Constructive Decision Theory: Short Summary

Abstract

In almost all current approaches to decision making under uncertainty, it is assumed that a decision problem is described by a set of states and set of outcomes, and the decision maker (DM) has a preference relation on a rather rich set of acts, which are functions from states to outcomes. The standard representation theorems of decision theory give conditions under which the preference relation can be represented by a utility function on outcomes and numerical representation of beliefs on states. For example, Savage [4] shows that if a DM’s preference order satisfies certain axioms, then the DM’s preference relation can be represented by a probability Pr on the state space and a utility function mapping outcomes to the reals such that she prefers act a to act b iff the expected utility of a (with respect to Pr) is greater than that of b. Moreover, the probability measure is unique and the utility function is unique up to affine transformations. Similar representations of preference can be given with respect to other representations of uncertainty (see, for example, [2,5]).

This is a short summary of a paper written with Lawrence Blume and David Easley [1]. Work supported in part by NSF under grants ITR-0325453, and IIS-0534064, by ONR under grants N00014-00-1-03-41 and N00014-01-10-511, and by the DoD Multidisciplinary University Research Initiative (MURI) program administered by the ONR under grant N00014-01-1-0795.