14 - Pascal’s Wager and Imprecise Probability

Summary

In chapter 14, Susanna Rinard asks what happens to Pascal’s Wager if we drop the usual assumption that a rational agent must have a sharp, real-valued credence p > 0 that God exists and suppose instead that it is reasonable to have an imprecise credence. For instance, your credence might be vague over the interval (0, 1/100) if you think that the probability that God exists is greater than 0 but less than 1/100. Rinard shows that decision theory can accommodate imprecise credences, and that Pascal’s Wager still succeeds for an agent whose credence that God exists is vague over a range that does not include 0. For an agnostic whose credence interval includes 0, Pascal’s Wager fails. However, Rinard provides three distinct arguments that for any contingent proposition P, including the proposition that God exists, no rational agent has a credence interval for P that includes 0. Thus, she concludes that the move from precise to imprecise credences makes no difference to the success of Pascal’s Wager for any rational agent.