Judgment aggregation and the problem of tracking the truth

The aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on those propositions has recently drawn much attention. Seemingly reasonable aggregation procedures, such as propositionwise majority voting, cannot ensure an equally consistent collective conclusion. In this paper, we motivate that quite often, we do not only want to make a factually right decision, but also to correctly evaluate the reasons for that decision. In other words, we address the problem of tracking the truth. We set up a probabilistic model that generalizes the analysis of Bovens and Rabinowicz (Synthese 150: 131–153, 2006) and use it to compare several aggregation procedures. Demanding some reasonable adequacy constraints, we demonstrate that a reasons- or premise-based aggregation procedure tracks the truth better than any other procedure. However, we also illuminate that such a procedure is not in all circumstances easy to implement, leaving actual decision-makers with a tradeoff problem.

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

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

[3]  Philippe Mongin,et al.  Factoring out the impossibility of logical aggregation , 2008, J. Econ. Theory.

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

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

[6]  Philippe Mongin,et al.  The premiss-based approach to judgment aggregation , 2010, J. Econ. Theory.

[7]  Gabriella Pigozzi,et al.  Reliable Methods of Judgment Aggregation , 2007 .

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

[9]  Gabriella Pigozzi,et al.  Reliable Methods of Judgement Aggregation , 2010, J. Log. Comput..

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

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

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

[13]  Philippe Mongin,et al.  The doctrinal paradox, the discursive dilemma, and logical aggregation theory , 2012 .

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

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

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