Probabilistic Opinion Pooling

How can several individuals’opinions on some factual matters be aggregated into uni…ed collective opinions? This question arises in many contexts. A panel of climate experts may have to aggregate the panelists’con‡icting opinions into a compromise view, in order to deliver a report to the government. A jury may have to arrive at a collective opinion on the facts of a case, despite disagreements between the jurors, so that the court can reach a verdict. In Bayesian statistics, we may wish to specify some all-things-considered prior probabilities by aggregating the subjective prior probabilities of di¤erent statisticians. In meta-statistics, we may wish to aggregate the probability estimates that di¤erent statistical studies have produced for the same events. An individual agent may wish to combine his or her own opinions with those of another, so as to resolve any peer disagreements. Finally, in a purely intra-personal case, an agent may seek to reconcile di¤erent ‘selves’by aggregating their con‡icting opinions on the safety of mountaineering, in order to decide whether to undertake a mountain hike and which equipment to buy.