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Orderings of Opportunity Sets

Author

Listed:
  • Vladimir Danilov

    (Central Institute of Economics and Mathematics RAS, Moscow, Russia)

  • Gleb Koshevoy

    (Central Institute of Economics and Mathematics RAS, Moscow, Russia)

  • Ernesto Savaglio

    (ernesto@unich.it)

Abstract

We consider an extension of the class of multi-utility hyper-relations, the class of semi-decent hyper-relations. A semi-decent hyper-relation satis es monotonicity, stability with respect to contraction, and the union property. We analyze the class of semi-decent hyper-relations both associating them to an appropriate class of choice functions and considering decomposition of a decent relations via elementaryones. Doing so, we consider images in the set of choice functions of three subclasses of semi-decent hyper-relations: the decent hyper-relations, the transitive decent hyper-relations , and transitive decent hyper-relations which satisfy the condition LE of lattice equivalence. We prove that the image of the set of decent hyper-relations coincides with of the set of heritage choice functions; the image of the set of transitive decent hyper-relations coincides with the set of closed choice functions; the image of the set of transitive decent hyper-relations which satisfy the LE coincides with the set of Plott functions. We consider, for each of the above subclasses of hyper-relations, the problem of the decomposition of a given hyper-relation into elementaryones, namely the representation of a given hyper-relation as the intersection of elementaryones.

Suggested Citation

  • Vladimir Danilov & Gleb Koshevoy & Ernesto Savaglio, 2012. "Orderings of Opportunity Sets," Working Papers 282, ECINEQ, Society for the Study of Economic Inequality.
    • Handle: RePEc:inq:inqwps:ecineq2012-282
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    File URL: http://www.ecineq.org/milano/WP/ECINEQ2012-282.pdf
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    References listed on IDEAS

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    Cited by:

    1. Danilov, V., 2015. "Beyond Classical Rationality: Two-Stage Rationalization," Journal of the New Economic Association, New Economic Association, vol. 26(2), pages 12-35.

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    More about this item

    Keywords

    Hyper-relations; opportuntiy sets; preference for flexibility.;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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