Citizen Candidate Model Advanced Political Economics Fall 2011 Riccardo Puglisi

BESLEY & COATE ’97: Main Features Idea. In representative democracies citizens elect one of them: citizens are the primitives. No difference between voters and politicians: all citizens are partisan & have preferences over policy The winner implements her most preferred policy: no commitment technology is available. The political process is composed of 3 stages: 1. Entry Decision 2. Voting Decision (over candidates) 3. Policy choice by the winner

Attractive Features: - The model provides a nice conceptualization of representative democracies - It allows to deal with multidimensional policy spaces BUT: Multiplicity of equilibria BESLEY & COATE ’97: Main Features

The Model: Basic Settings  Society composed of N citizens, i ∈ N = {1,2,…,N}  x is the policy alternative (could be multidimensional)  Every individual i has her specific set of policy alternatives (e.g., because of different abilities). is the set of all possible alternatives.

 Every citizen i receives an utility V i (x,j) which depends on the policy implemented x and on the identity of the representative j (ideological element). j ∈ N ∪ {0}, where j = 0 means no representatives (i.e. no candidates)  To run for election a citizen has to pay a utility cost δ  The election among candidates follows majoritarian voting rules. When nobody runs the policy outcome is a default policy x 0. The Model: Basic Settings

 Political process in 3 stages: I. Citizens candidate themselves II. Election among candidates III. Policy choice To find an equilibrium of this game, we need to analyze these stages backward… The Model: Basic Settings

Stage III. The Policy Choice  Lack of commitment implies that the winning candidate implements her bliss point:  is the utility to agent j. if there is no candidate.

Stage II: Voting  Citizens choose whom to vote for from the set of candidates C ⊂ N, or to abstain.  α j ∈ C ∪ {0} denotes citizen j’s decision: α j = i → citizen j vote for candidate i α j = 0 → citizen j abstains  Vector of voting decision is α = (α 1,…, α N )  Set of winning candidate is W( C,α) and the number of elements in the set is # W( C,α)

 Probability that candidate i ∈ C wins is therefore:  Each citizen anticipates the policy that would be chosen by candidates and vote strategically to maximize her utility, given the votes of the other citizens: Stage II: Voting

 Equilibrium in this voting game is a voting profile, such that  j ∈ N : 1) 2) is not a weakly dominated strategy (see footnote 3) Stage II. Voting Equilibrium

Stage I: Entry  Entry decision is strategic. A candidate may enter the race to win, or to avoid another candidate to win  A pure strategy for candidate i is s i ∈ {0,1}, where 0 identifies “no entry” and 1 “entry”. A pure strategy profile is s = (s 1,…,s N )  Set of candidates is C (s) = {i ∣ s i = 1}  The entry decision depends on the future behavior of the citizens, denoted by  ( C ). [Optimal voting choices of citizens, as a function of the candidate set..]

 Expected payoff to a citizen i from a strategy profile s is: where: is the probability that the default policy is implemented and  is the entry cost Stage I: Entry

Stage I: Entry Equilibrium  To ensure that an equilibrium of the entry game exists we need to allow for mixed strategy.   i is the mixed strategy for citizen i: it represents the probability that she will run the election (  i ∈ [0,1]).  Then an equilibrium of the entry game given  (.) is a mixed strategy profile  = (  1,…,  N ) such that  i,  i is a best response to  -i given  (.)

Political Equilibrium  A political equilibrium is a vector of entry decision  and a vector of voting behavior  (.) such that: 1)  is an equilibrium of the entry game given  (.) 2) for all non-empty candidate set C,  (C) is a voting equilibrium  Pure & Mixed Strategies: We have a pure strategy political equilibrium if every citizen employs pure strategies at the entry stage.

Characterization of Pure Strategy Equilibria  s is a pure strategy equilibrium of the entry game given  (.) if and only if these two conditions are satisfied: 1)  i  C (s) i.e. candidate i must be willing to run given the other candidates 2)  i  C (s) i.e. the equilibrium is entry proof : given the set of candidates no other citizen is willing to enter

Definition: Sincere partition  Given a candidate set C, a partition of the electorate (N i ) i  C ∪{0} is sincere if and only if: 1) l  N i → v li ≥ v lj  j  C 2) l  N 0 → v li = v lj  i, j  C  Idea: this partition divides the citizens among the candidates so that every citizen is associated with her preferred candidate

