ABSTRACT
The problem of the aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on the same propositions has recently drawn much attention. The difficulty lies in the fact that a seemingly reasonable aggregation procedure, such as propositionwise majority voting, cannot ensure an equally consistent collective outcome. The literature on judgment aggregation refers to such dilemmas as the doctrinal paradox. Three procedures have been proposed in order to overcome the paradox: the premise-based and conclusion-based procedures on the one hand, and the fusion approach on the other hand. In this paper we assume that the decision which the group is trying to reach is factually right or wrong. Hence, the question is how good the fusion approach is in tracking the truth, and how it compares with the premise-based and conclusion-based procedures. We address these questions in a probabilistic framework and show that belief fusion does especially well for individuals with a middling competence of hitting the truth of a proposition.
- L. Bovens and W. Rabinowicz. Democratic answers to complex questions. An epistemic perspective. Synthese, 150: 131--153, 2006.Google ScholarCross Ref
- F. Dietrich and C. List. Arrow's theorem in judgment aggregation. Social Choice and Welfare, forthcoming, 2006.Google Scholar
- S. Konieczny and E. Grégoire. Logic-based approaches to information fusion. Information Fusion, 7: 4--18, 2006. Google ScholarDigital Library
- S. Konieczny and R. Pino-Pérez. Merging with integrity constraints. In Fifth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU'99), pages 233--244, 1999. Google ScholarDigital Library
- L. A. Kornhauser and L. G. Sager. Unpacking the court. Yale Law Journal, 96: 82--117, 1986.Google ScholarCross Ref
- C. List. The discursive dilemma and public reason. Ethics, 116(2): 362--402, 2006.Google ScholarCross Ref
- C. List. Judgment aggregation - A bibliography on the discursive dilemma, the doctrinal paradox and decisions on multiple propositions. 2007. http://personal.lse.ac.uk/LIST/doctrinalparadox.htmGoogle Scholar
- C. List and P. Pettit. Aggregating sets of judgments: An impossibility result. Economics and Philosophy, 18: 89--110, 2002.Google ScholarCross Ref
- G. Pigozzi. Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation. Synthese, 152(2): 285--298, 2006.Google ScholarCross Ref
Recommendations
On judgment aggregation in abstract argumentation
Judgment aggregation is a field in which individuals are required to vote for or against a certain decision (the conclusion) while providing reasons for their choice. The reasons and the conclusion are logically connected propositions. The problem is ...
Judgement aggregation and distributed thinking
In recent years, judgement aggregation has emerged as an important area of social choice theory. Judgement aggregation is concerned with aggregating sets of individual judgements over logically connected propositions into a set of collective judgements. ...
Complexity of judgment aggregation
We analyse the computational complexity of three problems in judgment aggregation: (1) computing a collective judgment from a profile of individual judgments (the winner determination problem); (2) deciding whether a given agent can influence the ...
Comments