Representing subjective orderings of random variables: an extension

Subjective orderings on random variables are typically represented by an ex pectation functional, where a subjective probability measure is built using either Savage's original construction or some analogous model such as Ansc ombe and Aumann's. This amounts to assigning a projection functional onto t he one dimensional space of constants. Using this notion, we generalize the representation to partial preorders that can be represented by a condition al expectation, or in geometric terms, by a projection onto a probability s pace. Some interesting conclusions about the behavioral implications are dr awn and further extensions are proposed. (C) 2001 Elsevier Science B.V. All rights reserved.