Stability in electoral competition: A case for multiple votes

Abstract

It is well known that the Hotelling-Downs model generically fails to admit an equilibrium when voting takes place under the plurality rule ( Osborne, 1993). This paper studies the Hotelling-Downs model considering that each voter is allowed to vote for up to k candidates and demonstrates that an equilibrium exists for a non-degenerate class of distributions of voters' ideal policies - which includes all log-concave distributions - if and only if k≥ 2. That is, the plurality rule ( k= 1) is shown to be the unique k-vote rule which generically precludes stability in electoral competition. Regarding the features of k-vote rules' equilibria, first, we show that there is no convergent equilibrium and, then, we fully characterize all divergent equilibria. We study comprehensively the simplest kind of divergent equilibria (two-location ones) and we argue that, apart from existing for quite a general class of distributions when k≥ 2, they have further attractive properties - among others, they are robust to free-entry and to candidates' being uncertain about voters' preferences. © 2015 Elsevier Inc.