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Sourav Bhattacharya, Ph.D.

University of Pittsburgh, USA

Authors: Paulo Barelli, Sourav Bhattacharya, and Lucas Siga

Abstract: We provide a simple condition that is both necessary and sufficient for aggregation of private information in large elections where all voters have the same preference. In some states of the world, all voters prefer alternative A; and in other states, all voters prefer alternative B; and A wins if the corresponding vote share is higher than a threshold. Each voter draws a private signal independently from a distribution conditional on the state. According to our condition, 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: even under incomplete information, the preferred outcome obtains with a very high ex-ante likelihood. If the hyperplane 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.

Full Text:  “A Possibility Theorem on Information Aggregation in Elections”