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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2020, Volume 174, Pages 46–51 (Mi into567)  

Reduction theorems in the social choice theory

N. L. Poliakova, M. V. Shamolinb

a Laboratory of algebraic geometry and its applications, National Research University "Higher School of Economics" (HSE), Moscow
b Lomonosov Moscow State University

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 $\mathcal{D}$ by an arbitrary aggregation rule $f$ and the problem on the compatibility of the preference set $\mathcal{D}$ with a pair $(f,\mathcal{C})$ 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

DOI: https://doi.org/10.36535/0233-6723-2020-174-46-51

Full text: PDF file (191 kB)
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Bibliographic databases:

UDC: 510.63
MSC: 91B14

Citation: N. L. Poliakov, M. V. Shamolin, “Reduction theorems in the social choice theory”, Geometry and Mechanics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 174, VINITI, Moscow, 2020, 46–51

Citation in format AMSBIB
\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. Ser. 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://www.ams.org/mathscinet-getitem?mr=4150660}


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