Speaker: Matthew Ryan
Affiliation: The University of Auckland
Title: Path Independent Choice and the Ranking of Opportunity Sets
Date: Tuesday, 29 Mar 2011
Time: 4:00 pm
Location: Room 6115, Owen Glenn Building
An opportunity set is a non-empty subset of a given set X. A decision-maker, when confronted with an opportunity set, is allowed to choose one element from it.
We assume that the decision-maker has some reflexive and transitive ordering over opportunity sets. Such an ordering is called an “indirect utility ordering” if there
exists a weak order (preference relation) on X such that opportunity set A is weakly preferred to opportunity set B iff the most preferred element(s) from A∪B includes
at least one element of A. Necessary and sufficient conditions for an opportunity set ranking to be an indirect utility ordering are well-known (Kreps, 1979). We give
necessary and sufficient conditions for an ordering of opportunity sets to be consistent with a path independent choice function, or “Plott consistent”. That is, opportunity set A is weakly
preferred to opportunity set B iff the acceptable choice(s) from A∪B include at least one element of A. The proof employs results from the theory of abstract convex geometries.