Elections with Limited Information: A Multidimensional Model

We develop a game theoretic model of 2 candidate competition over a multidimensional policy space, where the participants have incomplete information about the preferences and strategy choices of other participants. The players consist of the voters and the candidates. Voters are partitioned into two classes, depending on the information they observe. Informed voters observe candidate strategy choices while uninformed voters do not. All players (voters and candidates alike) observe contemporaneous poll data broken down by various subgroups of the population. The main results of the paper give conditions on the number and distribution of the informed and uninformed voters which are sufficient to guarantee that any equilibrium (or voter equilibrium) extracts all information.