Generalized medians and electoral competition with valence
| DOI | http://doi.org/10.1177/09516298221130265 |
| Published date | 01 January 2023 |
| Date | 01 January 2023 |
| Subject Matter | Articles |
Generalized medians and
electoral competition with
valence
Tasos Kalandrakis
Department of Political Science and Department of Economics,
University of Rochester, Rochester, NY, USA
Abstract
I establish conditions for existence of pure strategy equilibria in K-candidate Downsian electoral
competition (K ≥2) with valence when the voting rule is monotonic, generalizing existing results
to non-proper rules and possibly continuous electorates. The conditions are sufficient when K ≥2
and (essentially) necessary in the K =2 candidate case. They compare the size of one candidate’s
valence advantage to the radius of a generalized median pivotal ball (P-ball). I flesh out the differ-
ence of this generalized median with a recent alternative which, in turn, I characterize both on the
basis of a weaker median property and using pivotal hyperplanes.
Keywords
Electoral competition, generalized medians, valence
1. Introduction
Two-candidate electoral competition with Downsian candidates (Downs, 1957), majority
rule, and an electorate with Euclidean preferences has an equilibrium in pure strategies if
(and, essentially, only if) one candidate has a sufficiently large valence advantage
(Ansolabehere and Snyder, 2000). While the voting rule is typically resolute in this
setting,
1
other voting rules may not be requiring additional election stages if the first elect-
oral contest produces no winner. This is the case when a supermajority is required for one
of the candidates to win, as is provided for the election of a Pope in the papal conclave. In
Corresponding author:
Tasos Kalandrakis, Department of Political Science and Department of Economics, University of Rochester,
Rochester, NY, USA.
Email: kalandrakis@rochester.edu
Article
Journal of Theoretical Politics
2023, Vol. 35(1) 58–71
© The Author(s) 2022
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DOI: 10.1177/ 09516298221130265
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