7. Voting with asymmetric information

The individuals in the models of voting in the previous chapters disagree about the desirability of the alternatives. The individuals in the models in this chapter differ in their information about the state of nature, which determines the desirability of each alternative. Some of them know the state, and some do not. Of the informed individuals, some (partisans) prefer one of the alternatives regardless of the state, while the remainder agree on the best alternative given the state. In an equilibrium under plurality rule, all the informed individuals vote, and the uninformed individuals vote in sufficient numbers to minimize the impact of the partisans' votes. Under unanimity rule, in an equilibrium all uninformed individuals vote for the non-default outcome, leaving the decision to the informed individuals. In a model in which every individual gets a signal about the state, but these signals vary in quality, an individual votes in equilibrium under plurality rule if and only if her signal quality is high. Under unanimity rule, each individual's voting for the alternative likely to be best according to her signal is not an equilibrium, because her vote makes a difference only if every other individual votes for the non-default alternative, which means that they all received signals that that alternative is best. So if everyone else votes for the alternative best according to her signal, and the number of individuals is large, the remaining individual should vote for the non-default alternative, regardless of her signal.