Reliable Methods of Judgment Aggregation

The aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on the same propositions has recently drawn much attention. Seemingly reasonable aggregation procedures, such as propositionwise majority voting, cannot ensure an equally consistent collective conclusion. The literature on judgment aggregation refers to such a problem as the discursive dilemma. In this paper we assume that the decision which the group is trying to reach is factually right or wrong. Hence, the question we address in this paper is how good the various approaches are at selecting the right conclusion. We focus on two approaches: distance-based procedures and Bayesian analysis. Under the former we also subsume the conclusion- and premise-based procedures discussed in the literature. Whereas we believe the Bayesian analysis to be theoretically optimal, the distance-based approaches have more parsimonious presuppositions and are therefore easier to apply.Working paper

[1]  P. Pettit.  Deliberative Democracy and the Discursive Dilemma , 2001 .

[2]  C. List,et al.  Aggregating Sets of Judgments: An Impossibility Result , 2002, Economics and Philosophy.

[3]  Franz Dietrich,et al.  Judgment aggregation: (im)possibility theorems , 2006, J. Econ. Theory.

[4]  Sébastien Konieczny,et al.  Merging with Integrity Constraints , 1999, ESCQARU.

[5]  Luc Bovens,et al.  Democratic Answers to Complex Questions – An Epistemic Perspective , 2006, Synthese.

[6]  Lawrence G. Sager,et al.  Unpacking the Court , 1986 .

[7]  Gabriella Pigozzi,et al.  Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation , 2006, Synthese.

[8]  Daniel N. Osherson,et al.  Methods for distance-based judgment aggregation , 2009, Soc. Choice Welf..

[9]  C. List,et al.  Judgment aggregation: A survey , 2009 .

[10]  Gabriella Pigozzi,et al.  Judgment aggregation and the problem of truth-tracking , 2007, TARK '07.

[11]  Lawrence G. Sager,et al.  The One and the Many: Adjudication in Collegial Courts , 1993 .

[12]  Éric Grégoire,et al.  Logic-based approaches to information fusion , 2006, Inf. Fusion.

[13]  Nick Baigent.  Preference Proximity and Anonymous Social Choice , 1987 .

[14]  Christian List,et al.  The probability of inconsistencies in complex collective decisions , 2005, Soc. Choice Welf..

[15]  Shmuel Nitzan.  More on the Preservation of Preference Proximity and Anonymous Social Choice , 1989 .

[16]  C. List.  The Discursive Dilemma and Public Reason* , 2006, Ethics.

[17]  James O. Berger,et al.  Statistical Decision Theory and Bayesian Analysis, Second Edition , 1985 .

[18]  C. List,et al.  Epistemic democracy : generalizing the Condorcet jury theorem , 2001 .

[19]  Christian List,et al.  Arrow’s theorem in judgment aggregation , 2005, Soc. Choice Welf..

[20]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .