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Judgmentaggregation theory has always focused on the attainment of rational collective judgments. But so far, rationality has been understood in static terms: as coherence of judgments at a given time, defined as consistency, completeness, and/or deductive closure. This paper asks whether collective judgments can be dynamically rational, so that they change rationally in response to new information. Formally, a judgment aggregation rule is dynamically rational with respect to a given revision operator if, whenever all individuals revise their judgments in light (...) 

It is often suggested that when opinions differ among individuals in a group, the opinions should be aggregated to form a compromise. This paper compares two approaches to aggregating opinions, linear pooling and what I call opinion agglomeration. In evaluating both strategies, I propose a pragmatic criterion, No Regrets, entailing that an aggregation strategy should prevent groups from buying and selling bets on events at prices regretted by their members. I show that only opinion agglomeration is able to satisfy the (...) 

SupraBayesianism is the Bayesian response to learning the opinions of others. Probability pooling constitutes an alternative response. One natural question is whether there are cases where probability pooling gives the supraBayesian result. This has been called the problem of Bayescompatibility for pooling functions. It is known that in a common prior setting, under standard assumptions, linear pooling cannot be nontrivially Bayescompatible. We show by contrast that geometric pooling can be nontrivially Bayescompatible. Indeed, we show that, under certain assumptions, geometric and (...) 

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 sigmaalgebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interestrate increase, but not in the probability of rain or (...) 

How can different individuals' probability functions on a given sigmaalgebra of events be aggregated into a collective probability function? Classic approaches to this problem often require 'eventwise independence': the collective probability for each event should depend only on the individuals' probabilities for that event. In practice, however, some events may be 'basic' and others 'derivative', so that it makes sense first to aggregate the probabilities for the former and then to let these constrain the probabilities for the latter. We formalize (...) 