Social Choice and Welfare

, Volume 48, Issue 2, pp 327–356 | Cite as

A partial taxonomy of judgment aggregation rules and their properties

  • Jérôme LangEmail author
  • Gabriella Pigozzi
  • Marija Slavkovik
  • Leendert van der Torre
  • Srdjan Vesic
Original Paper


The literature on judgment aggregation is moving from studying impossibility results regarding aggregation rules towards studying specific judgment aggregation rules. Here we give a structured list of most rules that have been proposed and studied recently in the literature, together with various properties of such rules. We first focus on the majority-preservation property, which generalizes Condorcet-consistency, and identify which of the rules satisfy it. We study the inclusion relationships that hold between the rules. Finally, we consider two forms of unanimity, monotonicity, homogeneity, and reinforcement, and we identify which of the rules satisfy these properties.



Gabriella Pigozzi and Srdjan Vesic benefited from the support of the project AMANDE ANR-13-BS02-0004 of the French National Research Agency (ANR). Jérôme Lang benefited from the support of the ANR Project 14-CE24-0007-01 CoCoRICo-CoDec. The authors would like to thank Denis Bouyssou, as well as the anonymous reviewers and associate editor.


  1. Baumeister D, Erdélyi G, Rothe J (2016) Judgment aggregation. In: Rothe J (ed) Economics and computation, chap 6. Springer, Berlin, pp 361–394CrossRefGoogle Scholar
  2. Brams S, Fishburn P (2004) Chapter 4: Voting procedures. In: Arrow K, Sen A, Suzumura K (eds) Handbook of social choice and welfare. Elsevier, AmsterdamGoogle Scholar
  3. Dietrich F (2014) Scoring rules for judgment aggregation. Soc Choice Welf 42(4):873–911CrossRefGoogle Scholar
  4. Dietrich F, List C (2007a) Arrow’s theorem in judgment aggregation. Soc Choice Welf 29(1):19–33CrossRefGoogle Scholar
  5. Dietrich F, List C (2007b) Judgment aggregation by quota rules: majority voting generalized. J Theor Polit 4(19):391–424CrossRefGoogle Scholar
  6. Dietrich F, List C (2007c) Strategy-proof judgment aggregation. Econ Philos 23:269–300CrossRefGoogle Scholar
  7. Dietrich F, List C (2008) A liberal paradox for judgment aggregation. Soc Choice Welf 31(1):59–78CrossRefGoogle Scholar
  8. Dietrich F, Mongin P (2010) The premise-based approach to judgment aggregation. J Econ Theory 145(2):562–582CrossRefGoogle Scholar
  9. Duddy C, Piggins A (2012) A measure of distance between judgment sets. Soc Choice Welf 39(4):855–867CrossRefGoogle Scholar
  10. Duddy C, Piggins A, Zwicker WS (2016) Aggregation of binary evaluations: a Borda-like approach. Soc Choice Welf 46(2):301–333. doi: 10.1007/s00355-015-0914-3
  11. Elkind E, Faliszewski P, Slinko A (2009) On distance rationalizability of some voting rules. In: Proceedings of the 12th conference on theoretical aspects of rationality and knowledge, pp 108–117Google Scholar
  12. Endriss U (2016) Judgment aggregation. In: Brandt F, Conitzer Brandt V, Endriss U, Lang J, Procaccia AD (eds) Handbook of computational social choice, chap 17. Cambridge University Press, CambridgeGoogle Scholar
  13. Endriss U, Grandi U, Porello D (2012) Complexity of judgment aggregation. J Artif Intell Res 45:481–514Google Scholar
  14. Endriss U, Grandi U, de Haan R, Lang J (2016) Succinctness of languages for judgment aggregation. In: Principles of knowledge representation and reasoning: proceedings of the fifteenth international conference, KR 2016, Cape Town, South Africa, April 25–29, 2016, pp 176–186Google Scholar
  15. Everaere P, Konieczny S, Marquis P (2014) Counting votes for aggregating judgments. In: International conference on autonomous agents and multi-agent systems, pp 1177–1184Google Scholar
  16. Everaere P, Konieczny S, Marquis P (2015) Belief merging versus judgment aggregation. In: Proceedings of the 2015 international conference on autonomous agents and multiagent systems, AAMAS 2015, Istanbul, Turkey, May 4–8, 2015, pp 999–1007Google Scholar
  17. Grandi U, Endriss U (2013) Lifting integrity constraints in binary aggregation. Artif Intell 199:45–66CrossRefGoogle Scholar
