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Extended Partial Orders: A Unifying Structure For Abstract Choice Theory

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  • Klaus Nehring
  • Clemens Puppe

Abstract

The concept of a strict extended partial order (SEPO) has turned out to be very useful in explaining (resp. rationalizing) non-binary choice functions. The present paper provides a general account of the concept of extended binary relations, i.e., relations between subsets and elements of a given universal set of alternatives. In particular, we define the concept of a weak extended partial order (WEPO) and show how it can be used in order to represent rankings of opportunity sets that display a "preference for opportunities." We also clarify the relationship between SEPOs and WEPOs, which involves a non-trivial condition, called "strict properness." Several characterizations of strict (and weak) properness are provided based on which we argue for properness as an appropriate condition demarcating "choice based" preference.

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  • Klaus Nehring & Clemens Puppe, "undated". "Extended Partial Orders: A Unifying Structure For Abstract Choice Theory," Department of Economics 97-06, California Davis - Department of Economics.
    • Handle: RePEc:fth:caldec:97-06
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    File URL: http://www.econ.ucdavis.edu/working_papers/97-6.pdf
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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. Alcantud, J. C. R., 2002. "Non-binary choice in a non-deterministic model," Economics Letters, Elsevier, vol. 77(1), pages 117-123, September.
    3. Andrikopoulos, Athanasios, 2009. "Szpilrajn-type theorems in economics," MPRA Paper 14345, University Library of Munich, Germany.
    4. 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.
    5. Herden, Gerhard & Pallack, Andreas, 2002. "On the continuous analogue of the Szpilrajn Theorem I," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 115-134, March.
    6. Athanasios Andrikopoulos, 2017. "Generalizations of Szpilrajn's Theorem in economic and game theories," Papers 1708.04711, arXiv.org.

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