This major work challenges some widely held positions in epistemology - those of Peirce and Popper on the one hand and those of Quine and Kuhn on the other.

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.

An examination of topics involved in statistical reasoning with imprecise probabilities. The book discusses assessment and elicitation, extensions, envelopes and decisions, the importance of imprecision, conditional previsions and coherent statistical models.

It is a commonplace that in making decisions agents often have to juggle competing values, and that no choice will maximise satisfaction of them all. However, the prevailing account of these cases assumes that there is always a single ranking of the agent's values, and therefore no unresolvable conflict between them. Isaac Levi denies this assumption, arguing that agents often must choose without having balanced their different values and that to be rational, an act does not have to be optimal, (...) only what Levi terms 'admissible'. This book explores the consequences of denying the assumption and develops a general approach to decision-making under unresolved conflict. Professor Levi discusses conflicts of value in several domains - those arising in moral dilemmas, the drawing of scientific inferences, decisions taken under uncertainty, and in social choice. In each of these he adapts his theoretical framework, showing how conflict may often be reduced though not always altogether eliminated. (shrink)

Acts are functions from states of nature into finite-support distributions over a set of ‘deterministic outcomes’. We characterize preference relations over acts which have a numerical representation by the functional J(f)=min>∫u∘ f dP¦PϵC where f is an act, u is a von Neumann-Morgenstern utility over outcomes, and C is a closed and convex set of finitely additive probability measures on the states of nature. In addition to the usual assumptions on the preference relation as transitivity, completeness, continuity and monotonicity, we (...) assume uncertainty aversion and certainty-independence. The last condition is a new one and is a weakening of the classical independence axiom: It requires that an act f is preferred to an act g if and only if the mixture of f and any constant act h is preferred to the same mixture of g and h. If non-degeneracy of the preference relation is also assumed, the convex set of priors C is uniquely determined. Finally, a concept of independence in case of a non-unique prior is introduced. (shrink)

We contrast three decision rules that extend Expected Utility to contexts where a convex set of probabilities is used to depict uncertainty: Γ-Maximin, Maximality, and E-admissibility. The rules extend Expected Utility theory as they require that an option is inadmissible if there is another that carries greater expected utility for each probability in a (closed) convex set. If the convex set is a singleton, then each rule agrees with maximizing expected utility. We show that, even when the option set is (...) convex, this pairwise comparison between acts may fail to identify those acts which are Bayes for some probability in a convex set that is not closed. This limitation affects two of the decision rules but not E-admissibility, which is not a pairwise decision rule. E-admissibility can be used to distinguish between two convex sets of probabilities that intersect all the same supporting hyperplanes. (shrink)