Probabilism, entropies and strictly proper scoring rules

Abstract

Accuracy arguments are the en vogue route in epistemic justifications of probabilism and further norms governing rational belief. These arguments often depend on the fact that the employed inaccuracy measure is strictly proper. I argue controversially that it is ill-advised to assume that the employed inaccuracy measures are strictly proper and that strictly proper statistical scoring rules are a more natural class of measures of inaccuracy. Building on work in belief elicitation I show how strictly proper statistical scoring rules can be used to give an epistemic justification of probabilism. An agent's evidence does not play any role in these justifications of probabilism. Principles demanding the maximisation of a generalised entropy depend on the agent's evidence. In the second part of the paper I show how to simultaneously justify probabilism and such a principle. I also investigate scoring rules which have traditionally been linked with entropies. • An accuracy argument justifying probabilism by tracking chances is provided. • An argument against the assumption that an inaccuracy measure is strictly proper is made. • Generalised entropy maximisation principles are justified in terms of worst case expected loss avoidance. • Generalised entropy maximisation principles are shown to entail the principle of indifference, in a number of cases. • The notion of locality applying to scoring rules defined on general belief functions is studied.