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Extended Partial Orders: A Unifying Structure For Abstract Choice Theory

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  • Klaus Nehring
  • Clemens Puppe
  • Selva Demiralp

    (Department of Economics, University of California Davis)

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.

Suggested Citation

  • Klaus Nehring & Clemens Puppe & Selva Demiralp, 2003. "Extended Partial Orders: A Unifying Structure For Abstract Choice Theory," Working Papers 976, University of California, Davis, Department of Economics.
  • Handle: RePEc:cda:wpaper:97-6
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    Cited by:

    1. Andrikopoulos, Athanasios, 2009. "Szpilrajn-type theorems in economics," MPRA Paper 14345, University Library of Munich, Germany.
    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. Matthew Ryan, 2016. "Essentiality and Convexity in the Ranking of Opportunity Sets," Working Papers 2016-01, Auckland University of Technology, Department of Economics.

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