Abstract: The subjective expected utility (SEU) model rests on very strong assumptions about the consistency of decision making across a wide range of situations. The descriptive validity of these assumptions has been extensively challenged by behavioral psychologists during the last few decades, and the normative validity of the assumptions has also been reappraised by many statisticians, philosophers, and economists, motivating the development of more general utility theories and decision models. These generalized models are characterized by features such as imprecise probabilities, nonlinearly weighted probabilities, source-dependent risk attitudes, and state-dependent utilities, permitting the pattern of the decision maker’s behavior to change with the decision context and to perhaps satisfy the usual SEU assumptions only locally. Recent research in the emerging field of neuroeconomics sheds light on the physiological basis of decision making, the nature of preferences and beliefs, and interpersonal differences in decision competence. These findings do not necessarily invalidate the use of SEU-based decision analysis tools, but they suggest that care needs to be taken to structure preferences and to assess beliefs and risk attitudes in a manner that is appropriate for the decision and also for the decision maker. Key words: subjective probability, expected utility, non-expected utility, Savage's axioms, surething

Since utilities and probabilities jointly determine choices, event-dependent utilities complicate the elicitation of subjective event probabilities. However, for the usual purpose of obtaining the information embodied in agent beliefs, it is su#cient to elicit objective probabilities, i.e., probabilities obtained by updating a known common prior with that agent's further information. Bayesians who play a Nash equilibrium of a certain insurance game before they obtain relevant information will afterward act regarding lottery ticket payments as if they had event-independent risk-neutral utility and a known common prior. Proper scoring rules paid in lottery tickets can then elicit objective probabilities.

This paper presents a complete, choice-based, axiomatic Bayesian decision theory. It introduces a new choice set consisting of information-contingent plans for choosing actions and bets and subjective expected utility model with effect-dependent utility functions and action-dependent subjective probabilities which, in conjunction with the updating of the probabilities using Bayes ’ rule, gives rise to a unique prior and a set of action-dependent posterior probabilities representing the decision maker’s prior and posterior beliefs.