The Burr dilemma in approval voting

Abstract

The first four United States presidential elections employed a variant of approval voting, a system that culminated in a constitutional crisis following the 1800 electoral tie between Thomas Jefferson and Aaron Burr. This outcome was not a mere coordination failure but the result of the Burr Dilemma, a strategic tension inherent in approval-based balloting. When two candidates appeal to the same voter base, they face a game-theoretic “Chicken” scenario: while mutual approval maximizes the group’s chance of victory, it also risks a tie that denies either candidate a clear win. Conversely, if candidates encourage “bullet voting” to secure an individual advantage, they risk splitting the majority and allowing a less-preferred third candidate to prevail. This dilemma persists in modern approval voting applications, as ambitious leaders and disciplined voting blocs can trigger a retaliatory spiral of strategic truncation, effectively reducing the system to a single-vote plurality contest. Given these vulnerabilities, alternative reforms utilizing preferential ballots, such as the Alternative Vote or the Coombs rule, may provide more robust solutions. These instant-runoff methods better manage the trade-offs between individual ambition and collective success, offering greater resistance to the strategic instabilities that characterized the early American experiment. – AI-generated abstract.