Abstract:
In the paper, combinatorial theorems relating to the theory of social choice are obtained. These theorems describe general conditions under which the problem on the preserving the preference set D by an arbitrary aggregation rule f and the problem on the compatibility of the preference set D with a pair (f,C) can be reduced to similar problems for two specific aggregation rules: the majority rule maj and the “counting rhyme” rule cog. Results are obtained within the framework of clone approach in the theory of social choice proposed by S. Shelah and developed by the authors.
Keywords:
social choice theory, aggregation rule, preference set.
Citation:
N. L. Poliakov, M. V. Shamolin, “Reduction theorems in the social choice theory”, Geometry and Mechanics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 174, VINITI, Moscow, 2020, 46–51
\Bibitem{PolSha20}
\by N.~L.~Poliakov, M.~V.~Shamolin
\paper Reduction theorems in the social choice theory
\inbook Geometry and Mechanics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 174
\pages 46--51
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into567}
\crossref{https://doi.org/10.36535/0233-6723-2020-174-46-51}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4150660}
Linking options:
https://www.mathnet.ru/eng/into567
https://www.mathnet.ru/eng/into/v174/p46
This publication is cited in the following 2 articles:
N. L. Polyakov, M. V. Shamolin, “Ob odnom klasse nelokalnykh pravil agregirovaniya”, Tr. sem. im. I. G. Petrovskogo, 33, Izdatelstvo Moskovskogo universiteta, M., 2023, 271–288
A. V. Karpov, “Structured preferences: a literature survey”, Autom. Remote Control, 83:9 (2022), 1329–1354
Citation in format AMSBIB
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