EXTENDED PARTIAL ORDERS - A UNIFYING STRUCTURE FOR ABSTRACT CHOICE THEORY

The concept of a strict extended partial order (SEPO) has turned out t o be very useful in explaining (resp. rationalizing) non-binary choice functions. The present paper provides a general account of the concep t of extended binary relations, i.e, relations between subsets and ele ments of a given universal set of alternatives. In particular, we defi ne 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 d isplay a ''preference for opportunities''. We also clarify the relatio nship between SEPOs and WEPOs, which involves a non-trivial condition, called ''strict properness''. Several characterizations of strict (an d weak) properness are provided, based on which we argue for propernes s as an appropriate condition demarcating ''choice based'' preference.