Political compromise : platforms and policies

WP núm. 193 Institut de Ciències Polítiques i Socials Barcelona, 2001 POLITICAL COMPROMISE: PLATFORMS AND POLICIES Humberto Llavador Universitat Pompeu Fabra 2 Humberto Llavador The Institut de Ciències Polítiques i Socials (ICPS) was created by the Universitat Autònoma de Barcelona and the Diputació de Barcelona in 1988. The ICPS is attached to the Universitat Autònoma de Barcelona. These "Working Papers" -thought of as subject for discussionare the result of research work in progress. Appearance in this series does not preclude further publication. This paper must not be reproduced without the author’s licence. © Humberto Llavador Design: Toni Viaplana Printer: A.bís c/ Leiva, 3, baixos. 08014 Barcelona ISSN: 1133-8962 LD: B-47.600-2001 3 Political compromise: platforms and policies Abstract It is frequently believed, and empirically observed, that the outcome of an election determines government action to at least some extent. However, the standard two-party spatial model of political competition trivializes any post-electoral policy-making process by assuming that the party that obtains more than fifty percent of the vote adopts the policy announced during the electoral campaign. Its best known implication is that, under an environment of perfect information, both candidates announce the same policy, which coincides with the policy preferred by the median voter. In this paper, we enrich the theoretical framework of party competition to allow for a non-trivial policy-setting process and for sophisticated voters who care not only about the policy implemented but also about the platform they support with their vote. First, we show that platform convergence is a non-robust feature created by the winner-takes-all assumption. The lightest influence of the opposition in the policy-making process provokes a divergent tendency in platform writing. Without abstention, an equilibrium is characterized by polarized platforms and a moderate implemented policy that consistently differs from the median voter ideal policy. When abstention is introduced into the analysis, parties announce differentiated yet non-extreme policies, voters concentrate around the platforms, and substantial turnout rates are generically obtained where abstention occurs among voters with extreme views as well as with moderate views. Key bords: Political competition, compromise, platforms, abstention. 4 Humberto Llavador 5 Political compromise: platforms and policies "It was not the kind of speech Mr. Bush would have delivered had he won the large victory his aides were predicting on election night. He offered nothing to the conservative wing of his party, and evoked none of the cultural issues that often divide the two parties". The New York Times. December 14, 2000 1. INTRODUCTION It is frequently believed that the outcome of an election determines government action to at least some extent1. Many empirical studies support this view. Papers like Budge and Hofferbert (1990, 1992), Hofferbert and Klingemann (1990), Klingemann et al. (1994), and King et al. (1993) analyze the relationship between party platforms and policies. They find that, while platforms and governmental outcomes consistently differ, there exist strong links between them. A second group of studies (Poole and Rosenthal, 1984b; Fiorina, 1974; Poole and Rosenthal, 1984a; Poole and Daniels, 1985; Poole and Rosenthal, 1991, 1997; Snyder, 1996; Alesina and Rosenthal, 1995) compare the perceived location of platforms and implemented policies, and conclude that while platforms tend to be polarized, policies are moderate or centrist2. But the standard two-party spatial model of political competition does not differentiate between platforms and policies. It assumes that the party that obtains more than fifty percent of the vote adopts the policy announced during the electoral campaign. As a consequence, any post-electoral policy-making process becomes a triviality. 6 Humberto Llavador On theoretical grounds, this assumption has been rejected by several authors as an unrealistic way to model the outcome of the political competition in many modern democratic societies (Ortuño-Ortín, 1997; Gerber and OrtuñoOrtín, 1998; Dixit et al., 2000; Alesina and Rosenthal, 1995, 1996; Austen-Smith and Banks, 1998; Grossman and Helpman, 1996). Ortuño-Ortín argues that a democratic society is integrated by different institutions and groups. Some of them will favor the policies announced by the winning party, some will favor the opposition’s platforms, but all may have some influence on the actions taken by the government, and their influence will be a non-decreasing function of the support received by the corresponding party: "Clearly a party winning 51% of the votes will have more difficult to carry out its proposal than one winning 80% of the votes" (Ortuño-Ortín, 1997, p. 428). Dixit, Grossman