When winning is the only thing: pure strategy Nash equilibria in a three-candidate spatial voting model (original) (raw)

Three-Candidate Spatial Competition When Candidates Have Valence: Asymmetric Voter Density and Plurality Maximization

2010

We study the effects of stochastic (probabilistic) voting on equilibrium locations, equilibrium vote shares and comparative statics in a setup with three heterogenous candidates and a single-dimensional issue space. Comparing the equilibria with and without stochastic voting, we find that under an appropriate level of uncertainty about voter behavior, the model has a pure strategy Nash Equilibrium (PSNE) that is free from several non-plausible features of the PSNE under deterministic voting. The results are robust to extensions to asymmetric density and plurality maximization.

Three-candidate spatial competition when candidates have valence: stochastic voting

Public Choice, 2011

A survey of equilibrium analysis in spatial models of elections

2005

Elections, as the institution through which citizens choose their political agents, are at the core of representative democracy. It is therefore appropriate that they occupy a central position in the study of democratic politics. The formal analysis of elections traces back to the work of , who apply mathematical methods to understand the equilibrium outcomes of elections. This work, and the literature stemming from it, has focused mainly on the positional aspects of electoral campaigns, where we conceptualize candidates as adopting positions in a "space" of possible policies prior to an election. We maintain this focus by considering the main results for the canonical model of elections, in which candidates simultaneously adopt policy platforms and the winner is committed to the platform on which he or she ran. These models abstract from much of the structural detail of elections, including party primary elections, campaign finance and advertising, the role of interest groups, etc. Nevertheless, in order to achieve a deep understanding of elections in their full complexity, it seems that we must address the equilibrium effects of position-taking by candidates in elections.

Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections

Journal of Economic Theory, 2002

We prove that the support of mixed strategy equilibria of two-player, symmetric, zero-sum games lies in the uncovered set, a concept originating in the theory of tournaments and the spatial theory of politics. We allow for uncountably in…nite strategy spaces, and, as a special case, we obtain a longstanding claim to the same e¤ect, due to , in the political science literature. Further, we prove the non-emptiness of the uncovered set under quite general assumptions, and we establish, under various assumptions, the measurability and coanalyticity of this set. In the concluding section, we indicate how the inclusion result may be extended to multi-player, non-zero-sum games. . In fact, more is proved: show that the support of the mixed strategy equilibrium lies in the minimal covering set, a smaller set introduced by Dutta (1988) in the context of tournaments; Dutta and Laslier (1998) extend the minimal covering set to …nite, two-player, symmetric, zero-sum games and obtain the same inclusion.

Equilibrium in multicandidate probabilistic spatial voting

1999

This paper presents a multicandidate spatial model of probabilistic voting in which voter utility functions contain a random element specific to each candidate. The model assumes no abstentions, sincere voting, and the maximization of expected vote by each candidate. We derive a sufficient condition for concavity of the candidate expected vote function with which the existence of equilibrium is related to the degree of voter uncertainty. We show that, under concavity, convergent equilibrium exists at a "minimum-sum point" at which total distances from all voter ideal points are minimized. We then discuss the location of convergent equilibrium for various measures of distance. In our examples, computer analysis indicates that non-convergent equilibria are only locally stable and disappear as voter uncertainty increases. * Tse-min Lin thanks the Asian/Pacific Studies Institute and the Department of Political Science at Duke University for support of this research while he was visiting during fall, 1995. He also thanks Sarah M. Brooks, J. Matthew Wilson, Jinseog Yu, and especially Sean M. Keel and Gary W. Cox for helpful comments and advice on an earlier version of this paper.

Recognizing majority-rule equilibrium in spatial voting games

Social Choice and Welfare, 1991

It is provably difficult (NP-complete) to determine whether a given point can be defeated in a majority-rule spatial voting game. Nevertheless, one can easily generate a point with the property that if any point cannot be defeated, then this point cannot be defeated. Our results suggest that majority-rule equilibrium can exist as a purely practical matter: when the number of voters and the dimension of the policy space are both large, it can be too difficult to find an alternative to defeat the status quo. It is also computationally difficult to determine the radius of the yolk or the N a k a m u r a number of a weighted voting game.

Probabilistic Voting in the Spatial Model of Elections: The Theory of Office-motivated Candidates

Studies in Choice and Welfare, 2005

We unify and extend much of the literature on probabilistic voting in two-candidate elections. We give existence results for mixed and pure strategy equilibria of the electoral game. We prove general results on optimality of pure strategy equilibria vis-a-vis a weighted utilitarian social welfare function, and we derive the well-known "mean voter" result as a special case. We establish broad conditions under which pure strategy equilibria exhibit "policy coincidence," in the sense that candidates pick identical platforms. We establish the robustness of equilibria with respect to variations in demographic and informational parameters. We show that mixed and pure strategy equilibria of the game must be close to being in the majority rule core when the core is close to non-empty and voters are close to deterministic. This contraverts the notion that the median (in a one-dimensional model) is a mere "artifact." Using an equivalence between a class of models including the binary Luce model and a class including additive utility shock models, we then derive a general result on optimality vis-a-vis the Nash social welfare function.

A spatial model of political competition and proportional representation

Social Choice and Welfare, 1997

A spatial model of party competition is studied in which: (i) Parties are supposed to have ideology. By this we mean that their goal is to maximize the welfare of their constituencies. (ii) The policy implemented after the election does not need to coincide with the one proposed by the winner. The policy implemented should be a compromise that considers the proposals made by the different parties. In the case of proportional representation this compromise is modeled as a convex combination of the proposed policies with weights proportional to the number of votes obtained by each party. We provide some existence theorems and compare the equilibrium in our model with the equilibrium that exists under some probabilistic models. It is also shown that proportional representation will create incentives for the parties to announce radical platforms.

Voting Equilibria in Multi-candidate Elections

Journal of Public Economic Theory, 2009

We consider a general plurality voting game with multiple candidates, where voter preferences over candidates are exogenously given. In particular, we allow for arbitrary voter indifferences, as may arise in voting subgames of citizencandidate or locational models of elections. We prove that the voting game admits pure strategy equilibria in undominated strategies. The proof is constructive: we exhibit an algorithm, the "best winning deviation" algorithm, that produces such an equilibrium in finite time. A byproduct of the algorithm is a simple story for how voters might learn to coordinate on such an equilibrium.

When winning is the only thing: pure strategy Nash equilibria in a three-candidate spatial voting model (original) (raw)

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