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Voter Priming Campaigns: Strategies, Equilibria, and Algorithms
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Studies equilibria of campaign spending for issue priming in multi-issue, multi-party elections, proving pure equilibria exist for parliamentary settings and two-candidate cases, and that some presidential variants lack equilibria.
Problem
Strategic campaign budget allocation across issues to shift issue salience (priming) among multiple competing candidates/parties in parliamentary and presidential elections, and whether equilibria exist and can be computed.
Approach
Models priming as linear salience increases from investment, aggregates voters into per-issue rank scores so that equilibria can be computed in time linear in voters, and studies a game-theoretic spending competition under several presidential utility variants (indicator, indicator plus fraction, max of indicator and fraction).
Key results
- In the parliamentary setting, a pure Nash equilibrium always exists and can be computed in time linear in the number of voters (exponential in issues and candidates in general).
- With two candidates, a pure equilibrium with each candidate investing its full budget in a single issue always exists, computable in O(|I|^2 + |V|) time.
- For presidential variants u_plus and u_max with three or more candidates, best responses (and hence Nash equilibria) need not exist; for u_ind a best response always exists but Nash existence is left open.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use parliamentary vote-share utility u_frac | Priming game · Parliamentary elections | pure Nash equilibrium existence | Helped |
| Restrict the parliamentary game to 2 candidates | u_frac priming game · Parliamentary elections, 2 candidates | focused pure Nash equilibrium existence | Helped |
| Use presidential utility u_plus, which includes vote share alongside winning | Priming game · Presidential elections, general case | Nash equilibrium existence | Hurt |
| Use presidential utility u_plus, which includes vote share alongside winning | Priming game · Presidential elections, general case | best-response existence | Hurt |
| Restrict the u_plus presidential game to 2 candidates | Priming game · Presidential elections, 2 candidates | focused pure Nash equilibrium existence | Helped |
| Use presidential utility u_max, taking the maximum of winning utility and vote share | Priming game · Presidential elections, general case | Nash equilibrium existence | Hurt |
| Use presidential utility u_max, taking the maximum of winning utility and vote share | Priming game · Presidential elections, general case | best-response existence | Mixed |
| Restrict the u_max presidential game to 2 candidates | Priming game · Presidential elections, 2 candidates | focused pure Nash equilibrium existence | Helped |
| Use presidential utility u_ind, based only on the victory indicator | Priming game · Presidential elections, general case | best-response existence | Helped |
| Restrict the u_ind presidential game to 2 candidates | Priming game · Presidential elections, 2 candidates | focused pure Nash equilibrium existence | Helped |
Surprising findings
- Under the pure-winning utility u_ind, Nash equilibria can be unnatural, with candidates investing against their own interest in issues where they are ranked low.
- Equilibria under the sole-goal presidential utility may require candidates to invest for the benefit of others.
Limitations
- Assumes linear salience response to investment, which implies focused (single-issue) investments and may not match real campaigns.
- Only considers priming, not persuasion or improving candidate quality per issue.
- Assumes large voter populations so that realized votes equal expectations.
Experimental setup
Metrics: utility of candidates vote share victory indicator
Builds on: spatial election models control by manipulation (priming) Nash's theorem
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