, Volume 187, Issue 1, pp 179–207 | Cite as

The theory of judgment aggregation: an introductory review

  • Christian List


This paper provides an introductory review of the theory of judgment aggregation. It introduces the paradoxes of majority voting that originally motivated the field, explains several key results on the impossibility of propositionwise judgment aggregation, presents a pedagogical proof of one of those results, discusses escape routes from the impossibility and relates judgment aggregation to some other salient aggregation problems, such as preference aggregation, abstract aggregation and probability aggregation. The present illustrative rather than exhaustive review is intended to give readers who are new to the field of judgment aggregation a sense of this rapidly growing research area.


Judgment aggregation Discursive dilemma Condorcet’s paradox Arrow’s impossibility theorem Social choice theory Democracy 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arrow K. (1951) Social choice and individual values. Wiley, New York, NYGoogle Scholar
  2. Black D. (1948) On the rationale of group decision-making. Journal of Political Economy 56(1): 23–34CrossRefGoogle Scholar
  3. Bovens L., Rabinowicz W. (2006) Democratic answers to complex questions—an epistemic perspective. Synthese 150(1): 131–153CrossRefGoogle Scholar
  4. Brennan G. (2001) Collective coherence?. International Review of Law and Economics 21(2): 197–211CrossRefGoogle Scholar
  5. Chapman B. (2002) Rational aggregation. Politics, Philosophy and Economics 1(3): 337–354CrossRefGoogle Scholar
  6. Dietrich F. (2006) Judgment aggregation: (Im)possibility theorems. Journal of Economic Theory 126(1): 286–298CrossRefGoogle Scholar
  7. Dietrich F. (2007a) A generalised model of judgment aggregation. Social Choice and Welfare 28(4): 529–565CrossRefGoogle Scholar
  8. Dietrich, F. (2007b). Aggregation theory and the relevance of some issues to others. Working Paper, University of Maastricht.Google Scholar
  9. Dietrich F. (2010) Bayesian group belief. Social Choice and Welfare 35(4): 595–626CrossRefGoogle Scholar
  10. Dietrich F., List C. (2007a) Arrow’s theorem in judgment aggregation. Social Choice and Welfare 29(1): 19–33CrossRefGoogle Scholar
  11. Dietrich F., List C. (2007b) Judgment aggregation by quota rules: Majority voting generalized. Journal of Theoretical Politics 19(4): 391–424CrossRefGoogle Scholar
  12. Dietrich F., List C. (2007c) Strategy-proof judgment aggregation. Economics and Philosophy 23: 269–300CrossRefGoogle Scholar
  13. Dietrich, F., & List, C. (2007d). Judgment aggregation with consistency alone. Working Paper, London School of Economics.Google Scholar
  14. Dietrich F., List C. (2008a) Judgment aggregation without full rationality. Social Choice and Welfare 31: 15–39CrossRefGoogle Scholar
  15. Dietrich, F., & List, C. (2008b). Opinion pooling on general agendas. Working Paper, London School of Economics.Google Scholar
  16. Dietrich F., List C. (2008c) A liberal paradox for judgment aggregation. Social Choice and Welfare 31: 59–78CrossRefGoogle Scholar
  17. Dietrich F., List C. (2008d) Judgment aggregation under constraints. In: Boylan T., Gekker R. (eds) Economics, rational choice and normative philosophy. Routledge, LondonGoogle Scholar
  18. Dietrich F., List C. (2010a) Majority voting on restricted domains. Journal of Economic Theory 145(2): 512–543CrossRefGoogle Scholar
  19. Dietrich F., List C. (2010b) The aggregation of propositional attitudes: Towards a general theory. Oxford Studies in Epistemology 3: 215–234Google Scholar
  20. Dietrich F., Mongin P. (2010) The premise-based approach to judgment aggregation. Journal of Economic Theory 145(2): 562–582CrossRefGoogle Scholar
  21. Dokow E., Holzman R. (2010a) Aggregation of binary evaluations. Journal of Economic Theory 145(2): 495–511CrossRefGoogle Scholar
  22. Dokow E., Holzman R. (2010b) Aggregation of binary evaluations with abstentions. Journal of Economic Theory 145(2): 544–561CrossRefGoogle Scholar
  23. Dryzek J., List C. (2003) Social choice theory and deliberative democracy: A reconciliation. British Journal of Political Science 33(1): 1–28CrossRefGoogle Scholar
  24. Gärdenfors P. (2006) An Arrow-like theorem for voting with logical consequences. Economics and Philosophy 22(2): 181–190CrossRefGoogle Scholar
  25. Genest C., Zidek J. V. (1986) Combining probability distributions: A critique and annotated bibliography. Statistical Science 1(1): 113–135Google Scholar
  26. Guilbaud G. Th. (1966) Theories of the general interest, and the logical problem of aggregation. In: Lazarsfeld P.F., Henry N.W. (eds) Readings in mathematical social science. MIT Press, Cambridge, MA, pp 262–307Google Scholar
  27. Knight J., Johnson J. (1994) Aggregation and deliberation: On the possibility of democratic legitimacy. Political Theory 22(2): 277–296CrossRefGoogle Scholar
