Subjective Expected Utility Theory with 'Small Worlds'

We introduce the notion of "small worlds" as context relevant state spaces which are distilled from a generalised event space. The basic idea is that the decision maker, for each group of related decisions, from the events in the "grand world" creates a "small world". Each small world reflects the events perceived to be relevant to the actions considered. Retaining preference axioms similar in spirit to the Savage axioms, we show that our use of "small worlds" contained in a more gen- eral event space naturally leads to a subjective expected utility theory which allows for an intuitive distinction between risk and uncertainty. In contrast to theories that rely on a standard state space formulation we capture both preferences for risk and uncertainty as local or context specific. We obtain simple numerical measures of risk and uncertainty aversion. We illustrate the use of the theory by revisiting the Ellsberg paradox.