Social Choice and Welfare 54:463–505 (2020)

Authors
Eric Pacuit
University of Maryland, College Park
Wesley H. Holliday
University of California, Berkeley
Abstract
In his classic monograph, Social Choice and Individual Values, Arrow introduced the notion of a decisive coalition of voters as part of his mathematical framework for social choice theory. The subsequent literature on Arrow’s Impossibility Theorem has shown the importance for social choice theory of reasoning about coalitions of voters with different grades of decisiveness. The goal of this paper is a fine-grained analysis of reasoning about decisive coalitions, formalizing how the concept of a decisive coalition gives rise to a social choice theoretic language and logic all of its own. We show that given Arrow’s axioms of the Independence of Irrelevant Alternatives and Universal Domain, rationality postulates for social preference correspond to strong axioms about decisive coalitions. We demonstrate this correspondence with results of a kind familiar in economics—representation theorems—as well as results of a kind coming from mathematical logic—completeness theorems. We present a complete logic for reasoning about decisive coalitions, along with formal proofs of Arrow’s and Wilson’s theorems. In addition, we prove the correctness of an algorithm for calculating, given any social rationality postulate of a certain form in the language of binary preference, the corresponding axiom in the language of decisive coalitions. These results suggest for social choice theory new perspectives and tools from logic.
Keywords social choice theory  Arrow's impossibility theorem  decisive coalitions  voting  independence of irrelevant alternatives
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: 59,700
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

No references found.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Independence of Irrelevant Alternatives Revisited.Susumu Cato - 2014 - Theory and Decision 76 (4):511-527.
Why Arrow's Impossibility Theorem is Invalid.Sidney Gendin - 1994 - Journal of Social Philosophy 25 (1):144-159.
Arrow's Theorem.Michael Morreau - 2014 - Stanford Encyclopedia of Philosophy: N/A.
Arrow’s Theorem and Theory Choice.Davide Rizza - 2014 - Synthese 191 (8):1-10.
Preference Aggregation.Paul Douglas Lyon - 1980 - Dissertation, Washington University
Arrow's Theorem in Judgment Aggregation.Franz Dietrich & Christian List - 2007 - Social Choice and Welfare 29 (1):19-33.

Analytics

Added to PP index
2019-11-10

Total views
14 ( #693,168 of 2,432,332 )

Recent downloads (6 months)
4 ( #170,320 of 2,432,332 )

How can I increase my downloads?

Downloads

My notes