  28. Konieczny S., Pino Pérez R. (2002) Merging information under constraints: A logical framework. Journal of Logic and Computation 12(5): 773–808CrossRefGoogle Scholar
  29. Kornhauser L. A. (1992) Modeling collegial courts. II. Legal doctrine. Journal of Law, Economics and Organization 8: 441–470Google Scholar
  30. Kornhauser L. A., Sager L. G. (1986) Unpacking the court. Yale Law Journal 96(1): 82–117CrossRefGoogle Scholar
  31. Kornhauser L. A., Sager L. G. (1993) The one and the many: Adjudication in collegial courts. California Law Review 81: 1–59CrossRefGoogle Scholar
  32. Kornhauser L. A., Sager L. G. (2004) The many as one: Integrity and group choice in paradoxical cases. Philosophy and Public Affairs 32: 249–276CrossRefGoogle Scholar
  33. List, C. (2003). A possibility theorem on aggregation over multiple interconnected propositions. Mathematical Social Sciences, 45(1), 1–13 (with Corrigendum in Mathematical Social Sciences, 52, 109–110).Google Scholar
  34. List C. (2004) A model of path-dependence in decisions over multiple propositions. American Political Science Review 98(3): 495–513CrossRefGoogle Scholar
  35. List C. (2006) The discursive dilemma and public reason. Ethics 116(2): 362–402CrossRefGoogle Scholar
  36. List C. (2011) Group deliberation and the revision of judgments: An impossibility result. Journal of Political Philosophy 19(1): 1–27CrossRefGoogle Scholar
  37. List C., Pettit P. (2002) Aggregating sets of judgments: An impossibility result. Economics and Philosophy 18(1): 89–110Google Scholar
  38. List C., Pettit P. (2004) Aggregating sets of judgments: Two impossibility results compared. Synthese 140(1–2): 207–235CrossRefGoogle Scholar
  39. List C., Pettit P. (2005) On the many as one. Philosophy and Public Affairs 33(4): 377–390CrossRefGoogle Scholar
  40. List C., Puppe C. (2009) Judgment aggregation: A survey. In: Anand P., Puppe C., Pattanaik P. (eds) Oxford handbook of rational and social choice. Oxford University Press, OxfordGoogle Scholar
  41. McConway K. (1981) Marginalization and linear opinion pools. Journal of the American Statistical Association 76: 410–414Google Scholar
  42. Miller D. (1992) Deliberative democracy and social choice. Political Studies 40(Special Issue): 54–67Google Scholar
  43. Mongin P. (1995) Consistent Bayesian aggregation. Journal of Economic Theory 66: 313–351CrossRefGoogle Scholar
  44. Mongin P. (2008) Factoring out the impossibility of logical aggregation. Journal of Economic Theory 141(1): 100–113CrossRefGoogle Scholar
  45. Nehring K. (2003) Arrow’s theorem as a corollary. Economics Letters 80(3): 379–382CrossRefGoogle Scholar
  46. Nehring, K., & Puppe, C. (2002). Strategyproof social choice on single-peaked domains: Possibility, impossibility and the space between. Working Paper, University of California at Davis.Google Scholar
  47. Nehring K., Puppe C. (2007) The structure of strategy-proof social choice—Part I: General characterization and possibility results on median spaces. Journal of Economic Theory 135(1): 269–305CrossRefGoogle Scholar
  48. Nehring K., Puppe C. (2010) Abstract Arrovian aggregation. Journal of Economic Theory 145(2): 467–494CrossRefGoogle Scholar
  49. Pauly M., van Hees M. (2006) Logical constraints on judgment aggregation. Journal of Philosophical Logic 35(6): 569–585CrossRefGoogle Scholar
  50. Pettit P. (2001) Deliberative democracy and the discursive dilemma. Philosophical Issues 11: 268–299CrossRefGoogle Scholar
  51. Pettit P. (2006) When to defer to majority testimony—and when not. Analysis 66: 179–187CrossRefGoogle Scholar
  52. Pigozzi G. (2006) Belief merging and the discursive dilemma: An argument-based account to paradoxes of judgment aggregation. Synthese 152(2): 285–298CrossRefGoogle Scholar
  53. Pivato, M. (2008). The discursive dilemma and probabilistic judgement aggregation. Munich Personal RePEc Archive.Google Scholar
  54. Riker W. (1982) Liberalism against populism. W. H. Freeman, San Franscisco, CAGoogle Scholar
  55. Rubinstein A., Fishburn P. C. (1986) Algebraic aggregation theory. Journal of Economic Theory 38(1): 63–77CrossRefGoogle Scholar
  56. Sen A. K. (1966) A possibility theorem on majority decisions. Econometrica 34(2): 491–499CrossRefGoogle Scholar
  57. Sen A. K. (1970) The impossibility of a Paretian liberal. Journal of Political Economy 78: 152–157CrossRefGoogle Scholar
  58. Spector H. (2009) The right to a constitutional jury. Legisprudence 3(1): 111–123Google Scholar
  59. Vacca, R. (1921). Opinioni Individuali e Deliberazioni Collettive. Rivista Internazionale di Filosofia del Diritto 52–59.Google Scholar
  60. Wilson R. (1975) On the theory of aggregation. Journal of Economic Theory 10(1): 89–99CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Departments of Government and PhilosophyLondon School of EconomicsLondonUK

Personalised recommendations