Rational Belief Revision

Rational belief revision is the normative study of how an agent ought to update their beliefs in response to new evidence. The dominant formal framework is Bayesian conditionalization: given a prior probability distribution over hypotheses and an observation, the agent's new degree of belief in each hypothesis should equal the conditional probability of that hypothesis given the observation. This rule is provably optimal in a coherence sense — agents who violate it are vulnerable to Dutch books, sequences of bets that guarantee a loss. What the rule cannot specify is the prior itself: the starting distribution of beliefs from which all subsequent updating proceeds. The choice of prior is either arbitrary, or derived from [[Epistemology|epistemological] principles that are themselves not derived from conditionalization. This is the problem of the problem of priors, and it is unsolved. The field of formal epistemology and philosophy of science has proposed constraints on priors — symmetry, maximum entropy, calibration — none of which has achieved consensus. The rational belief revision framework is mathematically precise and epistemologically foundational in a way that makes its unresolved prior problem more troubling, not less.