Measuring Epistemic Utility

Just as traditional epistemology takes belief as its main object of study, Bayesians focus instead on credence. Credences are gradational doxastic attitudes: an agent's credence in the proposition p is her degree of confidence that p is true.Moreover, just as traditional epistemology argues for norms of rational belief, Bayesians argue for norms of rational credence ('credal norms'). The two most discussed credal norms are Probabilism and Conditionalisation. Illustratively,one very plausible credal norm, entailed by Probabilism and given by (.), holds that an agent's credence in any conjunction should be no greater than her cre-dence in either of the conjuncts.One part of the Bayesian project involves justifying credal norms like (.), Prob-abilism and Conditionalisation. Traditional justifications ground such norms inan agent's instrumental reasons (Ramsey, 1926; Savage, 1971; De Finetti, 1974). Like many others, I am unsatisfied with these justifications. The Accuracy-First approach to Epistemic Utility Theory offers an alternative (Pettigrew, 2016). This approach posits a distinctly epistemic kind of value - namely,epistemic utility- and identifies it as accuracy. It then seeks to use facts about accuracy to justify credal norms. In order to get this project off the ground, proponents of Accuracy-First Epistemology must give an account of how to measure accuracy.I contend that there are serious problems with existing accounts of how to mea-sure accuracy. My proposed research will identify these problems, diagnose them and present a new account of the legitimate measures of accuracy that aims to overcome them.At present, the two most prominent characterisations of putative measures of accuracy are the strictly proper and the coherently admissible measures. Both these sets of measures contain many different accuracy measures. One major problem (amongst many) with these putative classes of measures is that they each contain measures that order the credence functions differently at some e.g. Christensen (1996); Joyce (1998)1
world.2 This result is very troubling. To see this consider the analogous sce-nario occurring with measures of length. Suppose there were two sticks, Stick 1 and Stick 2, and two measures of length,M1 and M2. If M1 led us to believe that Stick 1 was longer than Stick 2 and M2 led us to believe that Stick2 was longer than Stick 1, we would conclude something was very wrong with the measures M1 and M2. We should draw the same conclusions about the strictly proper and coherently admissible accuracy measures.My research will identify problems like this and attempt to diagnose what has gone wrong. In this case, a natural response is that the strictly proper and coherently admissible measures are too inclusive. Alternatively, the problem may arise from modelling accuracy as having the gradational structure of the real numbers.The next part of the project aims to offer a new, improved account of how to measure accuracy. I will present constraints that characterise a set of accuracy measures by modifying existing accounts3to avoid the problems I find with them. Justifying these constraints will require answering questions such as: Are all credence functions comparable with respect to accuracy? How many comparability relations are there? Is accuracy symmetric?Finally, I shall evaluate my characterisation of the inaccuracy measures, first, as an account of epistemic utility, and then, as part of arguments justifying credal norms.