A Strategic Problem in Approval Voting

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Abstract

Problems of multi-candidate races in U.S. presidential elections—exemplified by Ralph Nader’s spoiler effect in 2000—motivated the modern invention and advocacy of approval voting; but it has not previously been recognized that the first four U.S. presidential elections (1788–1800) were conducted using a variant of approval voting. That experiment ended disastrously in 1800 with an infamous Electoral College tie between Thomas Jefferson and Aaron Burr. The tie, this paper shows, resulted less from miscalculation than from a strategic tension built into approval voting, which forces two leaders appealing to the same voters to play a game of Chicken. All outcomes are possible, but none is satisfactory- mutual cooperation produces a tie, while all-out competition degrades the system to single-vote plurality, which approval voting was designed to replace. In between are two Nash equilibria that give the advantage to whichever candidate enjoys an initial lead or, in the case of initial parity, to the candidate who is less cooperative and more treacherous.