Nonconvergent Electoral Equilibria Under Scoring Rules: Beyond Plurality

39 Pages Posted: 11 Nov 2011 Last revised: 2 Jan 2013

See all articles by Dodge Cahan

Dodge Cahan

University of California, San Diego (UCSD)

Arkadii Slinko

University of Auckland - Department of Mathematics

John McCabe-Dansted

Independent

Date Written: November 10, 2011

Abstract

We use Hotelling's spatial model of competition to investigate the position-taking behaviour of political candidates under a class of electoral systems known as scoring rules. In a scoring rule election, voters rank all the candidates running for office, following which the candidates are assigned points according to a vector of nonincreasing scores. Convergent Nash equilibria in which all candidates adopt the same policy were characterised by Cox (1987). Here, we investigate nonconvergent equilibria, where candidates adopt divergent policies. We identify a number of classes of scoring rules exhibiting a range of different equilibrium properties. For some of these, nonconvergent equilibria do not exist. For others, nonconvergent equilibria in which candidates cluster at positions spread across the issue space are observed. In particular, we prove that the class of convex rules does not have Nash equilibria (convergent or nonconvergent) with the exception of some derivatives of Borda rule. Finally, we examine the special cases of four-, five- and six- candidate elections. In the former two cases, we provide a complete characterisation of nonconvergent equilibria.

Keywords: Nash equilibrium, scoring rule, political competition

JEL Classification: C7

Suggested Citation

Cahan, Dodge and Slinko, Arkadii and McCabe-Dansted, John, Nonconvergent Electoral Equilibria Under Scoring Rules: Beyond Plurality (November 10, 2011). Available at SSRN: https://ssrn.com/abstract=1957790 or http://dx.doi.org/10.2139/ssrn.1957790

Dodge Cahan

University of California, San Diego (UCSD) ( email )

9500 Gilman Drive
Mail Code 0502
La Jolla, CA 92093-0112
United States

Arkadii Slinko (Contact Author)

University of Auckland - Department of Mathematics ( email )

Auckland
New Zealand

John McCabe-Dansted

Independent ( email )

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
34
Abstract Views
505
PlumX Metrics