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Here we show that by adding some desirable axioms to May\u2019s 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\n                    <jats:italic>spoiler effects<\/jats:italic>\n                    and the so-called\n                    <jats:italic>strong no show paradox<\/jats:italic>\n                    . 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\n                    <jats:italic>Minimax<\/jats:italic>\n                    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.\n                  <\/jats:p>","DOI":"10.1007\/s00355-025-01598-7","type":"journal-article","created":{"date-parts":[[2025,6,13]],"date-time":"2025-06-13T07:51:42Z","timestamp":1749801102000},"page":"395-422","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An extension of May\u2019s Theorem to three alternatives: axiomatizing Minimax voting"],"prefix":"10.1007","volume":"66","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6054-9052","authenticated-orcid":false,"given":"Wesley H.","family":"Holliday","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0751-9011","authenticated-orcid":false,"given":"Eric","family":"Pacuit","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,6,13]]},"reference":[{"issue":"3","key":"1598_CR1","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1016\/S0165-1765(02)00014-9","volume":"75","author":"A\u00e7an G\u00f6ksel","year":"2002","unstructured":"G\u00f6ksel A\u00e7an, Remzi Sanver M (2002) Another characterization of the majority rule. 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