Updating on the Credences of Others: Disagreement, Agreement, and Synergy

We introduce a family of rules for adjusting one’s credences in response to learning the credences of others. These rules have a num- ber of desirable features. 1. They yield the posterior credences that would result from updating by standard Bayesian conditionalization on one’s peers’ reported credences, if one’s likelihood function takes a par- ticular simple form. 2. In the simplest form, they are symmetric among the agents in the group. 3. They map neatly onto the familiar Condorcet voting results. 4. They preserve shared agreement about independence in a wide range of case. 5. They commute with conditionalization and with multiple peer updates. Importantly, these rules have a surpris- ing property that we call synergy – peer testimony of credences can provide mutually supporting evidence raising an individual’s credence higher than any peer’s initial prior report. At first, this may seem to be a strike against them. We argue, however, that synergy is actually a desirable feature