Functional voting operators: The non-monotonic case
type: Item
instance of: scholarly article
title: Functional voting operators: The non-monotonic case
zbMATH Open document ID: 0791.90006
DOI: 10.1016/0165-4896(93)90004-3
author: John Duggan
author: Fuad T. Aleskerov
published in: Mathematical Social Sciences
publication date: 1993-01-01T00:00:00Z
full work available at URL: https://authors.library.caltech.edu/80752/
review text: We extend the non-binary framework of social choice introduced by \textit{M. A. Aizerman} and \textit{F. T. Aleskerov} [ibid. 11, 201-242 (1986; Zbl 0597.90006)], 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 theorem [see \textit{R. Wilson}, J. Econ. Theory 5, 478-486 (1972)].
Mathematics Subject Classification ID: 91B14
Mathematics Subject Classification ID: 91B12
zbMATH DE Number: 482254
zbMATH Keywords: functional voting operators
zbMATH Keywords: local operators
zbMATH Keywords: non-binary framework of social choice
zbMATH Keywords: non-monotonic operators
MaRDI profile type: Publication
OpenAlex ID: W2141902351
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description: scientific article; zbMATH DE number 482254