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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 inexplaining (resp. rationalizing) non-binary choice functions. The present paper provides ageneral account of the concept of extended binary relations, i.e. relations between subsetsand elements of a given universal set of alternatives. In particular, we define the concept ofa weak extended partial order (WEPO) and show how it can be used in order to representrankings of opportunity sets that display a “preference for opportunities”. We also clarifythe 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 “choicebased” preference. Copyright Kluwer Academic Publishers 1998

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  • Klaus Nehring & Clemens Puppe, 1998. "Extended partial orders:A unifying structure for abstract choice theory," Annals of Operations Research, Springer, vol. 80(0), pages 27-48, January.
    • Handle: RePEc:spr:annopr:v:80:y:1998:i:0:p:27-48:10.1023/a:1018924200436
    DOI: 10.1023/A:1018924200436
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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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