A quantitative discursive dilemma

The typical judgment aggregation problem in economics and other …elds 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 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. Keywords: Judgment aggregation, Dependent variables, Impossibility, Possibility JEL Classi…cation: D71 We thank two anonymous referees for detailed comments and suggestions, and Aanund Hylland and participants at the Judgment Aggregation Workshop in Freudenstadt September 2007 for discussions of this topic. The views presented here are our own and do not necessarily represent those of Norges Bank. yNorges Bank (Central Bank of Norway), P.O. Box 1179, Sentrum, 0107 Oslo, Norway (Phone : +47–22316104, fax : +47–22333568, Email : [email protected] / [email protected] ) zNorges Bank, (Central Bank of Norway), P.O. Box 1179, Sentrum, 0107 Oslo, Norway (Phone : +47–22316739, fax : +47–22333568, Email : [email protected])