This paper presents a multicandidate spatial model of probabilistic voting
in which voter utility functions contain a random element specific to each
candidate. The model assumes no abstentions, sincere voting, and the maximi
zation of expected vote by each candidate. We derive a sufficient condition
for concavity of the candidate expected vote function with which the exist
ence of equilibrium is related to the degree of voter uncertainty. We show
that, under concavity, convergent equilibrium exists at a "minimum-sum poin
t" at which total distances from all voter ideal points are minimized. We t
hen discuss the location of convergent equilibrium for various measures of
distance. In our examples, computer analysis indicates that non-convergent
equilibria are only locally stable and disappear as voter uncertainty incre
ases.