Martin Peterson

This up-to-date introduction to decision theory offers comprehensive and accessible discussions of decision-making under ignorance and risk, the foundations of utility theory, the debate over subjective and objective probability, Bayesianism, causal decision theory, game theory, and social choice theory. No mathematical skills are assumed, and all concepts and results are explained in non-technical and intuitive as well as more formal ways. There are over 100 exercises with solutions, and a glossary of key terms and concepts. An emphasis on foundational aspects of normative decision theory (rather than descriptive decision theory) makes the book particularly useful for philosophy students, but it will appeal to readers in a range of disciplines including economics, psychology, political science and computer science. • Has over 100 end of chapter review questions and exercises with solutions • Includes a chapter on how to draw a decision matrix • Explains the link between individual decision making, game theory and social choice theory Contents Preface; 1. Introduction; 2. The decision matrix; 3. Decisions under ignorance; 4. Decisions under risk; 5. Utility; 6. The mathematics of probability; 7. The philosophy of probability; 8. Why should we accept the preference axioms; 9. Causal vs. evidential decision theory; 10. Bayesian vs. non-Bayesian decision theory; 11. Game theory I: basic concepts and zero sum games; 12. Game theory II: nonzero sum and co-operative games; 13. Social choice theory; 14. Overview of descriptive decision theory; Appendix A. Glossary; Appendix B. Proof of the von Neumann-Morgenstern theorem; Further reading; Index.

Based on a modern reading of Aristotle’s theory of friendship, we argue that virtual friendship does not qualify as genuine friendship. By ‘virtual friendship’ we mean the type of friendship that exists on the internet, and seldom or never is combined with real life interaction. A ‘traditional friendship’ is, in contrast, the type of friendship that involves substantial real life interaction, and we claim that only this type can merit the label ‘genuine friendship’ and thus qualify as morally valuable. The upshot of our discussion is that virtual friendship is what Aristotle might have described as a lower and less valuable form of social exchange.

This article seeks to contribute to the discussion on the nature of choice in virtue theory. If several different actions are available to the virtuous agent, they are also likely to vary in their degree of virtue, at least in some situations. Yet, it is widely agreed that once an action is recognised as virtuous there is no higher level of virtue. In this paper we discuss how the virtue theorist could accommodate both these seemingly conflicting ideas. We discuss this issue from a modern Aristotelian perspective, as opposed to a purely exegetic one. We propose a way of resolving what seems to be a major clash between two central features of virtue ethics. Our proposal is based on the notion of parity, a concept which recently has received considerable attention in the literature on axiology. Briefly put, two alternatives are on a par (or are ‘roughly equal’) if they are comparable, although it is not the case that one is better than the other, nor that they are equally good. The advantages of applying the concept of parity to our problem are twofold. Firstly, it sheds new light on the account of choice in virtue theory. Secondly, some of the criticisms that have been mounted against the possibility of parity can be countered by considering the notion of choice from a virtue theory perspective

Some philosophers believe that two objects of value can be ‘roughly equal’, or ‘on a par’, or belong to the same ‘clump’ of value in a sense that is fundamentally different from that in which some objects are ‘better than’, ‘worse than’, or ‘equally as good as’ others. This article shows that if two objects are on a par, or belong to the same clump, then an agent accepting a few plausible premises can be exploited in a money-pump. The central premise of the argument is that value is choice-guiding. If one object is more valuable than another, then it is not permitted to choose the less valuable object; and if two objects are equally valuable it is permitted to choose either of them; and if two objects are on a par or belong to the same clump it is also permitted to choose either of them.

This article argues that, contrary to the received view, prioritarianism and egalitarianism are not jointly incompatible theories in normative ethics. By introducing a distinction between weighing and aggregating, the authors show that the seemingly conflicting intuitions underlying prioritarianism and egalitarianism are consistent. The upshot is a combined position, equality-prioritarianism, which takes both prioritarian and egalitarian considerations into account in a technically precise manner. On this view, the moral value of a distribution of well-being is a product of two factors: the sum of all individuals' priority-adjusted well-being, and a measure of the equality of the distribution in question. Some implications of equality-prioritarianism are considered.

The main result of this paper is a formal argument for the principle of maximizing expected utility that does not rely on the law of large numbers. Unlike the well-known arguments by Savage and von Neumann & Morgenstern, this argument does not presuppose the sure-thing principle or the independence axiom. The principal idea is to use the concept of transformative decision rules for decomposing the principle of maximizing expected utility into a sequence of normatively reasonable subrules. It is shown that this procedure provides a resolution of Allais's paradox that cannot be obtained by Savage-style or von Neumann & Morgenstern-style arguments.

Consequentialism, one of the major theories of normative ethics, maintains that the moral rightness of an act is determined solely by the act's consequences and its alternatives. The traditional form of consequentialism is one-dimensional, in that the rightness of an act is a function of a single moral aspect, such as the sum total of wellbeing it produces. In this book Martin Peterson introduces a new type of consequentialist theory: multidimensional consequentialism. According to this theory, an act's moral rightness depends on several separate dimensions, including individual wellbeing, equality and risk. Peterson's novel approach shows that moral views about equality and risk that were previously thought to be mutually incompatible can be rendered compatible, and his precise theoretical discussion helps the reader to understand better the distinction between consequentialist and non-consequentialist theories. His book will interest a wide range of readers in ethics.

This article introduces and explores a distinction between multi-dimensional and one-dimensional consequentialist moral theories. One-dimensional consequentialists believe that an act's deontic status depends on just one aspect of the act, such as the sum total of wellbeing it produces, or the sum total of priority- or equality-adjusted wellbeing. Multi-dimensional consequentialists believe that an act's deontic status depends on more than one aspect. They may, for instance, believe that the sum total of wellbeing produced by an act and the degree to which the wellbeing is equally distributed in the population affect the act's deontic status independently of each other. These two aspects cannot be reduced into any single (composite) aspect. Wellbeing and equality are two separate considerations that cannot be merged into some novel entity that accurately reflects both intuitions. On the multi-dimensional view I defend, such clashes between separate aspects are irresolvable and are best accounted for by claiming that moral rightness and wrongness are non-binary concepts. Some acts are, literally speaking, a little bit right (because they maximise wellbeing) and a little bit wrong (because they do not maximise equality).1

Pure time preference is a preference for something to come at one point in time rather than another merely because of when it occurs in time. In opposition to Sidgwick, Ramsey, Rawls, and Parfit we argue that it is not always irrational to be guided by pure time preferences. We argue that even if the mere difference of location in time is not a rational ground for a preference, time may nevertheless be a normatively neutral ground for a preference, and this makes it plausible to claim that the preference is rationally permitted