 When do they arise? PROPOSITION 2. A political equilibrium in which citizen i runs unopposed exists if and only if 1) v ii – v i0 ≥ δ [she is better off entering and paying than with x 0 ] 2)  k  N /{i} such that #N k ≥ #N i for all sincere partitions (N i,N k,N 0 ), then ½(v kk – v ki ) ≤ δ if there exists a sincere partition such that #N i = #N k and (v kk – v ki ) ≤ δ otherwise. [no other citizen who would win the race has an incentive to enter]  Notice that if δ is particularly small condition 2) is satisfied if and only if citizen i’s policy choice is a Condorcet winner One-Candidate Equilibria

 When do they arise? PROPOSITION 3. Suppose that a political equilibrium exists in which citizens i and j run against each other. Then 1) there exists a sincere partition (N i,N j,N 0 ), such that #N i = #N j [both candidates have to stand some chance of winning or they would not run!] 2) ½(v ii – v ij ) ≥ δ and ½(v jj – v ji ) ≥ δ Furthermore, if N 0 = {l  N ∣ v li = v lj } and #N 0 +1 < #N i = #N j, then 1) and 2) are sufficient conditions for an equilibrium to exist in which i and j run against each other Two-Candidates Equilibria

 The last statement in the proposition is justified by the fact that a supporter of i (j) may prefer the entrant, but continue to vote for i (j) since she fears that her switch will cause j (i) to win. So an entrant could only obtain the votes of the abstained citizens, which are not enough, under this condition, to win  Problem: any pair of candidates splitting the voters evenly can be an equilibrium → too many equilibria! Two-Candidates Equilibria

Equilibria with three or more candidates  This framework allows such equilibria to arise. When? The following proposition provides the necessary conditions for a set of winning candidates: PROPOSITION 4 (about winning candidates) Let {s,α(.)} be a political equilibrium with # C (s) ≥ 3, and let Ŵ(s) = W( C (s), α( C (s) )) denote the set of winning candidates. If # Ŵ(s) ≥ 2, there must exist a sincere partition (N i ) i  Ŵ(s) ∪{0} for the candidate set Ŵ(s) such that 1) #N i = #N j for all i, j  Ŵ(s) 2) for all i  Ŵ(s)  l  N i [Every citizen has to vote for her most preferred among the winning candidates or she could change the outcome of the election by switching vote]

 The next proposition identifies the losing candidates: PROPOSITION 5 (about losing candidates) Let {s,α(.)} be a political equilibrium with # C (s) ≥ 3, and let Ŵ(s) = W( C (s), α( C (s) )) denote the set of winning candidates. Then, for each losing candidate j  C (s)  Ŵ(s), 1) W( C (s)  {j}, α( C (s)  {j}) )  Ŵ(s) 2) there exists k  C (s) such that  Intuition: for a citizen to run the election and not to stand a chance to win it, she has to be able to change the result of the election by running (1), and she has to be better off by changing it (2). Equilibria with three or more candidates

 “For those who would like a clean empirical prediction, our multiple equilibria will raise a sense of dissatisfaction.” (Besley and Coate 1997, p. 98)  Besley and Coate 1997: very strong and relevant theoretical paper. It provides a different and intuitive framework to think about representative democracies. Meaningful equilibria exist in circumstances where the Downsian framework fails to provide them (e.g. truly multidimensional policy spaces)  But what about empirical testing? A different version of the model, which mixes up the citizen candidate aspect with the probabilistic voting framework. Testing (a version of) the model…

 Idea: Only citizens belonging to political parties can run for elections. Candidates belonging to a given party share the same ideological position on the usual left-right cleavage.  However, party members differ on a second dimension, e.g. whether they are pro-life or pro-choice in the abortion issue, or whether they are pro-consumer or pro-firm in the regulation of utilities.  As a function of the salience of the two issues, parties choose the type of candidate on the second dimension that would maximize the expected payoff of party members.  Salience: an issue is said to be more salient than another one for a given citizen if departures from the bliss point on this issue are more costly than departures on the less salient one. Testing the model (cont.)

 Typically it is optimal for parties to cater to the tastes of citizens on the more salient issue. Hence citizens (especially in the presence of lobbies) happen not to get the (utilitarian) optimum on the less salient issue, because it is bundled with the more salient one.  Issue bundling: Each citizen has only one vote to cast, even if there are two issues on which the politician decides.  Issue unbundling: referenda are a way to unbundle the less salient issue from the more salient one (Besley and Coate, QJPS 2008). The same is true for those states in the U.S. where the regulator of public utilities (natural monopolies) is directly elected by citizens, instead of being appointed by the elected governor (Besley and Coate, JEEA 2003).  Empirical result: consumer prices in regulated utilities are lower in states that elect the regulator than in states where the governor appoints her. Testing the model (cont.)