, Volume 81, Issue 2, pp 391–406 | Cite as

Local Supermajorities

  • Fabrizio Cariani
Original Article


This paper explores two non-standard supermajority rules in the context of judgment aggregation over multiple logically connected issues. These rules set the supermajority threshold in a local, context sensitive way—partly as a function of the input profile of opinions. To motivate the interest of these rules, I prove two results. First, I characterize each rule in terms of a condition I call ‘Block Preservation’. Block preservation says that if a majority of group members accept a judgment set, then so should the group. Second, I show that one of these rules is, in a precise sense, a judgment aggregation analogue of a rule for connecting qualitative and quantitative belief that has been recently defended by Hannes Leitgeb. The structural analogy is due to the fact that Leitgeb sets thresholds for qualitative beliefs in a local, context sensitive way—partly as a function of the given credence function.


Aggregation Rule Strategic Vote Judgment Aggregation Acceptance Rule Collective Judgment 
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.



Thanks to Branden Fitelson, Davide Grossi, Hannes Leitgeb, Gabriella Pigozzi and Patricia Rich for comments on earlier versions. Thanks to two reviewers for Erkenntnis for detailed and insightful reports. Special thanks to Branden Fitelson’s epistemology seminar at Rutgers where this material was presented in the Fall of 2014 and to the audience at the 2015 Formal Epistemology Workshop. Thanks also to Christian List for suggesting that I slice out one idea out of a much more baroque project and turn it into a paper in its own right (this one). The more baroque paper was delivered at DEON 2012 whose audience I also thank for their feedback.


  1. Briggs, R., Cariani, F., Easwaran, K., & Fitelson, B. (2014). Individual coherence and group coherence. In J. Lackey (Ed.), Essays in collective epistemology (pp. 215–249). Oxford: Oxford University Press.CrossRefGoogle Scholar
  2. Cariani, F., Pauly, M., & Snyder, J. (2008). Decision framing in judgment aggregation. Synthese, 163(1), 1–24.CrossRefGoogle Scholar
  3. Chandler, J. (2013). Acceptance, aggregation and scoring rules. Erkenntnis, 78(1), 201–217.CrossRefGoogle Scholar
  4. Chopra, S., Pacuit, E., & Parikh, R. (2004). Knowledge-theoretic properties of strategic voting. In J. J. Alferes, J. Leite (Eds.), Proceedings of logics in artificial intelligence: 9th European conference (JELIA) Google Scholar
  5. Conitzer, V., Walsh, T., & Xia, L. (2011). Dominating manipulations in voting with partial information. AAAI, 11, 638–643.Google Scholar
  6. Dietrich, F., & List, C. (2007a). Judgment aggregation by quota rules. Journal of Theoretical Politics, 19(4), 391–424.Google Scholar
  7. Dietrich, F., & List, C. (2007b). Strategy-proof judgment aggregation. Economics and Philosophy, 23, 269–300.CrossRefGoogle Scholar
  8. Dietrich, F., & List, C. (2015). From degrees of belief to beliefs: Lessons from judgment-aggregation Theory. Working Paper, University of East Anglia and LSE.Google Scholar
  9. Douven, I., & Romeijn, J. (2007). The discursive dilemma as a lottery paradox. Economics and Philosophy, 23, 301–319.CrossRefGoogle Scholar
  10. Endriss, U. (2015). Judgment aggregation. In F. Brandt, V. Conitzer, U. Endriss, J. Lang, & A. D. Procaccia (Eds.), Handbook of computational social choice. Cambridge: Cambridge University Press.Google Scholar
  11. Grossi, D., & Pigozzi, G. (2014). Judgment aggregation. A primer. San Rafael: Morgan & Claypool.Google Scholar
  12. Konieczny, S., Lang, J., & Marquis, P. (2004). DA2 merging operators. Artificial Intelligence, 157(1–2), 49–79.CrossRefGoogle Scholar
  13. Kornhauser, L. A., & Sager, L. G. (1986). Unpacking the court. The Yale Law Journal, 96(1), 82–117.CrossRefGoogle Scholar
  14. Kube, S., & Puppe, C. (2009). (When and how) do voters try to manipulate? Experimental evidence from Borda elections. Public Choice, 139, 39–52.CrossRefGoogle Scholar
  15. Lang, J., Pigozzi, G., Slovkovik, M., & van der Torre, L. (2011). Judgment aggregation rules based on minimization. In TARK (pp. 238–246).Google Scholar
  16. Lang, J., Pigozzi, G., Slovkovik, M., & van der Torre, L. (2012). Judgment aggregation rules based on minimization—Extended version, technical report. Université Paris-Dauphine.Google Scholar
  17. Leitgeb, H. (2014). The stability theory of belief. The Philosophical Review, 132(2), 131–171.CrossRefGoogle Scholar
  18. Levi, I. (2004). List and Pettit. Synthese, 140(1/2), 237–242.CrossRefGoogle Scholar
  19. List, C. (2014). When to defer to supermajority testimony and when not to. In J. Lackey (Ed.), Essays in collective epistemology (pp. 240–250). Oxford: Oxford University Press.CrossRefGoogle Scholar
  20. List, C., & Pettit, P. (2002). Aggregating sets of judgments: An impossibility result. Economics and Philosophy, 18(1), 89–110.Google Scholar
  21. Mongin, P. (2012). The doctrinal paradox, the discursive dilemma, and logical aggregation theory. Theory and Decision, 73(3), 315–355.CrossRefGoogle Scholar
  22. Miller, M., & Osherson, D. (2009). Methods for distance-based judgment aggregation. Social Choice and Welfare, 32, 575–601.CrossRefGoogle Scholar
  23. Nehring, K., & Pivato, M. (2011). Majority rule in the absence of a majority. 1–63 (manuscript).Google Scholar
  24. 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, 269–305.CrossRefGoogle Scholar
  25. Pigozzi, G. (2006). Belief merging and the discursive dilemma: An argument-based account to paradoxes of judgment aggregation. Synthese, 152, 285–298.CrossRefGoogle Scholar
  26. Pettit, P. (2006). When to defer to majority testimony and when not to. Analysis, 66(3), 179–187.CrossRefGoogle Scholar
  27. van Ditmarsch, H., Lang, J., & Saffidine, A. (2013). Strategic voting and the logic of knowledge. In Proceedings of the 14th conference on theoretical aspects of rationality and knowledge (TARK-2013).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of PhilosophyNorthwestern UniversityEvanstonUSA

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