Robust Political Equilibria Under Plurality and Runoff Rule

IGIER Working Paper No. 288

37 Pages Posted: 6 Nov 2005

See all articles by Matthias Messner

Matthias Messner

University of Cologne

Mattias Polborn

Vanderbilt University - College of Arts and Science - Department of Economics; CESifo (Center for Economic Studies and Ifo Institute)

Date Written: April 2005

Abstract

A central problem for the game theoretic analysis of voting is that voting games have very many Nash equilibria. In this paper, we consider a new refinement concept for voting games that combines two ideas that appear reasonable for voting games: First, trembling hand perfection (voters sometimes make mistakes when casting their vote) and second, coordination of voters with similar interests. We apply this refinement to an analysis of multicandidate elections under plurality rule and runoff rule.

For plurality rule, we show that our refinement implies Duverger's law: In all equilibria, (at most) two candidates receive a positive number of votes. For the case of 3 candidates, we can completely characterize the set of equilibria. Often, there exists a unique equilibrium satisfying our refinement; surprisingly, this is even true, if there is no Condorcet winner. We also consider the equilibria under a runoff rule and analyze when plurality rule and runoff rule yield different outcomes.

Keywords: strategic voting, runoff rule, plurality rule, equilibrium refinement, trembling hand perfection, coalition-proofness

JEL Classification: D720

Suggested Citation

Messner, Matthias and Polborn, Mattias K., Robust Political Equilibria Under Plurality and Runoff Rule (April 2005). IGIER Working Paper No. 288, Available at SSRN: https://ssrn.com/abstract=838085 or http://dx.doi.org/10.2139/ssrn.838085

Matthias Messner (Contact Author)

University of Cologne ( email )

Albertus Magnus Platz
Cologne, NRW 50923
Germany

Mattias K. Polborn

Vanderbilt University - College of Arts and Science - Department of Economics ( email )

Box 1819 Station B
Nashville, TN 37235
United States

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

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