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Functional Voting Operators: The Non-Monotonic Case

Aleskerov, Fuad and Duggan, John (1993) Functional Voting Operators: The Non-Monotonic Case. Social Science Working Paper, 858. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20170823-163016725

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Abstract

We extend the non-binary framework of social choice introduced by Aizerman and Aleskerov (1986) , in which individual choice functions are aggregated into a social choice function, by considering non-monotonic operators. We characterize the class of "local" operators and provide the explicit forms of local operators satisfying various combinations of normative and rationality conditions in the absence of monotonicity. Surprisingly, the restriction of monotonicity is not binding for operators satisfying the usual rationality conditions. We identify two rationality restrictions which do admit non-monotonic operators. One restriction admits every sovereign and neutral operator, and the other admits only dictatorship and anti-dictatorship operators. This last result is a direct non-binary counterpart to Wilson's (1972) theorem.


Item Type:Report or Paper (Working Paper)
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http://resolver.caltech.edu/CaltechAUTHORS:20170905-110801869Related ItemPublished Version
Additional Information:This paper was written during the first author's visit to the Division of the Humanities and Social Sciences at the California Institute of Technology. Partial financial support was received from the Caltech Laboratory for Experimental Economics and Political Science. Published as Aleskerov, Fuad, and John Duggan. "Functional voting operators: the non-monotonic case." Mathematical Social Sciences 26, no. 2 (1993): 175-201.
Group:Social Science Working Papers
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Funding AgencyGrant Number
Caltech Laboratory for Experimental Economics and Political ScienceUNSPECIFIED
Subject Keywords:Social choice; individual choice functions; local operators; voting operators; nonmonotonic operators
Series Name:Social Science Working Paper
Issue or Number:858
Record Number:CaltechAUTHORS:20170823-163016725
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170823-163016725
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80752
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:30 Aug 2017 18:42
Last Modified:03 Oct 2019 18:34

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