Optimal voting schemes with costly information acquisition

A group of individuals with identical preferences must make a decision under uncertainty about which decision is best. Before the decision is made, each agent can privately acquire a costly and imperfect signal. We discuss how to design a mechanism for eliciting and aggregating the collected information so as to maximize ex-ante social welfare. We first show that, of all mechanisms, a sequential one is optimal and works as follows. At random, one agent at a time is selected to acquire information and report the resulting signal. Agents are informed of neither their position in the sequence nor of other reports. Acquiring information when called upon and reporting truthfully is an equilibrium. We next characterize the ex-ante optimal scheme among all ex-post efficient mechanisms. In this mechanism, a decision is made when the precision of the posterior exceeds a cut-off that decreases with each additional report. The restriction to ex-post efficiency is shown to be without loss when the available signals are sufficiently imprecise. On the other hand, ex-post efficient mechanisms are shown to be suboptimal when the cost of information acquisition is sufficiently small. ∗We are grateful for helpful discussions to Eddie Dekel, Jeff Ely, Tim Federsen, Dino Gerardi, Ali Hortacsu, Motty Perry, Rob Shimer, and Hugo Sonnenschein, Leeat Yariv, and especially to Phil Reny. We thank seminar participants at UCLA, University of Chicago, Iowa State University, Tel Aviv University, Hebrew University, Boston University, Northwestern, Queen’s University, Harvard, MIT, Stanford, Penn, NYU, and Wisconsin Madison for comments. †Adenauerallee 24-42, Bonn, 53113, Germany. Email: [email protected]. ‡1126 E. 59th Street, Chicago, IL 60657, USA. Email: [email protected].