EXTENDED PARTIAL ORDERS: A UNIFYING STRUCTURE FOR ABSTRACT CHOICE THEORY

Klaus Nehring, Selva Demiralp and Clemens Puppe
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Clemens Puppe: Department of Economics, University of California Davis

No 91, Working Papers from University of California, Davis, Department of Economics

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.

Pages: 24
Date: 2003-01-07
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