## Abstract

We provide a new theory of expected utility with subjective events modeled by a lattice of projections. This approach allows us to capture the notion of a "small world" as a context dependent or local state space embedded into a subjective set of events, the "grand world". For each situation the decision makers' subjective "small world" reflects the events perceived to be relevant for the act under consideration. The subjective set of events need not be representable by a classical state space. Maintaining preference axioms similar in spirit to the classical axioms, we obtain an expected utility representation which is consistent across local state spaces and separates subjective probability and utility. An added benefit is that this alternative expected utility representation allows for an intuitive distinction between risk and uncertainty.

Original language | English |
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Pages (from-to) | 1-21 |

Number of pages | 21 |

Journal | Australian Journal of Mathematical Analysis and Applications |

Volume | 9 |

Issue number | 2 |

Publication status | Published - 2012 Nov 27 |

## Keywords

- Decision making under uncertainty
- Ellsberg's paradox
- Subjective events
- Subjective expected utility
- Uncertainty aversion

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics