Gandalf’s Solution to the Newcomb Problem


Συγγραφέας: Ralph Wedgwood


Ralph Wedgwood: Gandalf’s Solution to the Newcomb Problem (html, 358K)
Recently, some philosophers—the most prominent recent example is probably Andy Egan (2007)—have presented some compelling counterexamples to both causal decision theory (CDT) and to its main rival, evidential decision theory (EDT). In this paper, I shall present a new theory of rational decision, distinct from both CDT and EDT, that will be able to accommodate these intuitive counterexamples in a principled way. 1 Both CDT and EDT are versions of expected utility theory .2 We do not need to worry about which of the many possible interpretations of “utility” we should adopt here. The crucial point for our purposes is that both of these theories define a rational choice as a choice that maximizes expected utility—where the “expected utility” of a choice is the weighted sum of the choice’s utility according to each member of the relevant set of hypotheses about one’s situation, when each of these utilities is weighted by the relevant probability of the hypothesis. CDT and EDT differ from each other in two ways. First, they differ in their view of what I have just called “the relevant set of hypotheses about one’s situation.” Secondly, they differ in their view of the relevant sort of “probabilities”, which are to be used in defining the expected utility of the choice. On the first point, both CDT and EDT agree that the “relevant set of hypotheses about one’s situation” must form a partition—that is, a set of propositions about one’s situation such that one is rationally certain that exactly one of these propositions is true. However, the two theories differ on which sort of partition is relevant here. According to EDT, the relevant set of hypotheses can be any partition of propositions about one’s situation whatsoever.3 According to CDT, on the other hand, the relevant partition must be a partition of states of nature —that is, one must be rationally certain that it is completely beyond one’s control which of the propositions in this partition is true. 4 According to many versions of CDT, these “states of nature”—which are sometimes called “causal dependency hypotheses”—consist of conjunctions of “non backtracking” subjunctive conditionals, where each of these conditionals has the form ‘If I did act An, outcome Om would result’...