Great Expectations. Part I: On the Customizability of Generalized Expected Utility

Many different rules for decision making have been introduced in the literature. We present a single framework in which to study and compare these rules. This is done by defining expected utility with respect to general expectation structures, where a decision maker's beliefs are represented by plausibility measures and the decision maker's tastes are represented by general (i.e., not necessarily real-valued) utility functions. We call the resulting notion of expected utility <em>generalized EU</em> (GEU) and show that we can represent arbitrary preference relations on acts using GEU. We then show that each of Savage's postulates corresponds to an axiom on GEU. Thus, GEU can be customized to capture postulates of interest.