All existing impossibility theorems on judgment aggregation over logically connected propositions have one of two restrictions: they either use a controversial systematicity condition or apply only to special agendas of propositions with rich logical connections. An important open question is...

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...

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'...

When individual judgments ('yes' or 'no') on some propositions are aggregated into collective judgments, the agenda setter can sometimes reverse a collective judgment by changing the set of propositions under consideration (the agenda). I define different kinds of agenda manipulation, and...

I propose a new axiom on the aggregation of individual yes/no judgments on propositions into collective judgments: each collective judgment depends only on people's judgments on 'relevant' propositions. This contrasts with classical independence: each collective judgment depends only on people's...

The widely discussed `discursive dilemma' shows that majority voting in a group of individuals on logically connected propositions may produce irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of...

In this paper, the authors investigate judgment aggregation by assuming that some formulas of the agenda are singled out as premisses, and the Independence condition (formula-wise aggregation) holds for them, though perhaps not for others.

Within social choice theory, the new field of judgment aggregation aims at reaching collective judgments on a set of logically interconnected propositions. I investigate decision problems, in which the agenda is a network, composed of atomic propositions and connection rules between them....

In the emerging literature on judgment (as opposed to preference) aggregation, expert rights or liberal rights have not been investigated yet. When a group forms collective beliefs, it may assign experts with special knowledge on certain propositions the right to determine the collective...