Speaker:     Matthew Ryan
Affiliation: Economics Department, The University of Auckland
Title:       Mixture Sets – An Introduction
Date:        Monday, 22 Jun 2009
Time:        3:00 pm
Location:    Room 401, Science Centre

A mixture set is an abstract convex structure introduced by Herstein and Milnor (Econometrica, 1953) as a foundation for the expected utility representation theorem (representation of preferernces by a linear utility function).  Mixture sets combine a set X with a ternary relation T that maps (x,y,t) to an element of X for each x,y in X and each t in [0,1] — the t-mixture of x and y.  Herstein and Milnor consider infinite mixture sets, but the notion is well-defined even for finite X.  This raises the question of the relationship between mixture sets and abstract convex geometries (discussed by Arkadii in previous Workshops).  It appears that neither is a special case of the other. This talk will introduce mixture sets, and what is — and isn’t — known about them.