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Hyper-relations, choice functions, and orderings of opportunity sets

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  • V. Danilov
  • G. Koshevoy
  • E. Savaglio

Abstract

We prove a coincidence of the class of multi-preference hyper-relations and the class of decent hyper-relations (DHR), that is the class of binary relations on opportunity sets satisfying monotonicity, no-dummy, stability with respect to contraction and extension, and the union property. We study subclasses of DHR. In order to pursue our analysis, we establish a canonical bijection between DHR and the class of no-dummy heritage choice functions. From this we obtain that the no-dummy heritage choice functions have multi-criteria rationalizations with reflexive binary relations. We also prove that the restriction of this bijection to two subclasses of DHR, namely the transitive decent hyper-relations, and the ample hyper-relations, is a bijection between these subclasses and the classes of closed no-dummy choice functions and no-dummy path-independent choice functions (Plott functions), respectively. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • V. Danilov & G. Koshevoy & E. Savaglio, 2015. "Hyper-relations, choice functions, and orderings of opportunity sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 51-69, June.
    • Handle: RePEc:spr:sochwe:v:45:y:2015:i:1:p:51-69
    DOI: 10.1007/s00355-014-0844-5
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    References listed on IDEAS

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    Cited by:

    1. Matthew Ryan, 2016. "Essentiality and Convexity in the Ranking of Opportunity Sets," Working Papers 2016-01, Auckland University of Technology, Department of Economics.
    2. Matthew Ryan, 2016. "Essentiality and convexity in the ranking of opportunity sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 853-877, December.
    3. Koshevoy, Gleb & Savaglio, Ernesto, 2023. "On rational choice from lists of sets," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    4. Gleb Koshevoy & Ernesto Savaglio, 2017. "Enveloped choice functions and path-independent rationality," Department of Economics University of Siena 765, Department of Economics, University of Siena.
    5. Alfio Giarlotta & Angelo Petralia & Stephen Watson, 2022. "Semantics meets attractiveness: Choice by salience," Papers 2204.08798, arXiv.org, revised Aug 2022.

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