A generalised model of judgment aggregation
 Franz Dietrich
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
The new field of judgment aggregation aims to merge many individual sets of judgments on logically interconnected propositions into a single collective set of judgments on these propositions. Judgment aggregation has commonly been studied using classical propositional logic, with a limited expressive power and a problematic representation of conditional statements (“if P then Q ”) as material conditionals. In this methodological paper, I present a simple unified model of judgment aggregation in general logics. I show how many realistic decision problems can be represented in it. This includes decision problems expressed in languages of standard propositional logic, predicate logic (e.g. preference aggregation problems), modal or conditional logics, and some multivalued or fuzzy logics. I provide a list of simple tools for working with general logics, and I prove impossibility results that generalise earlier theorems.
 Bovens L, Rabinowicz W (2004) Democratic answers to complex questions – an epistemic perspective. Synthese (forthcoming)
 Brennan, G (2001) Collective coherence?. Int Rev Law Econ 21: pp. 197211 CrossRef
 Chapman, B (1998) More easily done than said: rules, reason and rational social choice. Oxford J Legal Stud 18: pp. 293329 CrossRef
 Chapman, B (2002) Rational aggregation. Polit Philos Econ 1: pp. 337354 CrossRef
 Dietrich F (2004) Judgment aggregation: (im)possibility theorems. J Econ Theory (forthcoming)
 Dietrich F (2005) The possibility of judgment aggregation for network agendas. Working paper, University of Konstanz
 Dietrich F, List C (2004a) Strategyproof judgment aggregation. Working paper, London School of Economics
 Dietrich F, List C (2004b) A liberal paradox for judgment aggregation. Working paper, London School of Economics
 Dietrich F, List C (2005) Judgment aggregation by Quota Rules. Working paper, London School of Economics
 Dokow E, Holzman R (2005) Aggregation of binary relations. Working paper, Technion Israel Institute of Technology
 Gärdenfors P (2004) An arrowlike theorem for voting with logical consequences. Working paper, Lund University
 Gekker R (2003) A probabilitybased doxastic logic. Working paper, Department of Economics, NUI, Galway
 Hintikka, J Some main problems of deontic logic. In: Hilpinen, R eds. (1971) Deontic logic: introductory and systematic readings.. D. Reidel, Dordrecht, pp. 59104
 Kornhauser, LA, Sager, LG (1986) Unpacking the court. Yale Law J 96: pp. 82117 CrossRef
 Kripke, S (1963) Semantical analysis of modal logic. I: Normal propositional calculi. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 9: pp. 6796
 Lewis, D (1973) Counterfactuals. Basil Blackwell, Oxford
 List, C (2003) A possibility theorem on aggregation over multiple interconnected propositions. Math Soc Sci 45: pp. 113 CrossRef
 List C (2004a) The probability of inconsistencies in complex collective decisions. Soc Choice Welfare (forthcoming)
 List, C (2004b) A model of path dependence in decisions over multiple propositions. Am Polit Sci Rev 98: pp. 495513 CrossRef
 List, C, Pettit, P (2002) Aggregating sets of judgments: an impossibility result. Econ Philos 18: pp. 89110
 List, C, Pettit, P (2004) Aggregating sets of judgments: two impossibility results compared. Synthese 140: pp. 207235 CrossRef
 Mendelssohn E (1979) Introduction to mathematical logic. D. Van Nostrand
 Mongin P (2005) Factoring out the impossibility of logical aggregation. Working paper, CNRS, Paris
 Nehring, K (2003) Arrow’s theorem as a corollary. Econ Lett 80: pp. 379382 CrossRef
 Nehring K, Puppe C (2002) Strategyproof social choice on singlepeaked domains: possibility, impossibility and the space between. Working paper, University of California at Davies
 Nehring K, Puppe C (2004) Consistent judgement aggregation: a characterization. Working paper, University of Karlsruhe
 Pauly M, van Hees M (2004) Logical constraints on judgment aggregation. J Philos Logic (forthcoming)
 Pettit, P (2001) Deliberative democracy and the discursive dilemma. Philos Issues 11: pp. 268299 CrossRef
 Pigozzi G (2004) Collective decisionmaking without paradoxes: an argumentbased account. Working paper, King’s College, London
 Priest, G (2001) An introduction to nonclassical logic. Cambridge University Press, Cambridge
 Stalnaker, R A theory of conditionals. In: Rescher, N. eds. (1968) Studies in logical theory.. Blackwell, Oxford
 van Hees M (2004) The limits of epistemic democracy. Working paper, University of Groningen
 Wagner Decew, J (1981) Conditional obligation and counterfactuals. J Philos Logic 10: pp. 5572 CrossRef
 Wilson, R (1975) On the theory of aggregation. J Econ Theory 10: pp. 8999 CrossRef
 Title
 A generalised model of judgment aggregation
 Journal

Social Choice and Welfare
Volume 28, Issue 4 , pp 529565
 Cover Date
 20070601
 DOI
 10.1007/s003550060187y
 Print ISSN
 01761714
 Online ISSN
 1432217X
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Authors

 Franz Dietrich ^{(1)}
 Author Affiliations

 1. Faculty of Economics, University of Maastricht, PO Box 616, Maastricht, 6200, MD, The Netherlands