Social Choice and Welfare

, Volume 28, Issue 4, pp 529–565 | Cite as

A generalised model of judgment aggregation

Original Paper


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 multi-valued or fuzzy logics. I provide a list of simple tools for working with general logics, and I prove impossibility results that generalise earlier theorems.


Aggregation Rule Atomic Proposition General Logic Classical Propositional Logic Judgment Aggregation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Bovens L, Rabinowicz W (2004) Democratic answers to complex questions – an epistemic perspective. Synthese (forthcoming)Google Scholar
  2. Brennan G (2001) Collective coherence?. Int Rev Law Econ 21(2):197–211CrossRefGoogle Scholar
  3. Chapman B (1998) More easily done than said: rules, reason and rational social choice. Oxford J Legal Stud 18:293–329CrossRefGoogle Scholar
  4. Chapman B (2002) Rational aggregation. Polit Philos Econ 1(3):337–354CrossRefGoogle Scholar
  5. Dietrich F (2004) Judgment aggregation: (im)possibility theorems. J Econ Theory (forthcoming)Google Scholar
  6. Dietrich F (2005) The possibility of judgment aggregation for network agendas. Working paper, University of KonstanzGoogle Scholar
  7. Dietrich F, List C (2004a) Strategy-proof judgment aggregation. Working paper, London School of EconomicsGoogle Scholar
  8. Dietrich F, List C (2004b) A liberal paradox for judgment aggregation. Working paper, London School of EconomicsGoogle Scholar
  9. Dietrich F, List C (2005) Judgment aggregation by Quota Rules. Working paper, London School of EconomicsGoogle Scholar
  10. Dokow E, Holzman R (2005) Aggregation of binary relations. Working paper, Technion Israel Institute of TechnologyGoogle Scholar
  11. Gärdenfors P (2004) An arrow-like theorem for voting with logical consequences. Working paper, Lund UniversityGoogle Scholar
  12. Gekker R (2003) A probability-based doxastic logic. Working paper, Department of Economics, NUI, GalwayGoogle Scholar
  13. Hintikka J (1971) Some main problems of deontic logic. In: Hilpinen R (eds). Deontic logic: introductory and systematic readings. D. Reidel, Dordrecht, pp. 59–104Google Scholar
  14. Kornhauser LA, Sager LG (1986) Unpacking the court. Yale Law J 96:82–117CrossRefGoogle Scholar
  15. Kripke S (1963) Semantical analysis of modal logic I: Normal propositional calculi. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 9:67–96Google Scholar
  16. Lewis D (1973) Counterfactuals. Basil Blackwell, OxfordGoogle Scholar
  17. List C (2003) A possibility theorem on aggregation over multiple interconnected propositions. Math Soc Sci 45(1):1–13CrossRefGoogle Scholar
  18. List C (2004a) The probability of inconsistencies in complex collective decisions. Soc Choice Welfare (forthcoming)Google Scholar
  19. List C (2004b) A model of path dependence in decisions over multiple propositions. Am Polit Sci Rev 98(3):495–513CrossRefGoogle Scholar
  20. List C, Pettit P (2002) Aggregating sets of judgments: an impossibility result. Econ Philos 18:89–110Google Scholar
  21. List C, Pettit P (2004) Aggregating sets of judgments: two impossibility results compared. Synthese 140(1–2):207–235CrossRefGoogle Scholar
  22. Mendelssohn E (1979) Introduction to mathematical logic. D. Van NostrandGoogle Scholar
  23. Mongin P (2005) Factoring out the impossibility of logical aggregation. Working paper, CNRS, ParisGoogle Scholar
  24. Nehring K (2003) Arrow’s theorem as a corollary. Econ Lett 80:379–382CrossRefGoogle Scholar
  25. Nehring K, Puppe C (2002) Strategy-proof social choice on single-peaked domains: possibility, impossibility and the space between. Working paper, University of California at DaviesGoogle Scholar
  26. Nehring K, Puppe C (2004) Consistent judgement aggregation: a characterization. Working paper, University of KarlsruheGoogle Scholar
  27. Pauly M, van Hees M (2004) Logical constraints on judgment aggregation. J Philos Logic (forthcoming)Google Scholar
  28. Pettit P (2001) Deliberative democracy and the discursive dilemma. Philos Issues 11:268–299CrossRefGoogle Scholar
  29. Pigozzi G (2004) Collective decision-making without paradoxes: an argument-based account. Working paper, King’s College, LondonGoogle Scholar
  30. Priest G (2001) An introduction to non-classical logic. Cambridge University Press, CambridgeGoogle Scholar
  31. Stalnaker R (1968): A theory of conditionals. In: Rescher N. (eds). Studies in logical theory. Blackwell, OxfordGoogle Scholar
  32. van Hees M (2004) The limits of epistemic democracy. Working paper, University of GroningenGoogle Scholar
  33. Wagner Decew J (1981) Conditional obligation and counterfactuals. J Philos Logic 10(1):55–72CrossRefGoogle Scholar
  34. Wilson R (1975) On the theory of aggregation. J Econ Theory 10:89–99CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Faculty of EconomicsUniversity of MaastrichtMaastrichtThe Netherlands

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