p.1367

Synopses in the Theory of Choice

Murat R. Sertel
Alexander Van der Bellen

Abstract

Defining a choice as a function which picks a subset of every set of alternatives, we consider a list of over thirty conditions (expressed as functional inequalities) which a choice may satisfy, demonstrating &-semilattices formed by certain sublists, thus summarily presenting as "synopses" all the implications obtaining between logical conjunctions formed within these sublists. The list studied includes many well known conditions, such as Plott's [13] path independence, for which we offer over a dozen new characterizations of various types.