Utility Independence with Incomplete Product Sets.
Abstract
Suppose that u is a von Neumann-Morgenstern utility function on a consequence set T which is a subset of a product set A x X. Extending Keeney's definition, it will be said that X is utility independent of A if there are real valued functions f and g on A, with g positive, and a real valued function h on X such that u(a,x) = f(a) + g(a)h(x) for all (a,x) in T. Necessary and sufficient conditions for utility independence have been given by Robert Pollak and Ralph Keeney when T = A x X. The present paper investigates conditions for utility independence when T is an arbitrary subset of A x X. The strongest of three increasingly stronger conditions on preferences between gambles is shown to be necessary and sufficient for utility independence when T is finite. Examples are given to show that this condition is not generally sufficient when T is infinite.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1975
- Accession Number
- ADA015313
Entities
People
- Peter C. Fishburn
Organizations
- Pennsylvania State University