Redoing the Foundations of Decision Theory

Lawrence E. Blume, Daid A. Easkey, and Joseph Y. Halpern

In almost all current approaches to decision making, it is assumed that a decision problem is described by a set of states and set of outcomes, and the decision maker (DM) has preferences over a rather rich set of acts, which are functions from states to outcomes. However, most interesting decision problems do not come with a state space and an outcome space. Indeed, in complex problems it is often far from clear what the state and outcome spaces would be. We present an alternate foundation for decision making, in which the primitive objects of choice are syntactic programs. A program can be given semantics as a function from states to outcomes, but does not necessarily have to be described this way. A representation theorem is proved in the spirit of standard representation theorems, showing that if the DM's preference relation on programs satisfies appropriate axioms, then there exist a set S of states, a set O of outcomes, a way of viewing program as functions from S to O, a probability on S, and a utility function on O, such that the DM prefers program a to program b if and only if the expected utility of a is higher than that of b. Thus, the state space and outcome space are subjective, just like the probability and utility; they are not part of the description of the problem.

Submitted: Mar 3, 2006

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