Online research in philosophy

Nicholas Rescher claims that rational decision theory “may leave us in the lurch”, because there are two apparently acceptable ways of applying “the standard machinery of expected-value analysis” to his Dr. Psycho paradox which recommend contradictory actions. He detects a similar contradiction in Newcomb’s problem. We consider his claims from the point of view of both Bayesian decision theory and causal decision theory. In Dr. Psycho and in Newcomb’s Problem, Rescher has used premisses about probabilities which he assumes to be independent. From the former point of view, we show that the probability premisses are not independent but inconsistent, and their inconsistency is provable within probability theory alone. From the latter point of view, we show that their consistency can be saved, but then the contradictory recommendations evaporate. Consequently, whether one subscribes to evidential or causal decision theory, rational decision theory is not in any way vitiated by Rescher’s arguments.

A theory of evidential probability is developed from two assumptions:(1) the evidential probability of a proposition is its probability conditional on the total evidence;(2) one's total evidence is one's total knowledge. Evidential probability is distinguished from both subjective and objective probability. Loss as well as gain of evidence is permitted. Evidential probability is embedded within epistemic logic by means of possible worlds semantics for modal logic; this allows a natural theory of higher-order probability to be developed. In particular, it is emphasized that it is sometimes uncertain which propositions are part of one's total evidence; some surprising implications of this fact are drawn out.

Probabilistic accounts of causality have long had trouble with ‘spurious’ evidential correlations. Such correlations are also central to the case for causal decision theory—the argument that evidential decision theory is inadequate to cope with certain sorts of decision problem. However, there are now several strong defences of the evidential theory. Here I present what I regard as the best defence, and apply it to the probabilistic approach to causality. I argue that provided a probabilistic theory appeals to the notions of agency and effective strategy, it can avoid the problem of spurious causes. I show that such an appeal has other advantages; and argue that it is not illegitimate, even for a causal realist.

An alleged counterexample to causal decision theory, put forward by Andy Egan, is studied in some detail. It is argued that Egan rejects the evaluation of causal decision theory on the basis of a description of the decision situation that is different from—indeed inconsistent with—the description on which causal decision theory makes its evaluation. So the example is not a counterexample to causal decision theory. Nevertheless, the example shows that causal decision theory can recommend unratifiable acts (acts that once decided upon appear sub-optimal) which presents a problem in the dynamics of intentions (as a decision is the forming of an intention to act). It is argued that we can defuse this problem if we hold that decision theory is a theory of rational decision making rather than a theory of rational acts. It is shown how decisions can have epistemic side-effects that are not mediated by the act and that there are cases where one can only bring oneself to perform the best act by updating by imaging rather than by conditioning . This provides a pragmatic argument for updating by imaging rather than by conditioning in these cases.

This paper looks at a dispute decision theory about how best to characterize expected utility maximization and express the logic of rational choice. Where A1, … , An are actions open to some particular agent, and S1, … , Sn are mutually exclusive states of the world such that the agent knows at least one of which obtains, does the logic of rational choice require an agent to consider the conditional probability of choice Ai given that some state Si obtains, Prob(Ai/Si). Or, is the logic of choice better represented by considering the probability of the counterfactual if Ai then Si, Prob(Ai ⟥-> Si). Causal decision theory, developed by Allan Gibbard, William Harper, and David Lewis defend the counterfactual analysis; whereas, Richard Jeffrey and others defend the conditional probability analysis, evidential decision theory. I argue that the problems posed by cases of decision instability favor evidential decision theory.

After a brief presentation of evidential decision theory, causal decision theory, and Newcomb type prima facie counterexamples to the evidential theory, three kinds of "metatickle" defenses of the evidential theory are discussed. Each has its weaknesses, but one of them seems stronger than the other two. The weaknesses of the best of the three, and the intricacy of metatickle analysis, does not constitute an advantage of causal decision theory over the evidential theory, however. It is argued, by way of an example, that causal decision theory also stands in need of a metatickle defense.

One of us (Eells 1982) has defended traditional evidential decision theory against prima facie Newcomb counterexamples by assuming that a common cause forms a conjunctive fork with its joint effects. In this paper, the evidential theory is defended without this assumption. The suggested rationale shows that the theory's assumptions are not about the nature of causality, but about the nature of rational deliberation. These presuppositions are weak enough for the argument to count as a strong justification of the evidential theory.

It is shown that even if a process of ideal evidential deliberation that paid attention to its own progress would in every case lead to credences that made things probabilistically independent of actions of which they were believed to be causally independent; it would not in every case lead to agreement in the ultimate dictates of evidential and causal decision theories. This point is made by a decision problem in which the action prescribed by causal decision theory is not (as it is in Newcomb's Problem) a dominant action. It is also shown that such non-dominance problems provide decisive objections to Ratificationism.