Optimal voting schemes with costly information acquisition

doi:10.1016/j.jet.2008.02.004

Journal of Economic Theory

Volume 144, Issue 1, January 2009, Pages 36-68

https://doi.org/10.1016/j.jet.2008.02.004 Get rights and content

Abstract

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.

References (24)

D. Gerardi et al.
Information acquisition in committees
Games Econ. Behav.
(2008)
C. Martinelli
Would rational voters acquire costly information?
J. Econ. Theory
(2006)
R.B. Myerson
Optimal coordination mechanisms in generalized principal-agent problems
J. Math. Econ.
(1982)
D. Austen-Smith et al.
Information aggregation, rationality, and the Condorcet Jury Theorem
Amer. Polit. Sci. Rev.
(1996)
D. Austen-Smith, T. Feddersen, The inferiority of deliberation under unanimity rule, Amer. Polit. Sci. Rev., in...
D. Bergemann et al.
Information acquisition and efficient mechanism design
Econometrica
(2002)
H. Cai, Costly participation and heterogeneous preferences in informational committees, Discussion Paper 257, UCLA...
M. Chwe
Minority voting rights can maximize majority welfare
Amer. Polit. Sci. Rev.
(1999)
J. Cremer et al.
Full extraction of the surplus in Bayesian and dominant strategy auctions
Econometrica
(1988)
M.H. DeGroot
Optimal Statistical Decisions
(1970)

E. Dekel et al.

Sequential voting procedures in symmetric binary elections

J. Polit. Economy

(2000)

T.J. Feddersen et al.

The swing voter's curse

Amer. Econ. Rev.

(1996)

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Optimal voting schemes with costly information acquisition

Abstract

Games Econ. Behav.

J. Econ. Theory

J. Math. Econ.

Information aggregation, rationality, and the Condorcet Jury Theorem

Amer. Polit. Sci. Rev.

Information acquisition and efficient mechanism design

Econometrica

Minority voting rights can maximize majority welfare