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)

"[This book] proposes new foundations for the Bayesian principle of rational action, and goes on to develop a new logic of desirability and probabtility."—Frederic Schick, _Journal of Philosophy_.

Within philosophy of action, there are three broad views about what, in addition to beliefs, answer the question of “what to do?” and so determine an agent’s motivation: desires, judgments about values/reasons, or states of the will, such as intentions. We argue that recent work in decision theory vindicates the volitionalist. “What to do?” isn’t settled by “what do I value” or “what reasons are there?” Rational motivation further requires determining how to trade off the possibility of a good outcome (...) against the possibility of a bad one—i.e., determining how much of a risk to take. The risk attitudes that embody this tradeoff seem best understood as intentions: as self-governing policies to weight desires or reasons in certain ways. That we need to settle our risk attitudes before making most decisions corroborates Bratman’s claim that self-governing policies are required for resolving impasses of evaluative and normative underdetermination. Moreover, far from being rare or confined to tie-breakings, cases that are underdetermined but for one’s risk attitudes are typical of everyday decision-making. The will is required for most rational action. (shrink)

This is the classic work upon which modern-day game theory is based. What began as a modest proposal that a mathematician and an economist write a short paper together blossomed, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry (...) it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. (shrink)

When making decisions, people naturally face uncertainty about the potential consequences of their actions due in part to limits in their capacity to represent, evaluate or deliberate. Nonetheless, they aim to make the best decisions possible. In Decision Theory with a Human Face, Richard Bradley develops new theories of agency and rational decision-making, offering guidance on how 'real' agents who are aware of their bounds should represent the uncertainty they face, how they should revise their opinions as a result of (...) experience and how they should make decisions when lacking full awareness of, or precise opinions on relevant contingencies. He engages with the strengths and flaws of Bayesian reasoning, and presents clear and comprehensive explorations of key issues in decision theory, from belief and desire to semantics and learning. His book draws on philosophy, economics, decision science and psychology, and will appeal to readers in all of these disciplines. (shrink)

According to the orthodox treatment of risk preferences in decision theory, they are to be explained in terms of the agent's desires about concrete outcomes. The orthodoxy has been criticised both for conflating two types of attitudes and for committing agents to attitudes that do not seem rationally required. To avoid these problems, it has been suggested that an agent's attitudes to risk should be captured by a risk function that is independent of her utility and probability functions. The main (...) problem with that approach is that it suggests that attitudes to risk are wholly distinct from people's (non-instrumental) desires. To overcome this problem, we develop a framework where an agent's utility function is defined over chance propositions (i.e., propositions describing objective probability distributions) as well as ordinary (non-chance) ones, and argue that one should explain different risk attitudes in terms of different forms of the utility function over such propositions. (shrink)

What value should we put on our chances of obtaining a good? This paper argues that, contrary to the widely accepted theory of von Neumann and Morgenstern, the value of a chance of some good G may be a nonlinear function of the value of G. In particular, chances may have diminishing marginal utility, a property that is termed chance uncertainty aversion. The hypothesis that agents are averse to uncertainy about chances explains a pattern of preferences often observed in the (...) Ellsberg paradox. While these preferences have typically been taken to refute Bayesian decision theory, it is shown that chance risk aversion is perfectly compatible with it. (shrink)

Chance Neutrality is the thesis that, conditional on some proposition being true, its chance of being true should be a matter of practical indifference. The aim of this article is to examine whether Chance Neutrality is a requirement of rationality. We prove that given Chance Neutrality, the Principal Principle entails a thesis called Linearity; the centerpiece of von Neumann and Morgenstern’s expected utility theory. With this in mind, we argue that the Principal Principle is a requirement of practical rationality but (...) that Linearity is not and, hence, that Chance Neutrality is not rationally required. (shrink)

Richard Jeffrey regarded the version of Bayesian decision theory he floated in ‘The Logic of Decision’ and the idea of a probability kinematics—a generalisation of Bayesian conditioning to contexts in which the evidence is ‘uncertain’—as his two most important contributions to philosophy. This paper aims to connect them by developing kinematical models for the study of preference change and practical deliberation. Preference change is treated in a manner analogous to Jeffrey’s handling of belief change: not as mechanical outputs of combinations (...) of intrinsic desires plus information, but as a matter of judgement and of making up one’s mind. In the first section Jeffrey’s probability kinematics is motivated and extended to the treatment of changes in conditional belief. In the second, analogous kinematical models are developed for preference change and in particular belief-induced change that depends on an invariance condition for conditional preference. The two are the brought together in the last section in a tentative model of pratical deliberation. (shrink)

A new explanation for the fairness of lotteries is presented. The explanation draws on elements of John Broome's and Richard Bradley's accounts, but is distinct from both of them. I start with Broome's idea that the fairness of lotteries has something to do with satisfying claims in a way which is proportional to their strength. I present an intuitive explication of.

Conditional attitudes are not the attitudes an agent is disposed to acquire in event of learning that a condition holds. Rather they are the components of agent's current attitudes that derive from the consideration they give to the possibility that the condition is true. Jeffrey's decision theory can be extended to include quantitative representation of the strength of these components. A conditional desirability measure for degrees of conditional desire is proposed and shown to imply that an agent's degrees of conditional (...) belief are conditional probabilities. Rational conditional preference is axiomatised and by application of Bolker's representation theorem for rational preferences it is shown that conditional preference rankings determine the existence of probability and desirability measures that agree with them. It is then proven that every conditional desirability function agrees with an agent's conditional preferences and, under certain assumptions, every desirability function agreeing with an agent's conditional preferences is a conditional desirability function agreeing with her unconditional preferences. (shrink)