Computing Equilibrium Nominations in Presidential Elections

TL;DR

This paper introduces a new preference restriction called party-aligned single-peakedness in plurality elections, providing polynomial algorithms for recognizing such preferences and for analyzing candidate nominations and equilibria.

Contribution

It defines party-aligned single-peakedness, offers recognition algorithms, and analyzes candidate nomination and equilibrium existence in this domain.

Findings

Polynomial-time recognition of party-aligned single-peaked preferences.

Algorithms for candidate nomination and winner determination under this preference model.

Existence of pure Nash equilibria guaranteed for elections with up to three parties.

Abstract

We study strategic candidate nomination by parties in elections decided by Plurality voting. Each party selects a nominee before the election, and the winner is chosen from the nominated candidates based on the voters' preferences. We introduce a new restriction on these preferences, which we call party-aligned single-peakedness: all voters agree on a common ordering of the parties along an ideological axis, but may differ in their perceptions of the positions of individual candidates within each party. The preferences of each voter are single-peaked with respect to their own axis over the candidates, which is consistent with the global ordering of the parties. We present a polynomial-time algorithm for recognizing whether a preference profile satisfies party-aligned single-peakedness. In this domain, we give polynomial-time algorithms for deciding whether a given party can become the winner under some (or all) nominations, and whether this can occur in some pure Nash equilibrium. We also prove a tight result about the guaranteed existence of pure strategy Nash equilibria for elections with up to three parties for single-peaked and party-aligned single-peaked preference profiles.