Seven independence concepts and continuous multiattribute utility functions

This paper examines seven independence concepts based on a preference relation on the set of simple probability measures defined on a set of multiattribute consequences. Three of the independence relations involve gambles and the other four are based on riskless preferences over the n-tuples in the consequence set. The main theorems state conditions under which one or more of the risky independence relations can be derived from a riskless independence relation in conjunction with other conditions. The other conditions include a risky independence condition which differs from the one(s) to be derived, the assumption that the consequence set is a convex subset of a finite-dimensional Euclidean space, and the assumption that the individual's von Neumann-Morgenstern utility function on the consequence set is continuous.