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Restricting the domain allows for weaker independence

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  • Justin Kruger
  • M. Remzi Sanver

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

Arrow’s classical axiom of independence of irrelevant alternatives may be more descriptively thought of as binary independence. This can then be weakened to ternary independence, quaternary independence, etc. It is known that under the full domain these are not real weakenings as they all collapse into binary independence (except for independence over the whole set of alternatives which is trivially satisfied). Here we investigate whether this still happens under restricted domains. We show that for different domains these different levels of independence may or may not be equivalent. We specify when and to what extent different versions of independence collapse into the same condition.
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Suggested Citation

  • Justin Kruger & M. Remzi Sanver, 2018. "Restricting the domain allows for weaker independence," Post-Print hal-02517236, HAL.
    • Handle: RePEc:hal:journl:hal-02517236
    DOI: 10.1007/s00355-018-1129-1
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    References listed on IDEAS

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    1. Blau, Julian H, 1971. "Arrow's Theorem with Weak Independence," Economica, London School of Economics and Political Science, vol. 38(152), pages 413-420, November.
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    6. Ugur Ozdemir & M. Sanver, 2007. "Dictatorial domains in preference aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 61-76, January.
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    Keywords

    arrow; social welfare;

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