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 κ other variables, i.e. y=D(χ1, ...χκ) . We analyze when it is possible for the group to arrive at collective judgements on the variables that respect D. We consider aggregators that ful ll 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.