I focus my discussion on the well-known Ellsberg paradox. I find good normative reasons for incorporating non-precise belief, as represented by sets of probabilities, in an Ellsberg decision model. This amounts to forgoing the completeness axiom of expected utility theory. Provided that probability sets are interpreted as genuinely indeterminate belief, such a model can moreover make the “Ellsberg choices” rationally permissible. Without some further element to the story, however, the model does not explain how an agent may come to have (...) unique preferences for each of the Ellsberg options. Levi holds that the extra element amounts to innocuous secondary “risk” or security considerations that are used to break ties when more than one option is rationally permissible. While I think a lexical choice rule of this kind is very plausible, I argue that it involves a greater break with xpected utility theory than mere violation of the ordering axiom. (shrink)

This paper contributes to a theory of rational choice for decision-makers with incomplete preferences due to partial ignorance, whose beliefs are representable as sets of acceptable priors. We focus on the limiting case of `Complete Ignorance' which can be viewed as reduced form of the general case of partial ignorance. Rationality is conceptualized in terms of a `Principle of Preference-Basedness', according to which rational choice should be isomorphic to asserted preference. The main result characterizes axiomatically a new choice-rule called `Simultaneous (...) Expected Utility Maximization'. It can be interpreted as agreement in a bargaining game (Kalai-Smorodinsky solution) whose players correspond to the (extremal) `acceptable priors' among which the decision maker has suspended judgment. An essential but non-standard feature of Simultaneous Expected Utility choices is their dependence on the entire choice set. This is justified by the conception of optimality as compromise rather than as superiority in pairwise comparisons. (shrink)

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.

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)

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)

This article examines Becker's thesis that the hypothesis that choices maximize expected utility relative to fixed and universal tastes provides a general framework for the explanation of behaviour. Three different models of preference revision are presented and their scope evaluated. The first, the classical conditioning model, explains all changes in preferences in terms of changes in the information held by the agent, holding fundamental beliefs and desires fixed. The second, the Jeffrey conditioning model, explains them in terms of changes in (...) both the information held by the agent and changes in her prior beliefs, holding her fundamental desires fixed. The final model, that of generalized conditioning, allows for explanations in terms of changes in the values of all three variables. Key Words: preference change • decision theory • probability • desirability • attitude change. (shrink)

... Press for their editorial perspicacity, to the National Institutes of Health for the partial financial support they gave me while I was writing some of the chapters, and to Donald Michie for suggesting the title Good Thinking.

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)