Redoing the Foundations of Decision Theory:
Decision Theory with Subjective State Spaces
Joe Halpern
(Brown University)
February 1
Lubrano Conference Room

Abstract

The standard approach in decision theory (going back to Savage) is to place a preference order on acts, where an act as a function from states to outcomes. This implicitly assumes that the decision maker knows what the states and outcomes are. That isn't reasonable in a complex situation. For example, in trying to decide whether or not to attack Iraq, what are the states and what are the outcomes? We redo Savage viewing acts essentially as syntactic programs. We don't need to assume either states or outcomes. However, among other things, we can get representation theorems in the spirit of Savage's theorems; for Savage, the agent's probability and utility are subjective; for us, in addition to the probability and utility being subjective, so is the state space and the outcome space. I discuss the benefits, both conceptual and pragmatic, of this approach.

This is joint work with Larry Blume and David Easley. No prior knowledge of Savage's work is assumed.