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No-Envy, Efficiency, and Collective Rationality

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  • Sakamoto, Norihito

Abstract

We consider the problem of a fair collective choice function (fair CCF) which maps each profile of extended preference orderings into the set of fair social states (the set consists of alternatives which are both Pareto efficient and envy-free) when such a set exists. Our main objective is to examine compatibility of fair social choices with collective rationality. We formulate desirable properties of collective rationality, and look for CCFs satisfying them. Next, we show that there is no CCF that satisfies most of the choice-consistency properties and a simple concept of fairness simultaneously. Moreover, we reveal that there exists no collective choice function that selects efficient and envy-free states cannot be rationalized by a social preference relation.

Suggested Citation

  • Sakamoto, Norihito, 2011. "No-Envy, Efficiency, and Collective Rationality," Discussion Papers 2011-08, Graduate School of Economics, Hitotsubashi University.
  • Handle: RePEc:hit:econdp:2011-08
    Note: This Version: August, 2011
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    1. Diamantaras, Dimitrios & Thomson, William, 1990. "A refinement and extension of the no-envy concept," Economics Letters, Elsevier, vol. 33(3), pages 217-222, July.
    2. Marc Fleurbaey & Alain Trannoy, 2003. "The impossibility of a Paretian egalitarian," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 243-263, October.
    3. Tadenuma, Koichi, 2002. "Efficiency First or Equity First? Two Principles and Rationality of Social Choice," Journal of Economic Theory, Elsevier, vol. 104(2), pages 462-472, June.
    4. Goldman, Steven M. & Sussangkarn, Chal, 1978. "On the concept of fairness," Journal of Economic Theory, Elsevier, vol. 19(1), pages 210-216, October.
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