Provisional Beliefs and Paradigm Shifts

Bayesian inference has the advantage of dynamic consistency, but the drawback of rigidity. When a decision-maker's initial model fails a hypothesis test, he may wish to form a new model, violating Bayes' rule. We show that if such "paradigm shifts" are rare, he will be "approximately" dynamically consistent. More specifically, we show that in our setting dynamic consistency is equivalent to the non-existence of Dutch books, and that a decision-maker who is almost always Bayesian will suffer from only "small" Dutch books. This gives the decision-maker some latitude to revise his model while bounding the pain of inconsistency.