Abstract
The probability of a given candidate winning a future election is worked out
in closed form as a function of (i) the current support rates for each
candidate, (ii) the relative positioning of the candidates within the political
spectrum, (iii) the time left to the election, and (iv) the rate at which noisy
information is revealed to the electorate from now to the election day, when
there are three or more candidates. It is shown, in particular, that the
optimal strategy for controlling information can be intricate and nontrivial,
in contrast to a two-candidate race. A surprising finding is that for a
candidate taking the centre ground in an electoral competition among a
polarised electorate, certain strategies are fatal in that the resulting
winning probability for that candidate vanishes identically.