Hotelling-Downs competition when voters have an option to contest

Osborne shows that for almost all distributions of voters’preferences, a pure strategy Nash equilibrium does not existin the classical Hotelling–Downs model of electoral compe-tition with free entry. We show that equilibrium is gener-ically possible if in addition one allows voters an optionto announce their candidacy to compete side-by-side withoffice-seeking players. The model studied in this paper ren-ders Osborne and the celebrated citizen-candidate model`alaOsborne and Slivinski as two extreme cases. We char-acterize the equilibrium set with two central questions: (i)can there be equilibria where only voters contest? and (ii)are equilibria with contesting office-seeking players possi-ble? We also show that in our general setting, extremists aretypically voter-candidates so that in every two-party contest,office-seeking politicians stay out of competition.