A Possibility Theorem on Information Aggregation in Elections
Royal Holloway, University of London
16th August, 2016 (Tuesday) at 3:00 PM
Venue : Seminar Room (First Floor)
Department of Economics, Delhi School of Economics
All are cordially invited
We study aggregation of private information in large elections where all voters have the same preference. There are many states of the world, and each state is identified with a preference ranking over alternatives and a probability distribution over signals. Each voter draws his private signal independently from the said distribution conditional on the state. When there are two alternatives (say A and B), we obtain a simple condition that is necessary and sufficient for asymptotic aggregation of information: there should be a hyperplane in the simplex over signals that separates the conditional distributions in states where A is preferred from those in states where B is preferred. If this condition is satisfied, information is aggregated in an equilibrium sequence; and If the condition is violated, there exists no feasible strategy profile that aggregates information. While the hyperplane condition is satisfied only in special environments, it holds generically if the state space is discrete and the number of available signals is more than or equal to the number of states. The Condorcet Jury theorem is obtained as a special case of this theorem when there are only two states. In the case of more than two alternatives (say A1, A2, …An), we find that information is aggregated if, for each pair of alternatives Ai and Aj , there is a hyperplane on the simplex that separates the set of distributions for which Ai is preferred over Aj from those for which Aj is preferred over Ai.