Approximation Measures

The focus of Chapter 3 is the central Bayesian tenet that a thinker’s unconditional credences should be probabilistically coherent. Plausibly, thinkers who don’t have coherent credences can be more or less incoherent, i.e. their credences can diverge from complying with the probability axioms only a little, or quite substantially. We can capture this intuitive idea by representing a thinker’s credence function as a vector, and measuring its distance to the closest probabilistically coherent credence function that is defined over the same set of propositions. The problem that arises in this context is that there are many possible measures we can use to determine the distance from coherence, and those measures can deliver incompatible rankings. I present a representative range of such measures and illustrate the ways in which they differ.