Abstract
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.
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