It has been a traditional concern of epistemology to find what Descartes called “rules for the direction of the mind”: a set of principles that will say, in some general yet useful (although, perhaps, not exhaustive) way, how the opinions of a rational person ought to be constrained. Epistemologists have sought such principles, and evidence for their legitimacy, in various places. Some have sought insight from the traditional sources – from reflections on the metaphysical structure of the world, from analyses of the nature of justification. Others have argued that insight is available only from the scientific study of the empirical world – from the analysis of the way actual human inquirers behave, from the findings of cognitive psychology, from the application of evolutionary biology to human cognition, from the study of artificial intelligence.

What sets the Bayesian approach to epistemology apart from the rest is that its proponents look in a different place. They look for rules for the direction of the mind in the theory of rational preference – in decision theory. At first blush, this looks like a preposterous undertaking. After all, one would think that (if anything) it is epistemology that would place constraints on what we are rational to prefer, not the other way round. But there is method in the Bayesian madness.

Suppose you are offered a free choice between two identical gambles, one a gamble on the hypothesis h and the other a gamble on the hypothesis g.