Computing Equilibrium Nominations in Presidential Elections

2025-11-14

AI Summary

This paper studies strategic party nomination under majority rule: given partisan-aligned single-peaked preferences—where voters agree on a common ideological axis ordering parties but hold heterogeneous beliefs about intra-party candidate positions—we investigate whether a party can win via strategic nomination and whether pure-strategy Nash equilibria (PSNE) exist. We formally define this preference structure and provide a polynomial-time algorithm to verify it. We present the first exact characterization and efficient algorithm for determining PSNE existence in multi-party elections. Specifically, we prove that PSNE always exist in three-party elections and devise efficient algorithms to decide both whether a given party can secure victory and whether a PSNE exists. Our contributions are threefold: (i) introducing a novel preference model capturing inter-party alignment with intra-party heterogeneity; (ii) designing the first polynomial-time algorithm for PSNE existence testing in this setting; and (iii) establishing tight existence guarantees, thereby advancing the intersection of computational social choice and game theory.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

Application Category

• Economics, Online Markets and Human Computation: Economics and fairness of platforms and recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization

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.

Problem

• Studying strategic candidate nomination in plurality voting elections
• Analyzing party-aligned single-peaked voter preferences in elections
• Developing algorithms for equilibrium analysis in nomination games

Innovation

• Introduces party-aligned single-peakedness for voter preferences
• Provides polynomial-time algorithm to verify preference profile
• Develops polynomial-time algorithms for nomination equilibrium analysis