Methods for distance-based judgment aggregation

  • Michael K. Miller
  • Daniel Osherson
Original Paper


Judgment aggregation theory, which concerns the translation of individual judgments on logical propositions into consistent group judgments, has shown that group consistency generally cannot be guaranteed if each proposition is treated independently from the others. Developing the right method of abandoning independence is thus a high-priority goal. However, little work has been done in this area outside of a few simple approaches. To fill the gap, we compare four methods based on distance metrics between judgment sets. The methods generalize the premise-based and sequential priority approaches to judgment aggregation, as well as distance-based preference aggregation. They each guarantee group consistency and implement a range of distinct functions with different properties, broadening the available tools for social choice. A central result is that only one of these methods (not previously considered in the literature) satisfies three attractive properties for all reasonable metrics.


Majority Rule Aggregation Rule Preference Aggregation Individual Judgment 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.


  1. Baigent N (1987) Preference proximity and anonymous social choice. Q J Econ 102: 161–170CrossRefGoogle Scholar
  2. Bovens L, Rabinowicz W (2006) Democratic answers to complex questions—an epistemic perspective. Synthese 150: 131–153CrossRefGoogle Scholar
  3. Brennan G (2001) Collective coherence. Int Rev Law Econ 21: 197–211CrossRefGoogle Scholar
  4. Dietrich F (2006) Judgment aggregation: (im)possibility theorems. J Econ Theory 126: 286–298CrossRefGoogle Scholar
  5. Dietrich F (2007) A generalised model of judgment aggregation. Soc Choice Welfare 28: 529–565CrossRefGoogle Scholar
  6. Dietrich F, List C (2007a) Arrow’s theorem in judgment aggregation. Soc Choice Welfare 29: 19–33CrossRefGoogle Scholar
  7. Dietrich F, List C (2007b) Strategy-proof judgment aggregation. Econ Philos 23: 269–300CrossRefGoogle Scholar
  8. Dietrich F, List C (2008) Judgment aggregation without full rationality. Soc Choice Welfare 31: 15–39CrossRefGoogle Scholar
  9. Dokow E, Holzman R (2008) Aggregation of binary evaluations. J Econ TheoryGoogle Scholar
  10. Eckert D, Mitlöhner J (2005) Logical representation and merging of preference information. Multidisciplinary IJCAI-05 workshop on advances in preference handling, pp 85–87Google Scholar
  11. Everaere P, Konieczny S, Marquis P (2005) Quota and Gmin merging operators. In: Proceedings of 19th international joint conference on artificial intelligenceGoogle Scholar
  12. Fishburn PC (1977) Condorcet social choice functions. SIAM J Appl Math 33: 469–489CrossRefGoogle Scholar
  13. Gärdenfors P (2006) A representation theorem for voting with logical consequences. Econ Philos 22: 181–190CrossRefGoogle Scholar
  14. Kasher A, Rubinstein A (1997) On the question ‘Who is a J’, a social choice approach. Logique et Analyse 160: 385–395Google Scholar
  15. Kemeny J (1959) Mathematics without numbers. Daedalus 88: 571–591Google Scholar
  16. Klamler C (2004) The Dodgson ranking and its relation to Kemeny’s method and Slater’s rule. Soc Choice Welfare 23: 91–102CrossRefGoogle Scholar
  17. Klamler C (2005) Borda and Condorcet: some distance results. Theory Decis 59: 97–109CrossRefGoogle Scholar
  18. Klamler C (2008) A distance measure for choice functions. Soc Choice Welfare 30: 419–425CrossRefGoogle Scholar
  19. Konieczny S (2004) Belief base merging as a game. J Appl Non-classical Logics 14: 275–294CrossRefGoogle Scholar
