Desirability and social ranking

Michele Aleandri (), Felix Fritz () and Stefano Moretti ()
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Michele Aleandri: LUISS University
Felix Fritz: Université Paris-Dauphine, Université PSL
Stefano Moretti: Université Paris-Dauphine, Université PSL

Social Choice and Welfare, 2025, vol. 65, issue 3, No 9, 763 pages

Abstract: Abstract We present an axiomatic study of various solutions to the social ranking problem, where a solution links any ranking of coalitions of players to a binary relation between individual players. We focus on solutions that align with the desirability relation, asserting that player i is more desirable than player j if any coalition including i but not j ranks higher than the corresponding coalition formed by replacing i with j. Unlike previous characterizations, our study highlights the central role of the desirability property as a foundational axiom in the characterization of five solutions from the related literature: Ceteris Paribus majority, lexicographic excellence and its dual, $$L^{(1)}$$ L ( 1 ) solution and its dual. Our main results reveal additional similarities among these five solutions and emphasize the essential features that should be considered when selecting the most appropriate solution for a given scenario. A practical application involving a bicameral legislature is also presented.

Date: 2025
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DOI: 10.1007/s00355-025-01590-1

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