Learning in Elections and Voter Turnout

Voter turnout in game theoretic models of voting has typically
been difficult to predict because of the problem of multiple
Nash equilibria (Palfrey and Rosenthal 1983, 1985).
Many of these equilibria require an extreme precision of beliefs
among voters that is unlikely to be reached in real elections.
At the same time, mechanisms like pre-election polls
exist to shape the beliefs of voters about expected turnout.
We combine these two features in a model of voter learning
in elections and characterize the asymptotically stable equilibria
of both complete and incomplete information games
in a simple symmetric setting with two candidates. We also
show how the model can be used to qualitatively explain
several phenomena observed in reality: increases in costs of
voting affect turnout adversely but there may be persistence
of turnout levels between elections even though costs and
other parameters change. Increase in uncertainty increases
turnout while increases in the size of the electorate decrease
it, in line with intuition.