Characterizing and Reasoning about Probabilistic and Non-Probabilistic Expectation

Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the underlying representation of uncertainty. We give sound and complete axiomatizations for the logic in the case that the underlying representation is (a) probability, (b) sets of probability measures, (c) belief functions, and (d) possibility measures. We show that this logic is more expressive than the corresponding logic for reasoning about likelihood in the case of sets of probability measures, but equi-expressive in the case of probability, belief, and possibility. Finally, we show that satisfiability for these logics is NP-complete, no harder than satisfiability for propositional logic.Comment: To appear in Journal of the AC

A Single-Stage Approach to Anscombe and Aumann's Expected Utility

expected utility theory;decision analysis;revealed preference

A logic for reasoning about upper probabilities

We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization for the logic, and show that the satisfiability problem is NP-complete, no harder than satisfiability for propositional logic.Comment: A preliminary version of this paper appeared in Proc. of the 17th Conference on Uncertainty in AI, 200

A Single-Stage Approach to Anscombe and Aumann's Expected Utility

Anscombe and Aumann showed that if one accepts the existence of a physical randomizing device such as a roulette wheel then Savage's derivation of subjective expected utility can be considerably simplified. They, however, invoked compound gambles to define their axioms. We demonstrate that the subjective expected utility derivation can be further simplified and need not invoke compound gambles. Our simplification is obtained by closely following the steps by which probabilities and utilities are elicited

The conjoint measurement problem

Call number: LD2668 .R4 1966 J7

Empirical Tests of Intransitivity Predicted by Models of Risky Choice

Recently proposed models of risky choice imply systematic violations of transitivity of preference. Five studies explored whether people show patterns of intransitivity predicted by four descriptive models. To distinguish ?true? violations from those produced by ?error,? a model was fit in which each choice can have a different error rate and each person can have a different pattern of true preferences that need not be transitive. Error rate for a choice is estimated from preference reversals between repeated presentations of the same choice. Results of five studies showed that very few people repeated intransitive patterns. We can retain the hypothesis that transitivity best describes the data of the vast majority of participants. --decision making,errors,gambling effect,reference points,regret,transitivity