and Gul (2000) obtain tacit collusion in a plurality political environment. They show that the ruling party will go to some extent towards the interests of the opposition expecting the same treatment when it itself becomes the opposition party. Of course, the party in power must know that its term will reach an end and must expect the other party to gain power sometime in the future. In this paper we follow this view and, in the spirit of the empirical results, let the implemented policy differ to some extent from the electoral platform of the winning party. In particular, we let the implemented policy depend on the electoral outcome and on the platforms announced by each party, in such a way that the higher the fraction of votes obtained by a party, the closer the implemented policy is to its proposal. This post-electoral policymaking process is what we call political compromise. Modifying the policy-setting process has important implications on voting behavior often overlooked by the literature on political compromise. In the winner-takes-all case, when the implemented policy is the platform announced by the winner, voting for the preferred candidate is always a 7 Political compromise: platforms and policies dominant strategy for all voters. The intuition is simple. Suppose that an agent prefers the policy proposed by party L to the policy proposed by party R. By voting, either he does not change the outcome or he increases the probability of winning for that party. Thus, he will always vote for his favorite platform. However, when electoral platforms and implemented policies may differ, voting for the preferred platform is not necessarily a dominant strategy. Consider, for instance, a voter with moderate views. She finds the proposal of the left party more appealing than the one from the right party. However, she expects that, due to an overwhelming support for the left party, the implemented policy will be "too left" for her. Then, she may decide to vote for the right party. That is, a voter who expects party L to win and who prefers the alternative offered by L to the one announced by party R may, nevertheless, vote for R to "moderate" L’s policy. On different grounds, when platforms and policies do not necessarily coincide, voters will base their decision not only on the implications over final policies, but also on the platforms announced by the parties. For example, many people would feel reluctant to vote for a nazi party regardless the impact that a larger support for that nazi party would have on the implemented policy. Their reluctance comes from the platform represented by such a party and not from the influence over the policy. If the nazi party were the only alternative to obtain a more conservative policy, we may expect many of those voters to abstain. Therefore, we distinguish two components in voting behavior. On the one hand, insofar as voters care about the policy outcome, they will choose to vote for one party or the other based on the effect that a larger support for each party have over the implemented policy. We refer to this component as the pragmatic component of preferences. On the other hand, citizens also consider the platform they support with their vote when deciding for whom 8 Humberto Llavador to vote. Because platforms and policies do not necessarily coincide, voters who would support a party from a purely pragmatic point of view may decide not to do it because they strongly disagree with the party’s platform. This is the ideological component of preferences. The final voting decision will depend then on both the pragmatic and the ideological components of preferences. We study an unidimensional political game with a dynamic structure. At period one, parties announce their campaign platforms. At period two, citizens observe the platforms and decide whether to vote for one of the two candidates, or to abstain. Their decisions are based on their preferences and their expectations about the outcome of the election. Finally, after the election, a policy-setting process takes place from which a policy arises as a function of both the platforms of each party and their electoral support. Our first result shows that platform convergence is a non-robust feature created by the winner-takes-all assumption. The lightest influence of the opposition in the policy making process provokes a divergent tendency in platform writing. Second, we find that, under reasonable assumptions, an equilibrium always exists. Without abstention, an equilibrium is characterized by polarized platforms and a moderate implemented policy that consistently differs from the median voter ideal policy. When abstention is incorporated into the analysis, parties announce differentiated, non-extreme policies, voters concentrate around the platforms, and abstention occurs among voters with extreme views as well as with moderate views. The reader is encouraged to look at Figure 4 where we show two typical examples of political equilibrium. 