Resolute and Correlated Bayesians

Abstract

This paper suggests a new normative approach for combining beliefs. We call it the evidence-first method. Instead of aggregating credences alone, as the prevailing approaches, we focus instead on eliciting a group’s full probability distribution on the basis of the evidence available to its members. This is an altogether different way of combining beliefs. The method has four main benefits: (1) it captures the weight, or resilience, of a group’s belief; (2) it is sensitive to correlation among its individuals; (3) it is commutative under updating; and (4) it can be seen as a generalization of weighted averaging and likelihood ratio approaches. More broadly, it encourages an overall rethinking of the belief combination problem away from aggregating bare credences and toward appropriately combining evidence.