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Different least square values, different rankings

Author

Listed:
  • 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)

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.

Suggested Citation

  • Vincent Merlin & Annick Laruelle, 2002. "Different least square values, different rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 533-550.
    • 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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    Cited by:

    1. Annick Laruelle & Federico Valenciano, 2005. "A critical reappraisal of some voting power paradoxes," Public Choice, Springer, vol. 125(1), pages 17-41, July.

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