Econometrica: Nov, 1979, Volume 47, Issue 6

Synopses in the Theory of Choice

https://doi.org/0012-9682(197911)47:6<1367:SITTOC>2.0.CO;2-A
p. 1367-1390

Alexander Van der Bellen, Murat R. Sertel

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.