On a Three-Alternative Condorcet Jury Theorem

19 Pages Posted: 27 May 2011

See all articles by Johanna Goertz

Johanna Goertz

University of Guelph

Francois Maniquet

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE)

Date Written: May 2011

Abstract

We investigate whether the simple plurality rule aggregates information efficiently in a large election with three alternatives. The environment is the same as in the Condorcet Jury Theorem (Condorcet (1785)). Voters have common preferences that depend on the unknown state of nature, and they receive imprecise private signals about the state of nature prior to voting. With two alternatives and strategic voters, the simple plurality rule aggregates information efficiently in elections with two alternatives (e.g., Myerson [1998]). We show that an efficient equilibrium always exists under the simple plurality rule when there are three alternatives as well. We characterize the set of inefficient equilibria with two alternatives and the condition under which they exist. There is only one type of inefficient equilibrium with two alternatives. In this equilibrium, voters vote unresponsively because they all vote for the same alternative. Under the same condition, the same type of equilibrium exists with three alternatives. However, we show that the number and types of coordination failures increase with three alternatives, and that this leads to the existence of other types of inefficient equilibria as well, including those in which voters vote informatively.

Keywords: efficient information aggregation, simple plurality rule, Poisson games, Condorcet Jury Theorem

JEL Classification: C720, D710, D720, D820

Suggested Citation

Goertz, Johanna and Maniquet, Francois, On a Three-Alternative Condorcet Jury Theorem (May 2011). CESifo Working Paper Series No. 3457, Available at SSRN: https://ssrn.com/abstract=1851325

Johanna Goertz (Contact Author)

University of Guelph ( email )

Guelph, Ontario
Canada

Francois Maniquet

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium
+32 10 474328 (Phone)
+32 10 474301 (Fax)

HOME PAGE: http://www.core.ucl.ac.be/staff/maniquetcore.htm

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