Eliaz (2004) has established a 'meta-theorem' for preference aggregation which implies both Arrow's Theorem (1963) and … preference aggregation is the mutual exclusiveness of Pareto optimality, individual responsiveness (preference reversal) and non …-dictatorship. Recent work on judgment aggregation has obtained important generalizations of both Arrow's Theorem (List and Pettit 2003 …

It is well known that the literature on judgment aggregation inherits the impossibility results from the aggregation of … preferences that it generalises. This is due to the fact that the typical judgment aggregation problem induces an ultrafilter on … with free ultrafilters in the literature on aggregation problems is however, the arbitrariness of their selection combined …

there exist nondictatorial aggregation functions of convex risk measures satisfying Arrow-type rationality axioms (weak …'s impossibility theorem for finite electorates. For infinite electorates, the possibility of rational aggregation depends on a uniform … theorem and Fishburn's possibility theorem. The proof methodology is based on a model-theoretic approach to aggregation theory …

The theory of Boolean algebras can be fruitfully applied to judgment aggregation: Assuming universality, systematicity … two general impossibility theorems for judgment aggregation on finite electorates, even without the Pareto principle. …