Modeling Expert Judgments for Bayesian Updating

This paper examines how a Bayesian decision maker would update his/her probability p for the occurrence of an event A in the light of a number of expert opinions expressed as probabilities q₁, ⋯, qₙ of A. It is seen, among other things, that the linear opinion pool, λ₀p + ∑ⁿi = 1 λᵢqᵢ, corresponds to an application of Bayes' Theorem when the decision maker has specified only the mean of the marginal distribution for (q₁, ⋯, qₙ) and requires his/her formula for the posterior probability of A to satisfy a certain consistency condition. A product formula similar to that of Bordley (1982) is also derived in the case where the experts are deemed to be conditionally independent given A (and given its complement).