Constructive decision theory

In most contemporary approaches to decision making under uncertainty, a decision problem is described by a set of states and set of outcomes, and a rich set of acts, which are functions from states to outcomes over which the decision maker (DM) has preferences. Many interesting decision problems, however, 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 alternative foundation for decision making, in which the primitive objects of choice are syntactic programs. A representation theorem is proved in the spirit of standard representation theorems, showing that if the DM's preference relation on objects of choice satisfies appropriate axioms, then there exist a set S of states, a set O of outcomes, a way of interpreting the objects of choice as functions from S to O, a probability on S, and a utility function on O, such that the DM prefers choice a to choice 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. In principle, a modeller can test for SEU behaviour without having access to states or outcomes. We illustrate the power of our approach by showing that it can capture decision makers who are subject to framing effects and those who are subject to failures of extensionality.