### Halpern: Constructive Decision Theory

#### by Yang Liu

CUNY SEMINAR IN LOGIC AND GAMES

**Constructive decision theory: Decision theory with subjective states and outcomes
**Joe Halpern (Cornell)

February 15, 2013, 4 PM,

CUNY Mathematics Lounge, 4th floor

*Abstract.*The standard approach in decision theory (going back to Savage) is to place a preference order on acts, where an act is a function from states to outcomes. If the preference order satisfies appropriate postulates, then the decision maker can be viewed as acting as if he has a probability on states and a utility function on outcomes, and is maximizing expected utility. This framework 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. As I show, among other things, it provides an elegant solution to framing problems.

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