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A Note on Selecting Maximals in Finite Spaces

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  • García-Bermejo, Juan Carlos

    () (Departamento de Análisis Económico (Teoría e Historia Económica). Universidad Autónoma de Madrid.)

Abstract

Given a choice problem, the maximization rule may select many alternatives. In such cases, it is common practice to interpret that the final choice will end up being made by some random procedure, assigning to any maximal alternative the same probability of being chosen. However, there may be reasons based on the same original preferences for which it is suitable to select certain maximal alternatives over others. This paper introduces two choice criteria induced by the original preferences such that maximizing with respect to each of them may give a finer selection of alternatives than maximizing with respect to the original preferences. Those criteria are built by means of several preference relations induced by the original preferences, namely, two (weak) dominance relations, two indirect preference relations and the dominance relations defined with the help of those indirect preferences. It is remarkable that as the original preferences approach being complete and transitive, those criteria become both simpler and closer to such preferences. In particular, they coincide with the original preferences when these are complete and transitive, in which case they provide the same solution as those preferences.

Suggested Citation

  • García-Bermejo, Juan Carlos, 2012. "A Note on Selecting Maximals in Finite Spaces," Working Papers in Economic Theory 2012/06, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
    • Handle: RePEc:uam:wpaper:201206
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    File URL: http://www.uam.es/departamentos/economicas/analecon/especifica/mimeo/wp20126.pdf
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    References listed on IDEAS

    as
    1. Begoña Subiza & Josep Peris, 2000. "Choice Functions: Rationality re-Examined," Theory and Decision, Springer, vol. 48(3), pages 287-304, May.
    2. Susanne Fuchs-Seliger & Oliver Mayer, 2003. "Rationality without Transitivity," Journal of Economics, Springer, vol. 80(1), pages 77-87, August.
    3. Begoña Subiza & Josep Peris, 2005. "Strong maximals: Elements with maximal score in partial orders," Spanish Economic Review, Springer;Spanish Economic Association, vol. 7(2), pages 157-166, June.
    4. Begoña Subiza & Josep Peris, 2005. "Condorcet choice functions and maximal elements," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(3), pages 497-508, June.
    5. Fishburn, Peter C, 1991. "Nontransitive Preferences in Decision Theory," Journal of Risk and Uncertainty, Springer, vol. 4(2), pages 113-134, April.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    maximal elements; maximization; acyclical preferences; rational choice; choice function; refinements of maximization rule.;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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