9 Political compromise: platforms and policies 2. THE MODEL The electoral arena is assumed to be represented by an unidimensional policy space We model the electoral process as a political game between parties and voters with a dynamic structure. Two parties, L and R, announce their campaign platform by choosing a location on the policy space. Citizens observe the platforms and vote for one of the two candidates, or abstain. Finally, after the election, a policy formation process takes place during which both parties play a role in shaping the implemented policy: one as the governing party, the other as the opposition. The following sections describe the three steps in the political game: platform announcement, voting, and policy formation. Following the standard backward induction methodology, we start from the last stage, and then work backward to describe the behavior of the players before. 2.1 Policy Formation A key feature of the present model is that the implemented policy may differ from the electoral platform of the winner. Policy is the result of a post-electoral process where both parties play a role (relative to their electoral support). For the purpose of this paper, it is convenient to model this postelection process in its reduced form by directly specifying a map from platforms and electoral outcomes to final policies. T = [t ,t] ⊂ ∇. Let T 2 = T × T. 16 Humberto Llavador Definition 2.3 We say that (tL, tR, is a political equilibrium if (i) (ii) (iii) 3. EXAMPLE We anticipate the main results with an illustrative example, before presenting their formal proofs. Consider a political process where two ideological parties, L and R, compete over a single issue, a tax rate, for example. Let T=[0,1] represent the policy space. The weight-of-votes function takes the following form (see Figure 2): Observe that, because g is concave for ν > ½ and convex for ν < ½, winning the election makes a difference: the weight of the platform of the winner party in the policy-setting process is more than proportional to the share of votes received by that party. Figure 2 Weight of Votes Function ν ) ν ∈ χ(tL,tR)) L ˆ π(tL, tR,ν) ≥ L ˆ π(t, tR,ν) ∀t ∈ T and ∀ν ∈ χ(t,tR), and R ˆ π(tL, tR,ν) ≥ R ˆ π(tL,t,ν) ∀t ∈ T and ∀ν ∈ χ(tL,t). 2 )(cos1 )(gνπ− =ν (3.1) 17 Political compromise: platforms and policies Voters care about the implemented policy (the tax rate). Let the preferences of voters over tax rates be represented by the following Euclidean utility function: Then, the pragmatic component of voting is given by (see(2.3)). On the other hand, voters also care about the platform they are supporting with their vote. Let the ideological component of voting represent the dis-utility of supporting a platform far from one’s ideal policy. In particular, we take ideological voting to be a linear function of the distance between the "ideology" of the voter and the platform of the party: η(t; π) = - 2 | t - π |. Finally, if a citizen abstains, her utility of voting is zero, since both the pragmatic component and the ideological component are zero. In summary, the utility of voting (the sum of the pragmatic and the ideological components of voting) of a citizen τ is Let the electorate be distributed according to a triangular distribution with mode m (see Figure 3 for a few members of this family of density functions). u(t; τ) = - 2 1(t - τ)2 (3.2) w(L; tL, tR, ν, τ) = (t ˆ (tL, tR, ν) - τ) g’(ν) (tR - tL) w(R; t L, t R , ν, τ) = (τ - t ˆ(t L, t R , ν)) g’(ν) (t R - t L ) v(L; tL, tR, ν, τ) = (t ˆ(tL, tR, ν) - τ) g’(ν) (tR - tL) - 2 | t - π | v(R; tL, tR, ν, τ) = (τ - t ˆ(tL, tR, ν)) g’(ν) (tR - tL) - 2 | t - π | v(A; t L, t R , ν , τ ) = 0 18 Humberto Llavador Figure 3 Family of Triangular Density Functions Finally, parties also have Euclidean preferences represented by We take the ideal policy of the left party to be τL= 0.3, while the right party’s ideal policy is τR= 0.8. After several manipulations, it is easy to show that, given (tL, tR, ν), active voting occurs on two intervals around the electoral platforms: [λ1, λ2] tA and [ρ1, ρ2] tB. That is10, VL(tL, tR, ν) = F(λ2) – F(λ1), VR(tL, tR, ν) = F(ρ2) – F(ρ1). First, we analyze the case when the electorate is symmetrically distributed: m πJ(t) = - 2 1 (t - τJ)2. ∋ ∋ = 2 1. 