Coherent Assessment of Subjective Probability

Abstract : This report discusses the role of coherence considerations in the definition and measurement of subjective probability. A general version of De Finetti's coherence theorem--that either a set of betting probabilities obeys the laws of probability or else a sure win is possible for the better--is proved, using a variant of Farka's Lemma. This theorem provides the basis for several admissibility theorems for scoring-rule probabilities, under a generalization of scoring rules suggested by Lindley. Linear programming methods for identifying and reconciling incoherence are discussed, and a comparison is made with Bayesian reconciliation methods.