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Voter Priming Campaigns: Strategies, Equilibria, and Algorithms

Jonathan Shaki, Yonatan Aumann, Sarit Kraus

TL;DR

This paper studies how political campaigns allocate budgets across issues to prime voter salience under multi-issue, multi-party elections. It introduces a formal priming game with linear salience increases and probabilistic voter choices, then derives aggregated scores and several election settings: parliamentary (vote-share maximization) and presidential (winner-take-all) with three utility variants $u_{ind}$, $u_{plus}$, and $u_{max}$. The authors prove that parliamentary games always have a pure Nash equilibrium, and provide a linear-in-voter algorithm to compute it; in the two-candidate case, equilibria are pure and focused on a single issue. In contrast, presidential settings exhibit non-existence of equilibria in many variants, especially with secondary goals, though some cases (e.g., $u_{ind}$ with two candidates) admit best responses and equilibria. The results illuminate the tractability and limitations of equilibrium analysis in priming games and highlight directions for extending the model, such as diminishing returns on salience or coupling priming with candidate quality.

Abstract

Issue salience is a major determinant in voters' decisions. Candidates and political parties campaign to shift salience to their advantage - a process termed priming. We study the dynamics, strategies and equilibria of campaign spending for voter priming in multi-issue multi-party settings. We consider both parliamentary elections, where parties aim to maximize their share of votes, and various settings for presidential elections, where the winner takes all. For parliamentary elections, we show that pure equilibrium spending always exists and can be computed in time linear in the number of voters. For two parties and all settings, a spending equilibrium exists such that each party invests only in a single issue, and an equilibrium can be computed in time that is polynomial in the number of issues and linear in the number of voters. We also show that in most presidential settings no equilibrium exists. Additional properties of optimal campaign strategies are also studied.

Voter Priming Campaigns: Strategies, Equilibria, and Algorithms

TL;DR

This paper studies how political campaigns allocate budgets across issues to prime voter salience under multi-issue, multi-party elections. It introduces a formal priming game with linear salience increases and probabilistic voter choices, then derives aggregated scores and several election settings: parliamentary (vote-share maximization) and presidential (winner-take-all) with three utility variants , , and . The authors prove that parliamentary games always have a pure Nash equilibrium, and provide a linear-in-voter algorithm to compute it; in the two-candidate case, equilibria are pure and focused on a single issue. In contrast, presidential settings exhibit non-existence of equilibria in many variants, especially with secondary goals, though some cases (e.g., with two candidates) admit best responses and equilibria. The results illuminate the tractability and limitations of equilibrium analysis in priming games and highlight directions for extending the model, such as diminishing returns on salience or coupling priming with candidate quality.

Abstract

Issue salience is a major determinant in voters' decisions. Candidates and political parties campaign to shift salience to their advantage - a process termed priming. We study the dynamics, strategies and equilibria of campaign spending for voter priming in multi-issue multi-party settings. We consider both parliamentary elections, where parties aim to maximize their share of votes, and various settings for presidential elections, where the winner takes all. For parliamentary elections, we show that pure equilibrium spending always exists and can be computed in time linear in the number of voters. For two parties and all settings, a spending equilibrium exists such that each party invests only in a single issue, and an equilibrium can be computed in time that is polynomial in the number of issues and linear in the number of voters. We also show that in most presidential settings no equilibrium exists. Additional properties of optimal campaign strategies are also studied.

Paper Structure

This paper contains 33 sections, 37 theorems, 42 equations, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Summary of Results
  3. Related Work
  4. Model
  5. Parliamentary Elections
  6. Presidential Elections
  7. The Priming Game.
  8. Simplifications
  9. Parliamentary Elections
  10. Best Response Strategies
  11. Split investments.
  12. Nash Equilibrium
  13. Finding the Equilibrium.
  14. Algorithm 1: computing Nash equilibrium.
  15. Two Candidates
  16. ...and 18 more sections

Key Result

Lemma 1

When introducing an issue $0$ for which all candidates are ranked $0$ by all voters (i.e. $q^v_0(c) = 0$ for all $v \in V, c \in C$), the utilities of all candidates are identical whether they do not invest part of their budget or whether they invest it in issue $0$.

Theorems & Definitions (58)

  • Claim 1
  • Lemma 1
  • Theorem 1
  • Definition 2.1
  • Theorem 2
  • Theorem 3
  • Lemma 2
  • Lemma 3
  • proof
  • Proposition 1
  • ...and 48 more