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Orderings of Opportunity Sets

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Listed:
  • Vladimir Danilov

  • Gleb Koshevoy

  • Ernesto Savaglio

Abstract

We consider an extension of the class of multi-utility hyper-relations, the class of semidecent hyper-relations. A semi-decent hyper-relation satisfies 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 'elementary' ones. 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 `elementary' ones, namely the representation of a given hyper-relation as the intersection of `elementary'ones.

Suggested Citation

  • Vladimir Danilov & Gleb Koshevoy & Ernesto Savaglio, 2012. "Orderings of Opportunity Sets," Department of Economics University of Siena 660, Department of Economics, University of Siena.
    • Handle: RePEc:usi:wpaper:660
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    References listed on IDEAS

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    4. Caspard, N. & Monjardet, B., 2000. "The Lattice of Closure Systems, Closure Operators and Implicational Systems on a Finite Set : A Survey," Papiers d'Economie Mathématique et Applications 2000.120, Université Panthéon-Sorbonne (Paris 1).
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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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    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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