19 Political compromise: platforms and policies Figure 4 Display of Typical Equilibria for Different Distributions of the Electorate Figure 4(a) depicts the political equilibrium. The following implications are worth emphasizing (we will prove in Section 5 that they are not particular to the present example, but characteristic of a symmetrically distributed electorate): (i) parties announce differentiated, non-extreme, symmetric platforms: (ii) the equilibrium policy coincides with the mean and the median: (iii) each party receives 50% of the vote cast; (iv) a substantial fraction of the population prefers voting to abstaining: turnout ≈ 37 %; and (v) abstention occurs for voters with extreme views as well as with moderate views. * L t= .25 and * R t = .75; * R t = .5; 20 Humberto Llavador Observe that the symmetric features of the equilibrium are a consequence of the symmetry imposed on the electorate, since parties are not symmetric: τL= .3 and τR= .8. How important is the symmetry assumption in the previous case? In a second exercise we consider a right skewed electorate: m = 0.7. The equilibrium is presented in Figure 4(b). Not surprisingly, symmetry vanishes. However, and more interestingly, the substance of the equilibrium does not change: parties announce differentiated platforms, abstention occurs for extreme and moderate voters, and there is a substantial turnout (40.5%). Unlike in the symmetric case, the equilibrium policy differs from the median =0.58 <0.61 = median). Finally, one party wins (party R receives 55% of the vote). This is an important finding since most models of political competition, even those with uncertainty built in, unrealistically predict that each party always obtains (or expects to obtain) fifty percent of the vote. In this section, we have worked out an example that anticipates the most relevant results of the paper. Section 5 presents the formal analysis of the existence and characterization of equilibria. First, however, we find interesting to consider the particular case where voting is purely pragmatic. 4. PURELY PRAGMATIC VOTING By abstracting from non-pragmatic voting we are able to recreate the standard political competition model with perfect information, except that here the implemented policy function substitutes a winner-takes-all assumption. Therefore, this particular case isolates the impact that incorporating political compromise has in the study of electoral politics. (* t 21 Political compromise: platforms and policies A standard result in the political competition literature is that, in an environment of perfect information, the parties’ platforms converge (Roemer, 1996). Moreover, no citizen has an incentive to vote: because both parties announce identical platforms, the probability of being pivotal is zero for all citizens. We obtain completely opposite results when political compromise replaces the winner-takes-all postulate: parties propose extreme platforms and "everybody" prefers active voting to abstaining11. Moreover, it is notable that, without additional assumptions beyond single-peakedness, an equilibrium always exists and is unique for any distribution of the electorate. This is an important finding in a field where existence of equilibrium is a permanent struggle (Roemer, 1997). For the rest of this section we assume that voting behavior is fully driven by its pragmatic component. Assumption 2 (A2) η(t;τ) = 0 for all t ∈ T and for all agent τ. Observe that A2 is equivalent to Lemma 4.1 Let A1 and A2 hold. Then: Proof: All the proofs are presented in the Appendix. ♦ v(s; t L, t R , ν ; τ ) = w τ (s; t L, t R , ν ). (i) Given tL, tR ∈ T and ν ∈ [0,1], everybody votes. Moreover, for tL < TR, everybody to the left of t ˆ (tL,tR,ν) votes for L while everybody to the right of t ˆ (tL,tR,ν) votes for R. That is, VL(tL,tR,ν) = [t, t ˆ (tL,tR,ν)), and VR(tL,tR,ν) = ( t ˆ (tL,tR,ν), t ]. (ii) χ(tL, tR) is non-empty and single-valued for all (tL, tR)∈T2. (iii) χ is continuous, except may be at tL = tR. 22 Humberto Llavador Because χ is a function, we are able to formulate the implemented policy and the parties’ utilities in their reduced form. Let be defined by And, for J = L, R, let be defined by Lemma 4.2 The functions and are continuous on T2. We follow the standard procedure to prove the existence of a Nash equilibrium: first, we construct the best-response correspondences, then we look for a fixed point. The best-response correspondence of party J = L, R assigns to each alternative the set of utility maximizers. That is, Before the formal statement of the existence theorem, Lemma 4.3 shows that if a party cannot ensure the implementation of its ideal policy, then its best choice is to propose an extreme platform, namely, t for L or for R. Lemma 4.3 Let A1 and A2 hold. (i) (ii) (iii) t ~ : T2 à T ( ) ( ) ( ) RLRLRLt,t,t,tt ˆ t,tt ~ χ= . (4.1) J ~ π: T à T ( ) ( ) ( ) RLJRLJt,tt ~ t,t ~ π=π . (4.2) J ~ π t ~ ( ) ( ) { } Tt:t,t ~ maxargtBR RLRL∈π= ( ) ( ){ } Tt:t,t ~ maxargtBR LRLR∈π= t The best-response correspondence of party J, BRJ, is singlevalued and continuous (thus it can be viewed as a continuous function), J = L,R. Given tR ≥ τL, if there exists a 0 L t such that ( ) LR 0 Lt,tt ~τ=, then ( ) { } 0 LRLttBR =; otherwise, ( ) {} ttBR RL=. Given tL ≤ τL, if there exists a 0 R t such that ( ) R 0 RLt,tt ~τ=, then ( ) { } 0 RLRttBR =; otherwise, ( ) {} ttBR LR=. 