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The limitations of the Arrovian consistency of domains with a fixed preference

Nguyen, J; (2019) The limitations of the Arrovian consistency of domains with a fixed preference. Theory and Decision , 87 pp. 183-199. 10.1007/s11238-019-09702-x. Green open access

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Abstract

In this paper I investigate the properties of social welfare functions defined on domains where the preferences of one agent remain fixed. Such a domain is a degenerate case of those investigated, and proved Arrow consistent, by Sakai and Shimoji (Soc Choice Welf 26(3):435–445, 2006). Thus, they admit functions from them to a social preference that satisfy Arrow’s conditions of Weak Pareto, Independence of Irrelevant Alternatives, and Non-dictatorship. However, I prove that according to any function that satisfies these conditions on such a domain, for any triple of alternatives, if the agent with the fixed preferences does not determine the social preference on any pair of them, then some other agent determines the social preference on the entire triple.

Type: Article
Title: The limitations of the Arrovian consistency of domains with a fixed preference
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s11238-019-09702-x
Publisher version: https://doi.org/10.1007/s11238-019-09702-x
Language: English
Additional information: © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
Keywords: Social choice, Arrow, Fixed preferences, Restricted domains
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities > Dept of Philosophy
URI: https://discovery.ucl.ac.uk/id/eprint/10073193
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