Taking Stock of Infinite Value: Pascal's Wager and Relative Utilities

Among recent objections to Pascal’s Wager, two are especially compelling. The first is that decision theory, and specifically the requirement of maximizing expected utility, is incompatible with infinite utility values. The second is that even if infinite utility values are admitted, the argument of the Wager is invalid provided that we allow mixed strategies. Furthermore, Hájek (Philosophical Review 112, 2003) has shown that reformulations of Pascal’s Wager that address these criticisms inevitably lead to arguments that are philosophically unsatisfying and historically unfaithful. Both the objections and Hájek’s philosophical worries disappear, however, if we represent our preferences using relative utilities (generalized utility ratios) rather than a one-place utility function. Relative utilities provide a conservative way to make sense of infinite value that preserves the familiar equation of rationality with the maximization of expected utility. They also provide a means of investigating a broader class of problems related to the Wager.