Existence of electoral equilibria with probabilistic voting (original) (raw)
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Wiley StatsRef: Statistics Reference Online, 2014
This paper is about game-theoretic models of electoral competitionwith an emphasis on models where there is probabilistic voting. Section 1 has (i) an example in which the voters' choices are assumed to be deterministic and (ii) an example in which the voters' choices are assumed to have probabilities that satisfy Luce's axiom of "independence from irrelevant alternatives". Section 2 has a more general model, which includes the two examples as special cases. Section 3 discusses some work that has been done on deterministic voting models. Section 4 discusses some work that has been done on probabilistic voting models. Forthcoming in: Methods and Applications of Statistics in the Social and Behavioral Sciences, Wiley
Unidimensional median voter results in probabilistic voting models
Economics Letters, 1984
This paper studies the policy outcomes that can be expected to occur when candidates are uncertain about voter behavior. Its analysis begins with an example that illustrates how the ' Comaner-Hinich effect' (i.e., the possibility of non-median outcomes) can occur under such circumstances. This example is then modified in ways which restore a median outcome. After this is done, the method of restoration is generalized to obtain a unidimensional median voter result for probabilistic voting models.
Davis-Hinich conditions and median outcomes in probabilistic voting models
Journal of Economic Theory, 1984
Recent work has established that, in general, median voter results do not hold when there is probabilistic voting. This has, quite naturally, led to the following question: When, under such circumstances, will median outcomes occur? In this paper, it is shown that directly generalizing certain conditions that have previously been shown to be sufficient for multidimensional median voter results in deterministic voting models leads to conditions that are, themselves, sufftcient for median outcomes in probabilistic voting models. This generalization includes both discrete and continuous distributions of voters. In addition, it also applies to both unidimensional and multidimensional policy spaces.
Probabilistic voting in models of electoral competition
Handbook of Social Choice and Voting
The pioneering model of electoral competition was developed by Harold Hotelling and Anthony Downs. The model developed by Hotelling and Downs and many subsequent models in the literature about electoral competition have assumed that candidates embody policies and, if a voter is not indifferent between the policies embodied by two candidates, then the voter's choices are fully determined by his preferences on possible polices. More specifically, those models have assumed that if a voter prefers the policies embodied by one candidate then the voter will definitely vote for that candidate. Various authors have argued that i) factors other than policy can affect a voter's decision and ii) those other factors cause candidates to be uncertain about who a voter will vote for. These authors have modeled the candidates' uncertainty by using a probabilistic description of the voters' choice behavior. This paper provides a framework that is useful for discussing the model developed by Hotelling and Downs and for discussing other models of electoral competition. Using that framework, the paper discusses work that has been done on the implications of candidates being uncertain about whom the individual voters in the electorate will vote for.
Probabilistic voting equilibria under alternative candidate payoff functions
2010
In this paper I analyze the equilibrium in a probabilistic voting model where the candidates have preferences other than the maximization of the expected number of votes or the probability of win maximization. I derive the comparative statics for two voters and one-dimensional policy space. Each voter cares about both the policy platform and the identity of the candidate. It is shown that an increase in the value of exactly one vote causes each candidate to choose a position closer to that of its partisan voter. Numeric computation of equilibria show that these results can be generalized to three or more voters.
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.
Social utility functions for strategic decisions in probabilistic voting models
Mathematical Social Sciences, 1983
This paper studies societies which have probabilistic voting that is smooth, scalable and unbiased. Its results establish that, in such societies, the decisions of vote-seeking candidates who start at a common location'(such as the status quo for the society's policies and/or the same allocation of campaign resources) contain implicit rationality properties. In particular, it shows that in every such society there exist social utility functions which simultaneously rationalize the directional Nash behavior of candidates, the stationary electoral equilibria, and the noadegenerate local electoral equilibria which can occur at these locations. This is shown to be true both for unconstrained and for constrained sets of possible candidate locations. An example of such a utility function (which occurs in every one of the societies under consideration) is also provided.
Consistent Voting Systems with a Continuum of Voters
Social Choice and Welfare, 2006
Voting problems with a continuum of voters and finitely many alternatives are considered. Since the Gibbard-Satterthwaite theorem persists in this model, we relax the non-manipulability requirement as follows: are there social choice functions (SCFs) such that for every profile of preferences there exists a strong Nash equilibrium resulting in the alternative assigned by the SCF? Such SCFs are called exactly and strongly consistent. The paper extends the work of Peleg (Econometrica 46:153-161, 1978a) and others. Specifically, a class of anonymous SCFs with the required property is characterized through blocking coefficients of alternatives and through associated effectivity functions.
Majority and Positional Voting in a Probabilistic Framework
The Review of Economic Studies, 1979
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