Two Approaches to Belief Revision

In this paper, we compare and contrast two methods for the revision of qualitative (viz., “full”) beliefs. The first (“Bayesian”) method is generated by a simplistic diachronic Lockean thesis requiring coherence with the agent’s posterior credences after conditionalization. The second (“Logical”) method is the orthodox AGM approach to belief revision. Our primary aim is to determine when the two methods may disagree in their recommendations and when they must agree. We establish a number of novel results about their relative behavior. Our most notable (and mysterious) finding is that the inverse of the golden ratio emerges as a non-arbitrary bound on the Bayesian method’s free-parameter—the Lockean threshold. This “golden threshold” surfaces in two of our results and turns out to be crucial for understanding the relation between the two methods.