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A contribution is made to the problem of combining the subjective probability density functions f₁, , fₙ of n individuals for some parameter. More precisely, the situation is addressed which occurs when the members of a group share a common likelihood for some data and want to ensure that combining their posterior distributions for will yield the same result obtained by applying Bayes' rule to the aggregated prior distribution. Under certain regularity conditions to be discussed below, the logarithmic opinion pool ⁿ₈=₁ f^wᵢᵢ / ⁿ₈=₁ f^wᵢᵢ d with wᵢ 0 and ⁿ₈=₁ wᵢ = 1 is shown to be the only pooling formula which satisfies this criterion of group rationality.
Christian Genest (Sat,) studied this question.