  18. Grossi D, Pigozzi G (2014) Judgment aggregation: a primer. Synthesis lectures on artificial intelligence and machine learning. Morgan & Claypool Publishers, San Rafael. doi: 10.2200/S00559ED1V01Y201312AIM027
  19. Konieczny S, Pino-Pérez R (2002) Merging information under constraints: a logical framework. J Log Comput 12(5):773–808CrossRefGoogle Scholar
  20. Lang J (2015) Twenty-five years of preferred subtheories. In: Eiter T, Strass H, Truszczynski M, Woltran S (eds.) Advances in knowledge representation, logic programming, and abstract argumentation—essays dedicated to Gerhard Brewka on the occasion of his 60th birthday. Lecture notes in computer science, vol 9060, pp 157–172. Springer, BerlinGoogle Scholar
  21. Lang J, Slavkovik M (2013) Judgment aggregation rules and voting rules. In: Proceedings of the 3rd international conference on algorithmic decision theory. Lecture notes in artificial intelligence, vol 8176, pp 230–244. Springer, BerlinGoogle Scholar
  22. Lang J, Pigozzi G, Slavkovik M, van der Torre L (2011) Judgment aggregation rules based on minimization. In: TARK XIII Proceedings of the 13th conference on theoretical aspects of rationality and knowledge, Groningen, The Netherlands, 12–14 July 2011. ACM, New York, NY, USA, pp 238–246Google Scholar
  23. List C, Pettit C (2004) Aggregating sets of judgments: two impossibility results compared. Synthese 104(1–2):207–235Google Scholar
  24. List C, Puppe C (2009) Judgment aggregation: a survey. In: Handbook of rational and social choice. Oxford University Press, Oxford, pp 457–482Google Scholar
  25. Miller M, Osherson D (2009) Methods for distance-based judgment aggregation. Soc Choice Welf 32(4):575–601CrossRefGoogle Scholar
  26. Nehring K, Pivato M (2013) Majority rule in the absence of a majority. MPRA Paper 46721, University Library of Munich, Germany.
  27. Nehring K, Pivato M (2016) The median rule in judgment aggregation. Technical reportGoogle Scholar
  28. Nehring K, Pivato M, Puppe C (2014) The Condorcet set: majority voting over interconnected decisions. J Econ Theory 151:268–303CrossRefGoogle Scholar
  29. Nehring K, Pivato M, Puppe C (2015) Unanimity overruled: majority voting and the burden of history. J Theor Polit. doi: 10.1177/0951629815586884 Google Scholar
  30. Pigozzi G (2006) Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation. Synthese 152(2):285–298CrossRefGoogle Scholar
  31. Pigozzi G, Slavkovik M, van der Torre L (2009) A complete conclusion-based procedure for judgment aggregation. In: Rossi F, Tsoukiàs A (eds.) 1rst International conference on algorithmic decision theory, Venice, Italy, October 20–23, 2009. Proceedings. Lecture notes in computer science, vol 5783, pp 1–13. Springer, BerlinGoogle Scholar
  32. Slavkovik M, Ågotnes T (2014) Measuring dissimilarity between judgment sets. In: Logics in artificial intelligence. Lecture notes in computer science, vol 8761, pp 609–617. Springer International Publishing, BerlinGoogle Scholar
  33. Tideman TN (1987) Independence of clones as a criterion for voting rules. Soc Choice Welf 4(3):185–206CrossRefGoogle Scholar
  34. Young H (1977) Extending Condorcet’s rule. J Econ Theory 16(2):335–353CrossRefGoogle Scholar
  35. Young H, Levenglick A (1978) A consistent extension of Condorcet’s election principle. SIAM J Appl Math 2(35):285–300CrossRefGoogle Scholar
  36. Zwicker W (2011) Towards a Borda count for judgment aggregation. Working paperGoogle Scholar
  37. Zwicker W (2014) Voting: an introduction. In: Handbook of computational social choice. Oxford University Press, OxfordGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Jérôme Lang
    • 1
    Email author
  • Gabriella Pigozzi
    • 2
  • Marija Slavkovik
    • 3
  • Leendert van der Torre
    • 4
  • Srdjan Vesic
    • 5
  1. 1.LAMSADE, CNRS, Université Paris-DauphineParis Cedex 16France
  2. 2.Université Paris-Dauphine, PSL Research University, CNRS, LAMSADEParisFrance
  3. 3.University of BergenDepartment of Information Science and Media StudiesBergenNorway
  4. 4.Computer Science and CommunicationUniversity of LuxembourgEsch-sur-AlzetteLuxembourg
  5. 5.CRIL CNRS & Univ. ArtoisRue Jean Souvraz SP 18LensFrance

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