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Good election rules with more than three candidates are Borda

2024/11/28 by Gabriel Gendler, Gendler, Gabriel
Health Professions · Social Sciences · #91B12 #91B14 #Combinatorics (math.CO) #European and International Law Studies #FOS: Mathematics #Health Services Management and Policy

paper · pdf · doi:10.48550/arxiv.2411.19407

openalex publication_date 2024/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Arrow proved that for three or more candidates, the IIA condition is enough to forbid all non-dictatorial election rules (or Social Welfare Functions). Maskin introduced the weaker MIIA condition, which permits the ``Borda'' election rules where each voter assigns points linearly to each candidate according to their order of preference. However, in previous work we demonstrated that there exist Social Welfare Functions between three candidates and satisfying the MIIA condition which are far from being Borda rules. We demonstrate that this phenomenon is unique to the case of three candidates. As soon as a fourth candidate is introduced, and indeed for any larger number of candidates, the only good election rules are the unweighted Borda rules.

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