An extension of May's Theorem to three alternatives: axiomatizing Minimax voting
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915260131180544 |
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| author | Holliday, Wesley H. Pacuit, Eric |
| author_facet | Holliday, Wesley H. Pacuit, Eric |
| contents | May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to May's axioms, we can uniquely determine how to vote on three alternatives (setting aside tiebreaking). In particular, we add two axioms stating that the voting method should mitigate spoiler effects and avoid the so-called strong no show paradox. We prove a theorem stating that any preferential voting method satisfying our enlarged set of axioms, which includes some weak homogeneity and preservation axioms, must choose from among the Minimax winners in all three-alternative elections. When applied to more than three alternatives, our axioms also distinguish Minimax from other known voting methods that coincide with or refine Minimax for three alternatives. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_14256 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An extension of May's Theorem to three alternatives: axiomatizing Minimax voting Holliday, Wesley H. Pacuit, Eric Theoretical Economics Computer Science and Game Theory Multiagent Systems 91B12, 91B14, 91B10 I.2.11 May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to May's axioms, we can uniquely determine how to vote on three alternatives (setting aside tiebreaking). In particular, we add two axioms stating that the voting method should mitigate spoiler effects and avoid the so-called strong no show paradox. We prove a theorem stating that any preferential voting method satisfying our enlarged set of axioms, which includes some weak homogeneity and preservation axioms, must choose from among the Minimax winners in all three-alternative elections. When applied to more than three alternatives, our axioms also distinguish Minimax from other known voting methods that coincide with or refine Minimax for three alternatives. |
| title | An extension of May's Theorem to three alternatives: axiomatizing Minimax voting |
| topic | Theoretical Economics Computer Science and Game Theory Multiagent Systems 91B12, 91B14, 91B10 I.2.11 |
| url | https://arxiv.org/abs/2312.14256 |