If a group is modelled as a single Bayesian agent, what should its beliefs be? I propose an axiomatic model that connects group beliefs to beliefs of the group members. The group members may have different information, different prior beliefs and even different domains (algebras) within which...

How can different individuals’ probability assignments to some events be aggregated into a collective probability assignment? Although there are several classic results on this problem, they all assume that the ‘agenda’of relevant events forms a -algebra, an overly demanding assumption for...

How can different individuals' probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events -- the agenda -- is a σ-algebra and is thus closed under disjunction (union) and conjunction...

This paper characterizes different belief revision rules in a unified framework: Bayesian revision upon learning some event, Jeffrey revision upon learning new probabilities of some events, Adams revision upon learning some new conditional probabilities, and `dual-Jeffrey' revision upon learning...

What is the relationship between degrees of belief and (all-or-nothing) beliefs? Can the latter be expressed as a function of the former, without running into paradoxes? We reassess this “belief-binarization” problem from the perspective of judgmentaggregation theory. Although some...

How can different individuals' probability functions on a given σ-algebra of events be aggregated into a collective probability function? Classic approaches to this problem often require `event-wise independence': the collective probability for each event should depend only on the individuals'...

This review article introduces and evaluates various ways to aggregate probabilistic opinions of different individuals. For each of these three ways, an axiomatic characterization result is presented (a new one in the case of multiplicative pooling). The three ways satisfy different axioms and...