This paper provides new foundations for Bayesian Decision Theory based on a representation theorem for preferences defined on a set of prospects containing both factual and conditional possibilities. This use of a rich set of prospects not only provides a framework within which the main theoretical claims of Savage, Ramsey, Jeffrey and others can be stated and compared, but also allows for the postulation of an extended Bayesian model of rational belief and desire from which they can be derived as (...) special cases. The main theorem of the paper establishes the existence of a such a Bayesian representation of preferences over conditional prospects, i.e. the existence of a pair of real-valued functions respectively measuring the agent’s degrees of belief and desire and which satisfy the postulated rationality conditions on partial belief and desire. The representation of partial belief is shown to be unique and that of partial desire, unique up to a linear transformation. (shrink)

Adams' famous thesis that the probabilities of conditionals are conditional probabilities is incompatible with standard probability theory. Indeed it is incompatible with any system of monotonic conditional probability satisfying the usual multiplication rule for conditional probabilities. This paper explores the possibility of accommodating Adams' thesis in systems of non-monotonic probability of varying strength. It shows that such systems impose many familiar lattice theoretic properties on their models as well as yielding interesting logics of conditionals, but that a standard complementation operation (...) cannot be defined within them, on pain of collapsing probability into bivalence. (shrink)

I show that David Lewis’s principal principle is not preserved under Jeffrey conditionalization. Using this observation, I argue that Lewis’s reason for rejecting the desire as belief thesis and Adams’s thesis applies also to his own principal principle. 1 Introduction2 Adams’s Thesis, the Desire as Belief Thesis, and the Principal Principle3 Jeffrey Conditionalization4 The Principal Principles Not Preserved under Jeffrey Conditionalization5 Inadmissible Experiences.

According to Stalnaker’s Hypothesis, the probability of an indicative conditional, $\Pr(\varphi \rightarrow \psi),$ equals the probability of the consequent conditional on its antecedent, $\Pr(\psi | \varphi)$ . While the hypothesis is generally taken to have been conclusively refuted by Lewis’ and others’ triviality arguments, its descriptive adequacy has been confirmed in many experimental studies. In this paper, we consider some possible ways of resolving the apparent tension between the analytical and the empirical results relating to Stalnaker’s Hypothesis and we argue (...) that none offer a satisfactory resolution. (shrink)