Social Choice and Welfare

, Volume 29, Issue 1, pp 19–33 | Cite as

Arrow’s theorem in judgment aggregation

Original Paper


In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using “systematicity” and “independence” conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we thereby provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model.


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  1. Bovens L, Rabinowicz W (2006) Democratic answers to complex questions: an epistemic perspective. Synthese 150(1):131–153CrossRefGoogle Scholar
  2. Dietrich F (2006) Judgment aggregation: (Im)possibility theorems. J Econ Theory 126(1):286–298CrossRefGoogle Scholar
  3. Dietrich F (forthcoming) A generalized model of judgment aggregation. Soc Choice and WelfareGoogle Scholar
  4. Dietrich F, List C (2005) Judgment aggregation by quota rules. Working paper, LSEGoogle Scholar
  5. Dokow E, Holzman R (2005) Aggregation of binary evaluations. Working paper, Technion Israel Institute of TechnologyGoogle Scholar
  6. Gärdenfors P (forthcoming) An Arrow-like theorem for voting with logical consequences. Econ PhilosGoogle Scholar
  7. Guilbaud GT (1966) Theories of the general interest, and the logical problem of aggregation. In: Lazarsfeld PF, Henry NW (eds) Readings in mathematical social science. MIT Press, Cambridge, pp 262–307Google Scholar
  8. van Hees M (forthcoming) The limits of epistemic democracy. Soc Choice WelfareGoogle Scholar
  9. List C (2003) A possibility theorem on aggregation over multiple interconnected propositions. Math Soc Sci 45(1):1–13CrossRefGoogle Scholar
  10. List C (2004) A model of path dependence in decisions over multiple propositions. Am Polit Sci Rev 98(3):495–513CrossRefGoogle Scholar
  11. List C (2005) The probability of inconsistencies in complex collective decisions. Soc Choice Welfare 24:3–32CrossRefGoogle Scholar
  12. List C, Pettit P (2001/2004) Aggregating sets of judgments: two impossibility results compared. Social and Political Theory Paper W20 (technical report ID 931), Australian National published in Synthese 140(1–2):207–235Google Scholar
  13. List C, Pettit P (2002) Aggregating sets of judgments: an impossibility result. Econ Philos 18:89–110Google Scholar
  14. Nehring K (2003) Arrow’s theorem as a corollary. Econ Lett 80:379–382CrossRefGoogle Scholar
  15. Nehring K, Puppe C (2002) Strategy proof social choice on single-peaked domains: possibility, impossibility and the space between. Working paper, University of California, DavisGoogle Scholar
  16. Nehring K, Puppe C (2005) Consistent judgment aggregation: a characterization. Working paper, University of KarlsruheGoogle Scholar
  17. Pauly M, van Hees M (2006) Logical constraints on judgment aggregation. J Philos Logic 35:569–585CrossRefGoogle Scholar
  18. Pettit P (2001) Deliberative democracy and the discursive dilemma. Philos Issues 11:268–299CrossRefGoogle Scholar
  19. Pigozzi G (forthcoming) Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation. SyntheseGoogle Scholar
  20. 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.Department of Quantitative EconomicsUniversity of MaastrichtMaastrichtThe Netherlands
  2. 2.Department of GovernmentLondon School of EconomicsLondonUK

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