23 Political compromise: platforms and policies Theorem 4.1 Let A1 and A2 hold. Then: (i) (ii) This section has recreated the standard political competition model with perfect information, substituting the winner-takes-all assumption for a political compromise policy-setting process. The main observation is the disappearance of the convergence tendency of parties’ proposals. We obtain just the opposite result: the smallest influence of the opposition’s platform in the determination of the implemented policy provokes a divergence tendency that takes parties to radicalize their platforms. In the following section we expand the model to allow for ideological voting. We obtain that typically parties announce differentiated, but nonextreme platforms. The key element to understand the intuition is abstention. By announcing an extreme platforms, a party alienates part of its constituency (who cares now about the platform.) If this alienation effect is strong enough, it will drive parties away from radicalizing their platforms. 5. PRAGMATIC AND IDEOLOGICAL VOTING The main conclusion from the previous section appears in Theorem 4.1: convergence of parties’ platforms, traditionally associated with political competition, is an artifact created by the winner-takes-all assumption. As soon as we perturb this assumption a little bit and let the opposition intervene (to some extent) into policy-setting, a tendency towards divergence appears. Recall that an almost winner-takes-all implemented policy function (like the one in Figure 1(a)) would be enough to make parties announce radical a political equilibrium exists, and if (tL*,tR*) are the platforms at equilibrium, either (tL*,tR*) = (t, t) or t ~(t L *,t R *) = τ J , for some J=L,R. 24 Humberto Llavador platforms. One may object that this result is as unrealistic as the standard Median Voter Theorem, where parties propose exactly the same policy and everybody votes. However, we claim that the "pathological" behavior found here is the consequence of an unrealistic feature of the model studied in Section 4, namely the absence of ideological voting. We will see that under a more realistic (and more complicated) structure, already presented in Section 2, parties’ and voters’ behavior resemble closer what we observe in reality. The inclusion of a non-pragmatic component of voting that depends on the platforms of the parties opens the possibility to abstention. Because abstention notably complicates the analysis, we sacrifice some generality and work within a simpler framework. First, we substitute Assumption 1 with the following assumption: Assumption 3 (A3) That is, we take the implemented policy to be equivalent to proportional representation12. Second, consider a continuum of voters with Euclidean preferences over policies represented by the following utility function: Assumption 4 (A4) Third, let the ideological component of voting be a non-increasing and concave function of the distance between the platform of the party and the "ideology" of the voter: Assumption 5 (A5) ( ) ( ) RLRLt1t,ttt ~ ν−+ν=ν, for all ( ) ν,tt RL. ( ) ( ) 2 t 2 1 ;tuτ−−=τ η (t: τ ) = ζ (|t - τ |) , with ζ ’< 0 (decreasing), ζ ”< 0 (concave), and (concave), and ζ(0) = 0. 25 Political compromise: platforms and policies Finally, it is convenient for the exposition to adopt the convention T=[0,1]. We want to emphasize that all specifications have been imposed on citizen’s preferences and none on parties’ preferences, which are only assumed to be single-peaked. A first result (Theorem 5.1) proves what we already observed in the examples presented in Section 3: the support for each party is an interval around the platform announced by that party. It will follow (Theorem 5.2) that there exists one and only one consistent electoral outcome associated to each pair of platforms. Theorem 5.1 Let A3, A4, and A5 hold. Given tL, tR, and n, with tL ¹ tR, there exist two intervals such that if τ votes for L, then τ∈Iλ, and if τ votes for R, then τ∈Iρ. Thus Moreover, VL(tL,tR,n) + VR(tL,tR,n) > 0, VL and VR are continuous, VL is non-increasing in ν, and VR is non-decreasing in ν. Lemma 5.2 Let A3, A4, and A5 hold. The consistent electoral outcome correspondence c is non-empty, single-valued, and continuous for all tL ≠ tR. The previous lemma shows that there exists a unique electoral outcome associated to each pair of differentiated platforms. When both parties propose identical platforms, the implemented policy is unmistakably the common Iλ(tL,tR,ν) = [λ1(tL,tR,ν), λ2(tL,tR,ν)], and I ρ (t L ,t R , ν ) = [ ρ 1 (t L ,t R , ν ), ρ 2 (t L ,t R , ν )] VL(tL,tR,ν) = µ(Iλ(tL,tR,ν)) and V R (t L ,t R , ν ) = µ (I ρ (t L ,t R , ν )) . 32 Humberto Llavador REFERENCES ALESINA, Alberto; ROSENTHAL, Howard: Partisan Politics. Cambridge, Cambridge University Press, 1995. ALESINA, Alberto; ROSENTHAL, Howard: “A theory of divided government”, Econometrica, 64(6), 1995, p. 1311-1341. 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