Nonconvergent Electoral Equilibria Under Scoring Rules: Beyond Plurality (original) (raw)
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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.
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Scoring Elimination Rules (SER), that give points to candidates according to their rank in voters' preference orders and eliminate the candidate(s) with the lowest number of points, constitute an important class of voting rules. This class of rules, that includes some famous voting methods such as Plurality Runoff or Coombs Rule, suffers from a severe pathology known as monotonicity paradox or monotonicity failure, that is, getting more points from voters can make a candidate a loser and getting fewer points can make a candidate a winner. In this paper, we study three-candidate elections and we identify, under various conditions, which SER minimizes the probability that a monotonicity paradox occurs. We also analyze some strategic aspects of these monotonicity failures. The probability model on which our results are based is the Impartial Anonymous Culture condition, often used in this kind of study. 1 See also Miller (2012) for a (more or less) real-world example. second round is organized which confronts the two candidates with the highest number of votes in the first round and the one who obtains the majority of votes wins. Suppose there are 127 voters whose rankings of the three candidates, a, b and c, are as follows:
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Introduction In many real-life collective decision making situations, the set of candidates (or alternatives) may vary while the voting process goes on, and may change at any time before the de-cision is final: some new candidates may join, whereas some others may ...
Electoral competition with policy-motivated candidates
Games and Economic Behavior, 2005
In the multi-dimensional spatial model of elections with two policy-motivated candidates, we prove that the candidates must adopt the same policy platform in equilibrium. Moreover, when the number of voters is odd, if the gradients of the candidates' utility functions point in different directions, then they must locate at some voter's ideal point and a strong symmetry condition must be satisfied: in particular, it must be possible to pair some voters so that their gradients point in exactly opposite directions. If the number of dimensions is more than two, then our condition is knife-edge. When the number of voters is even, the situation is worse: such equilibria never exist, regardless of the dimensionality of the policy space. 2005 Elsevier Inc. All rights reserved. JEL classification: D72; C72
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.