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Closure and Preferences

Author

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  • Christopher Chambers
  • Alan Miller
  • M. Bumin Yenmez

Abstract

We investigate the results of Kreps (1979), dropping his completeness axiom. As an added generalization, we work on arbitrary lattices, rather than a lattice of sets. We show that one of the properties of Kreps is intimately tied with representation via a closure operator. That is, a preference satis es Kreps' axiom (and a few other mild conditions) if and only if there is a closure operator on the lattice, such that preferences over elements of the lattice coincide with dominance of their closures. We tie the work to recent literature by Richter and Rubinstein (2015). Finally, we carry the concept to the theory of path-independent choice functions.

Suggested Citation

  • Christopher Chambers & Alan Miller & M. Bumin Yenmez, 2015. "Closure and Preferences," GSIA Working Papers 2015-E36, Carnegie Mellon University, Tepper School of Business.
    • Handle: RePEc:cmu:gsiawp:-942662566
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    Cited by:

    1. Chambers, Christopher P. & Miller, Alan D., 2018. "Benchmarking," Theoretical Economics, Econometric Society, vol. 13(2), May.
    2. Vladimir Danilov, 2022. "Complementary choice functions," Papers 2209.06514, arXiv.org.
    3. Brian Duricy, 2023. "Preferences on Ranked-Choice Ballots," Papers 2301.02697, arXiv.org.
    4. Hamed Hamze Bajgiran & Federico Echenique, 2022. "Closure operators: Complexity and applications to classification and decision-making," Papers 2202.05339, arXiv.org, revised May 2022.

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