Cеминар международного центра анализа и выбора решений

Arrow’s Theorem, May’s Axioms, and Borda’s Rule

Eric Maskin (Harvard University and HSE University)

We argue that Arrow’s (1951) independence of irrelevant alternatives condition (IIA) is unjustifiably stringent. Although, in elections, it has the desirable effect of ruling out spoilers (Candidate A spoils the election for B if B beats C when all voters rank A low, but C beats B when some voters rank A high - - A “siphons” off support from B), it is stronger than necessary for this purpose. Worse, it makes a voting rule insensitive to voters’ preference intensities. Accordingly, we propose a modified version of IIA to address these problems. Rather than obtaining an impossibility result, we show that a voting rule satisfies modified IIA, Arrow’s other conditions, and May’s (1952) axioms for majority rule if and only if it is the Borda count (Borda 1781), i.e., rank-order voting.

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