A quantitative discursive dilemma

The typical judgment aggregation problem in economics and other fields is the following: A group of people has to judge (estimate) the value of an uncertain variable y which is a function of k other variables, i.e. y = D(x1,...xk) . We analyze when it is possible for the group to arrive at collective judgments on the variables that respect D. We consider aggregators that fulfill Arrow's IIA-condition and neutrality. We show how possibility and impossibility depend on the functional form of D, and generalize Pettit's (2001) binary discursive dilemma. (revised ed. 2008)