# Anonymity and Neutrality in Arrow's Theorem with Restricted Coalition Algebras

*H. Mihara*

Public Economics from EconWPA

**Abstract:**
In the very general setting of Armstrong (1980) for Arrow's Theorem, I show two results. First, in an infinite society, Anonymity is inconsistent with Unanimity and Independence if and only if a domain for social welfare functions satisfies a modest condition of richness. While Arrow's axioms can be satisfied, unequal treatment of individuals thus persists. Second, Neutrality is consistent with Unanimity (and Independence). However, there are both dictatorial and nondictatorial social welfare functions satisfying Unanimity and Independence but not Neutrality. In Armstrong's setting, one can naturally view Neutrality as a stronger condition of informational simplicity than Independence. {Keywords} Arrow impossibility theorem, informational simplicity, coalitions, Boolean algebras, ultrafilters.

**JEL-codes:** D71 (search for similar items in EconPapers)

**Date:** 1994-11-20, Revised 1998-09-07

**Note:** LaTeX2.09 file; Appeared in Social Choice and Welfare (1997) 14: 503--512

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**Related works:**

Journal Article: Anonymity and neutrality in Arrow's Theorem with restricted coalition algebras (1997)

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**Persistent link:** http://EconPapers.repec.org/RePEc:wpa:wuwppe:9411001

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