Aggregation mechanisms for surjective classifications are nearly dictatorial with high probability unless functions are nearly constant, with a full characterization of always-surjective mechanisms.
Arrow's Impossibility Theorem Without Unanimity
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abstract
Arrow's Impossibility Theorem states that any constitution which satisfies Transitivity, Independence of Irrelevant Alternatives (IIA) and Unanimity is a dictatorship. Wilson derived properties of constitutions satisfying Transitivity and IIA for unrestricted domains where ties are allowed. In this paper we consider the case where only strict preferences are allowed. In this case we derive a new short proof of Arrow theorem and further obtain a new and complete characterization of all functions satisfying Transitivity and IIA.
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2026 1verdicts
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Classification aggregation: a quantitative impossibility theorem
Aggregation mechanisms for surjective classifications are nearly dictatorial with high probability unless functions are nearly constant, with a full characterization of always-surjective mechanisms.