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We study a spatial model of electoral competition among three office-motivated candidates of unequal valence (one advantaged and two equally disadvantaged candidates) under majority rule assuming that candidates are uncertain about the voters' policy preferences and that the policy space consists of three alternatives (one at each extreme of the linear policy spectrum and one in the center) and we characterize mixed strategy Nash equilibriums of the game. Counterintuitively, we show that (a) when uncertainty about voters' preferences is high, the advantaged candidate might choose in equilibrium a more extremist strategy than the disadvantaged candidates and that (b) when uncertainty about voters' preferences is low, there exist equilibriums in which one of the disadvantaged candidates has a larger probability of election than the disadvantaged candidate of the equivalent two-candidate (one advantaged and one disadvantaged candidate) case. Adapted from the source document.

AbstractWe study electoral competition under the so‐called Apostolic voting rule (AVR) in the framework of the Hotelling–Downs model (Osborne 1993). The AVR is a two‐stage election procedure composed of a voting stage and a lottery stage: the voters vote for the candidate they like best, and each of the two most‐voted candidates is elected with even probability. Under standard assumptions regarding the voters' preferences, we show that the AVR leads to a unique—up to permutations of the players' identities—equilibrium: only two candidates enter in the electoral race, and they choose distinct policy platforms. This is the first rule proven to support an essentially unique equilibrium in this popular model. Our analysis highlights that, as long as candidates do not compete for a single first place (as in standard plurality or runoff elections) but for a number of them (as under the AVR), strategic incentives alter dramatically and lead to stable and predictable configurations.

In this paper we consider a multi-party electoral competition model in which parties, which care both about implemented policy and their electoral performance, strategically promise a redistribution scheme while their social ideologies are considered to be known and fixed (differentiated parties). Voters, who differ both in income and in social ideologies, vote sincerely for the party that they cumulatively like the most (that is, taking into account both the redistribution scheme proposals and parties' social ideologies). Formal analysis of this game uncovers a moderates-vs-extremists equilibrium: parties with moderate social ideologies tend to favor generous redistribution in order to capture the votes of the poor majority, while parties with extremist social ideologies are more likely to be non-competitive in the economic dimension by proposing policies that do not reflect the interests of the poor. An implication of this result is that, ceteris paribus, an increase in income inequality should lead to an increase in the cumulative vote share of moderate parties and, hence, in a decrease in party-system fragmentation.

In this paper we consider a multi-party electoral competition model in which parties, which care both about implemented policy and their electoral performance, strategically promise a redistribution scheme while their social ideologies are considered to be known and fixed (differentiated parties). Voters, who differ both in income and in social ideologies, vote sincerely for the party that they cumulatively like the most (that is, taking into account both the redistribution scheme proposals and parties' social ideologies). Formal analysis of this game uncovers a moderates-vs-extremists equilibrium: parties with moderate social ideologies tend to favor generous redistribution in order to capture the votes of the poor majority, while parties with extremist social ideologies are more likely to be non-competitive in the economic dimension by proposing policies that do not reflect the interests of the poor. An implication of this result is that, ceteris paribus, an increase in income inequality should lead to an increase in the cumulative vote share of moderate parties and, hence, in a decrease in party-system fragmentation.