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.