Two partition-theorems are proved for a particular causal decision theory. One is restricted to a certain kind of partition of circumstances, and analyzes the utility of an option in terms of its utilities in conjunction with circumstances in this partition. The other analyzes an option's utility in terms of its utilities conditional on circumstances and is quite unrestricted. While the first form seems more useful for applications, the second form may be of theoretical importance in foundational exercises. Comparisons are made (...) with theorems of Richard Jeffrey, Brad Armendt, and Peter Fishburn. (shrink)

In The Logic of Decision Richard Jeffrey defends a version of expected utility theory that advises agents to choose acts with an eye to securing evidence for thinking that desirable results will ensue. Proponents of "causal" decision theory have argued that Jeffrey's account is inadequate because it fails to properly discriminate the causal features of acts from their merely evidential properties. Jeffrey's approach has also been criticized on the grounds that it makes it impossible to extract a unique probability/utility representation (...) from a sufficiently rich system of preferences (given a zero and unit for measuring utility). The existence of these problems should not blind us to the fact that Jeffrey's system has advantages that no other decision theory can match: it can be underwritten by a particularly compelling representation theorem proved by Ethan Bolker; and it has a property called partition invariance that every reasonable theory of rational choice must possess. I shall argue that the non-uniqueness problem can be finessed, and that it is impossible to adequately formulate causal decision theory, or any other, without using Jeffrey's theory as one's basic analysis of rational desire. (shrink)

Richard Jeffrey long held that decision theory should be formulated without recourse to explicitly causal notions. Newcomb problems stand out as putative counterexamples to this ‘evidential’ decision theory. Jeffrey initially sought to defuse Newcomb problems via recourse to the doctrine of ratificationism, but later came to see this as problematic. We will see that Jeffrey’s worries about ratificationism were not compelling, but that valid ratificationist arguments implicitly presuppose causal decision theory. In later work, Jeffrey argued that Newcomb problems are not (...) decisions at all because agents who face them possess so much evidence about correlations between their actions and states of the world that they are unable to regard their deliberate choices as causes of outcomes, and so cannot see themselves as making free choices. Jeffrey’s reasoning goes wrong because it fails to recognize that an agent’s beliefs about her immediately available acts are so closely tied to the immediate causes of these actions that she can create evidence that outweighs any antecedent correlations between acts and states. Once we recognize that deliberating agents are free to believe what they want about their own actions, it will be clear that Newcomb problems are indeed counterexamples to evidential decision theory. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

I apply some of the lessons from quantum theory, in particular from Bell’s theorem, to a debate on the foundations of decision theory and causation. By tracing a formal analogy between the basic assumptions of causal decision theory (CDT)—which was developed partly in response to Newcomb’s problem— and those of a local hidden variable theory in the context of quantum mechanics, I show that an agent who acts according to CDT and gives any nonzero credence to some possible causal interpretations (...) underlying quantum phenomena should bet against quantum mechanics in some feasible game scenarios involving entangled systems, no matter what evidence they acquire. As a consequence, either the most accepted version of decision theory is wrong, or it provides a practical distinction, in terms of the prescribed behaviour of rational agents, between some metaphysical hypotheses regarding the causal structure underlying quantum mechanics. (shrink)

Causal decision theory (CDT) is the best theory of rational choice now available.2 I intend to provide some support for that claim in part I of this paper by responding to two criticisms of CDT. The first criticism says that CDT is superfluous, since it does no better in the problems that matter than does evidential decision theory (EDT) at recommending correct choices. A second criticism says that CDT by itself is flawed: according to this view, there are problems in (...) which CDT makes bad recommendations, unless it is supplemented with an additional deliberation mechanism, either involving metatickles or screening for ratifiable choices.3 I will argue in response to the first criticism that CDT is genuinely better than any EDT of the most sophisticated sort: there are problems where CDT gives better recommendations, and they are problems that do matter. (shrink)