Social Choice and Welfare 55:243-253 (2020)

Authors
Wesley H. Holliday
University of California, Berkeley
Mikayla Kelley
Stanford University
Abstract
In Arrovian social choice theory assuming the independence of irrelevant alternatives, Murakami (1968) proved two theorems about complete and transitive collective choice rules that satisfy strict non-imposition (citizens’ sovereignty), one being a dichotomy theorem about Paretian or anti-Paretian rules and the other a dictator-or-inverse-dictator impossibility theorem without the Pareto principle. It has been claimed in the later literature that a theorem of Malawski and Zhou (1994) is a generalization of Murakami’s dichotomy theorem and that Wilson’s (1972) impossibility theorem is stronger than Murakami’s impossibility theorem, both by virtue of replacing Murakami’s assumption of strict non-imposition with the assumptions of non-imposition and non-nullness. In this note, we first point out that these claims are incorrect: non-imposition and non-nullness are together equivalent to strict non-imposition for all transitive collective choice rules. We then generalize Murakami’s dichotomy and impossibility theorems to the setting of incomplete social preference. We prove that if one drops completeness from Murakami’s assumptions, his remaining assumptions imply (i) that a collective choice rule is either Paretian, anti-Paretian, or dis-Paretian (unanimous individual preference implies noncomparability) and (ii) that adding proposed constraints on noncomparability, such as the regularity axiom of Eliaz and Ok (2006), restores Murakami’s dictator-or-inverse-dictator result.
Keywords social choice without Pareto  non-imposition   strict non-imposition  citizens’ sovereignty  Wilson’s Theorem  incomplete social preference  regularity  minimal comparability  asusuke Murakam
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 59,848
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Social Choice and the Arrow Conditions.Allan F. Gibbard - 2014 - Economics and Philosophy 30 (3):269-284.
Arrow's Decisive Coalitions.Wesley H. Holliday & Eric Pacuit - 2020 - Social Choice and Welfare 54:463–505.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Arrow's Decisive Coalitions.Wesley H. Holliday & Eric Pacuit - 2020 - Social Choice and Welfare 54:463–505.
Harsanyi's Social Aggregation Theorem and Dictatorship.Osamu Mori - 2003 - Theory and Decision 55 (3):257-272.
Arrow's Theorem in Judgment Aggregation.Franz Dietrich & Christian List - 2007 - Social Choice and Welfare 29 (1):19-33.
Why Arrow's Impossibility Theorem is Invalid.Sidney Gendin - 1994 - Journal of Social Philosophy 25 (1):144-159.
Factoring Out the Impossibility of Logical Aggregation.Philippe Mongin - 2008 - Journal of Economic Theory 141:p. 100-113.
Liberty, Preference, and Choice.Robert Sugden - 1985 - Economics and Philosophy 1 (2):213-229.

Analytics

Added to PP index
2020-01-15

Total views
7 ( #1,019,463 of 2,432,819 )

Recent downloads (6 months)
2 ( #294,235 of 2,432,819 )

How can I increase my downloads?

Downloads

My notes