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Different least square values, different rankings

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Author Info
Vincent Merlin () (CNRS and GEMMA, MRSH bureau 230, Université de Caen, Esplanade de la Paix, 14032 Caen Cedex, France)
Annick Laruelle () (Departamento de Fundamentos del Analisis Economico, Universidad de Alicante, Campus San Vicente, E-03071 Alicante, Spain)

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Abstract

The semivalues (as well as the least square values) propose different linear solutions for cooperative games with transferable utility. As a byproduct, they also induce a ranking of the players. So far, no systematic analysis has studied to which extent these rankings could vary for different semivalues. The aim of this paper is to compare the rankings given by different semivalues or least square values for several classes of games. Our main result states that there exist games, possibly superadditive or convex, such that the rankings of the players given by several semivalues are completely different. These results are similar to the ones D. Saari discovered in voting theory: There exist profiles of preferences such that there is no relationship among the rankings of the candidates given by different voting rules.

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Publisher Info
Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 19 (2002)
Issue (Month): 3 ()
Pages: 533-550
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Handle: RePEc:spr:sochwe:v:19:y:2002:i:3:p:533-550

Note: Received: 5 November 2000/Accepted: 12 February 2001
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  1. Federico Valenciano & Annick Laruelle, 2004. "A Critical Reappraisal Of Some Voting Power Paradoxes," Working Papers. Serie AD 2004-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
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