  20. Konieczny S, Lang J, Marquis P (2004) DA2 merging operators. Artif Intell 157: 49–79CrossRefGoogle Scholar
  21. Konieczny S, Pino-Pérez R (1998) On the logic of merging. Proceedings of KR’98, pp 488–498Google Scholar
  22. Konieczny S, Pino-Pérez R (1999) Merging with integrity constraints. In: Proceedings of ECSQARU’99, pp 233–244Google Scholar
  23. Konieczny S, Pino-Pérez R (2002) Merging information under constraints: a logical framework. J Logic Comput 12: 773–808CrossRefGoogle Scholar
  24. Konieczny S, Pino-Pérez R (2004) On merging strategy-proofness. In: Proceedings of the ninth conference on principles of knowledge representation and reasoning (KR’04)Google Scholar
  25. Kornhauser LA, Sager LG (1993) The one and the many: adjudication in collegial courts. California Law Rev 81: 1–59CrossRefGoogle Scholar
  26. List C (2005) The probability of inconsistencies in complex collective decisions. Soc Choice Welfare 24: 3–32CrossRefGoogle Scholar
  27. List C (2006) The discursive dilemma and public reason. Ethics 116: 362–402CrossRefGoogle Scholar
  28. List C (2008) Which worlds are possible? a judgment aggregation problem. J Philos Logic 37: 57–65CrossRefGoogle Scholar
  29. List C, Pettit P (2002) Aggregating sets of judgments: an impossibility result. Econ Philos 18: 89–110Google Scholar
  30. List C, Pettit P (2004) Aggregating sets of judgments: two impossibility results compared. Synthese 140: 207–235CrossRefGoogle Scholar
  31. List C, Pettit P (2006) Group agency and supervenience. Southern J Philos 44: 85–105Google Scholar
  32. List C, Puppe C (2008) Judgment aggregation: a survey. In: Anand P, Puppe C, Pattanaik P (eds) Oxford handbook of rational and social choice.. Oxford University Press, NY, USA (forthcoming)Google Scholar
  33. May KO (1952) A set of independent necessary and sufficient conditions for simple majority decision. Econometrica 20: 680–684CrossRefGoogle Scholar
  34. Miller MK (2008) Judgment aggregation and subjective decision-making. Econ Philos 24: 205–231Google Scholar
  35. Mongin P (2008) Factoring out the impossibility of logical aggregation. J Econ Theory 141: 100–113CrossRefGoogle Scholar
  36. Nehring K (2003) Arrow’s theorem as a corollary. Econ Lett 80: 379–382CrossRefGoogle Scholar
  37. Nehring K, Puppe C (2007) The structure of strategy-proof social choice. Part I. General characterization and possibility results on median spaces. J Econ Theory 135: 269–305CrossRefGoogle Scholar
  38. Nehring K, Puppe C (2008) Consistent judgment aggregation: the truth-functional case. Soc Choice Welfare 31: 41–57CrossRefGoogle Scholar
  39. Nurmi H (2004) A comparison of some distance-based choice rules in ranking environments. Theory Decis 57: 5–24CrossRefGoogle Scholar
  40. Pauly M, van Hees M (2006) Logical constraints on judgment aggregation. J Philos Logic 35: 569–585CrossRefGoogle Scholar
  41. Pettit P (2003) Groups with minds of their own. In: Schmitt F (eds) Socializing metaphysics. Rowan and Littlefield, New York, pp 167–194Google Scholar
  42. Pigozzi G (2006) Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation. Synthese 152: 285–298CrossRefGoogle Scholar
  43. Saari DG (2008) Disposing dictators, demystifying voting paradoxes: social choice analysis. Cambridge University Press, NY,USAGoogle Scholar
  44. Saari DG, Merlin VR (2000) A geometric examination of Kemeny’s rule. Soc Choice Welfare 17: 403–438CrossRefGoogle Scholar
  45. Young HP, Levenglick A (1978) A consistent extenstion of Condorcet’s election principle. SIAM J Appl Math 35: 285–300CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Princeton UniversityPrincetonUSA
  2. 2.Princeton UniversityPrincetonUSA

Personalised recommendations