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Orderings of Opportunity Sets

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  • 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 ’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.

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File URL: http://www.ecineq.org/milano/WP/ECINEQ2012-282.pdf
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Bibliographic Info

Paper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 282.

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Length: 17 pages
Date of creation: Dec 2012
Date of revision:
Handle: RePEc:inq:inqwps:ecineq2012-282

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Keywords: Hyper-relations; opportuntiy sets; preference for fl‡exibility.;

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  1. Puppe, Clemens, 1996. "An Axiomatic Approach to "Preference for Freedom of Choice"," Journal of Economic Theory, Elsevier, vol. 68(1), pages 174-199, January.
  2. repec:hal:cesptp:halshs-00203346 is not listed on IDEAS
  3. repec:hal:journl:halshs-00203346 is not listed on IDEAS
  4. Bernard Monjardet & Vololonirina Raderanirina, 2004. "Lattices of choice functions and consensus problems," Social Choice and Welfare, Springer, vol. 23(3), pages 349-382, December.
  5. 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).
  6. Clemens Puppe & Yongsheng Xu, 2010. "Essential alternatives and freedom rankings," Social Choice and Welfare, Springer, vol. 35(4), pages 669-685, October.
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