Large electorates and decisive minorities

There are many instances in which even in a democracy, the political preferences held by a minority of the electorate are reflected in political outcomes. It is sho\vn that for a simple two-alternative election environment characterized by costly voting and private information, when the expected population is very large the alternative preferred by more expected "zealous" voters, who have either large stakes in the outcome of the election or small costs of participating, wins with high probability in any equilibrium, even if the expected proportion of the entire electorate that shares that preference is arbitrarily small. This is an undesirable outcome under either of two natural but very different normative criteria.