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(x ₁, . . . , x _k ). We analyze when it is possible for the group to arrive at collective judgements 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 to quantitative judgements.