Subjective Expected Utility Theory with “Small Worlds”

We model the notion of a "small world" as a context dependent state space embedded into the "grand world". For each situation the decision maker creates a "small world" reflecting the events perceived to be relevant for the act under consideration. The "grand world" is represented by an event space which is a more general construction than a state space. We retain preference axioms similar in spirit to the Savage axioms and obtain, without abandoning linearity of expectations, a subjective expected utility theory which allows for an intuitive distinction between risk and uncertainty. We also obtain separation of subjective probability and utility as in the state space models.