Newcomb's problem and similar cases show the need to incorporate causal distinctions into the theory of rational decision; the usual noncausal decision theory, though simpler, does not always give the right answers. I give my own version of causal decision theory, compare it with versions offered by several other authors, and suggest that the versions have more in common than meets the eye.

Counterfactuals is David Lewis' forceful presentation of and sustained argument for a particular view about propositions which express contrary to fact conditionals, including his famous defense of realism about possible worlds and his theory of laws of nature.

At least one of these conceptions of probability underlies any theory of statistical inference (or, to use Neyman's phrase, 'inductive behavior'). ...

The approach to decision theory floated in my 1965 book is reviewed (I), challenged in various related ways (II–V) and defended, firstad hoc (II–IV) and then by a general argument of Ellery Ells's (VI). Finally, causal decision theory (in a version sketched in VII) is exhibited as a special case of my 1965 theory, according to the Eellsian argument.

"[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_.

After clarifying the probabilistic conception of causality suggested by Good (1961-2), Suppes (1970), Cartwright (1979), and Skyrms (1980), we prove a sufficient condition for transitivity of causal chains. The bearing of these considerations on the units of selection problem in evolutionary theory and on the Newcomb paradox in decision theory is then discussed.

In past years, the traditional Bayesian theory of rational decision making, based on subjective calculations of expected utility, has faced powerful attack from philosophers such as David Lewis and Brian Skyrms, who advance an alternative causal decision theory. The test they present for the Bayesian is exemplified in the decision problem known as 'Newcomb's paradox' and in related decision problems and is held to support the prescriptions of the causal theory. As well as his conclusions, the concepts and methods of (...) Professor Eells introduces in the course of his analyses have extensive implications, not solely for probability theorists narrowly conceived, but for economists, statisticians and psychologists concerned with decision making and the employment of Bayesian principles. They and their students will, in addition, find the early chapters of great use as a background and introduction to the subject as a whole. (shrink)

Finally, I examine Newcomb's paradox in detail and show that, contrary to what has generally been thought, one can consistently be both a conditional expected utility maximizer and a "two-boxer". ;An important by-product of my argument is a method of detecting a variety of an agent's causal beliefs--including those that are crucial to the alleged counterexamples--by facts about his subjective probabilities over propositions that do not involve causal concepts. The versatility of this method, together with a series of theorems I (...) prove relating conditional expected utility to K-expectation, is interpreted as indicating that PMCEU will prescribe the correct act in decision situations that are more complex than, but share some of the crucial causal features of, those of the original prima facie counterexamples. ;Recently a number of prima facie counterexamples to the Principle of Maximizing Conditional Expected Utility , all inspired by Newcomb's paradox, have been constructed. These involve decision situations that seem to establish a conflict between the Principle of Dominance and PMCEU and in which it seems that the former gives the correct prescription. Central to the alleged counterexamples is the observation that PMCEU seems not to be sensitive to causal beliefs of a certain kind that a decision-maker might have. ;I examine in detail and raise objections to two current solutions to the problem: namely, Skyrms' "K-expectation" approach and Gibbard and Harper's "U-maximization" approach. I then argue for a third approach that is immune to the objections I raise. Appealing to a more than usually detailed examination of the causal structure of the decision situations of the alleged counterexamples, I argue, in fact, that PMCEU really gives the correct prescriptions--indeed, the same given by the Principle of Dominance and by the rules proposed in Skyrms' and in Gibbard and Harper's solutions. (shrink)