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The Ordinal Egalitarian Solution for Finite Choice Sets

Author

Listed:
  • Simon Wilkie
  • John P. Conley

Abstract

Rubinstein Safra and Thomson (1992) introduced the Ordinal Nash Bargaining Solution. They proved that Pareto Optimality, Ordinal Invariance, Ordinal Symmetry, and IIA characterize this solution. They restrict attention to a domain of social choice problem with an infinite set of basic alternatives. In this paper we show this restriction is necessary. More specifically, we demonstrate that no solution can satisfy their list of axioms on any finite domain nor even on the space of lotteries defined over a finite set of alternatives. We then introduce the Ordinal Egalitarian Bargaining Solution. We show both for a space of finite social choice problems and for the space of lotteries over a finite set of social alternatives, that this solution is characterized by the axioms of Pareto Optimality, Ordinal Invariance, Ordinal Symmetry, and Independence of Pareto Irrelevant Alternatives.

Suggested Citation

  • Simon Wilkie & John P. Conley, 2004. "The Ordinal Egalitarian Solution for Finite Choice Sets," Econometric Society 2004 North American Summer Meetings 662, Econometric Society.
  • Handle: RePEc:ecm:nasm04:662
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    More about this item

    Keywords

    ordinal solution; egalitarian; bargaining;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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