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Orders on Subsets Rationalised by Abstract Convex Geometries

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Abstract

We find conditions on the order on subsets of a finite set which are necessary and sufficient for the relative ranking of any two subsets in this order to be determined by their extreme elements relative to an abstract convex geometry. It turns out that this question is closely related to the rationalisability of path independent choice functions by hyper-relations.

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Authors and Affiliations

  1. CIREQ/Département de sciences économiques, Université de Montréal, Montréal, Canada

    Walter Bossert

  2. Department of Economics, University of Auckland, Auckland, New Zealand

    Matthew J. Ryan

  3. Department of Mathematics, University of Auckland, Auckland, New Zealand

    Arkadii Slinko

Authors
  1. Walter Bossert
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  2. Matthew J. Ryan
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  3. Arkadii Slinko
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Correspondence to Arkadii Slinko.

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Bossert, W., Ryan, M.J. & Slinko, A. Orders on Subsets Rationalised by Abstract Convex Geometries. Order 26, 237–244 (2009). https://doi.org/10.1007/s11083-009-9121-0

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  • DOI: https://doi.org/10.1007/s11083-009-9121-0

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