader because his utility also increasingly derives from national posi￾tions, and winning the local race may determine which party has the majority in the legislature. From this per￾spective, nominating a more moderate candidate ap￾pears more attractive, and the net effect of γ on polar￾ization close to γ = 1 is therefore unclear. Proposition 3 analyzes this case. Proposition 3 Consider a district where the positions of the local party leaders are symmetric around the median voter’s expected position (i.e., ri − μi = μi − di). Suppose that, starting from a situation in which all voters only care about local candidates’ positions (i.e., γ = 1), γ de￾creases slightly.Then,the position of the candidate of the advantaged party (i.e., the one whose national position the expected median voter prefers) moves toward μi, and the opponent’s position moves away from μi. Moreover, the first-order change in local polarization is zero, i.e., ∂ ∂γ (xi,R − xi,D)|γ =1 = 0. Proof. See Appendix. With the symmetry assumption with respect to the two local leaders, it is easy to characterize the equilibrium of the Calvert-Wittman model. Leaders choose positions to trade off the benefit of choos￾ing a more moderate position—an increased winning probability—with the cost of a more moderate posi￾tion, namely that the policy, if the candidate wins, is farther away from the leader’s preferred position. The two candidates’ equilibrium positions are symmetric about the position of the expected median voter, and the Democrat wins if and only if the realized median voter is to the left of the expected median voter, hence with probability 1/2. What happens when γ is now slightly decreased? For concreteness, suppose that the expected median voter in district i prefers the Democratic national po￾sition. If γ < 1 and the realized median voter is equal to the expected one, then the Democrat wins, so that the indifferent voter type is now more conservative than in the case of γ = 1. The effect on the strate￾gic location incentives of both local leaders is as fol￾lows: For the same extent of moderation, the indiffer￾ent voter type is more responsive to movements in the Democratic candidate’s position than to that of the Re￾publican because the indifferent voter is farther away from the Democrat’s position than from the Republi￾can’s position.15 Thus, the Democrat’s marginal benefit from moderation increases, and the Republican’s bene￾fit from moderation decreases. Since the marginal cost of moderation is unchanged for both, this means that the Democratic equilibrium position will become more moderate, and the Republican one less so. This intuition is similar to the one in Groseclose (2001), who analyzes the effect of a candidate’s va￾lence advantage on the positions chosen by the (policy￾motivated) candidates and finds that a small valence advantage induces the favored candidate to move to￾ward the expected median voter, and the disadvan￾taged candidate to move away, with the latter move￾ment being bigger so that polarization, as measured by the distance between the candidates, increases. How￾ever, there is an interesting difference: While valence in Groseclose’s model is uniformly appreciated by all voter types, the extent and even the sign of the Demo￾crat’s net advantage varies with the preference type of the realized median voter in our model. This is the reason why the polarization result is different in our model, that is, for small changes of γ away from 1, the distance between the equilibrium Democratic and Re￾publican position is unchanged (to the first order). A CLOSER LOOK AT THE EFFECTS OF GERRYMANDERING In this section, we analyze how a change in the distri￾bution of district median voters affects the equilibrium degree of polarization, in particular in those districts that are not directly affected by the preference change. For our model, it does not matter whether the change in the district median distribution was brought about intentionally, through gerrymandering, or unintention￾ally through voter sorting (say, conservatives moving to conservative states, and liberals to liberal states). In the next subsection, we focus on the effect that works 15 Remember that, with a strictly concave utility function, the median voter appreciates the same amount of policy moderation the more, the farther away a candidate is. 816 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