IDEAS home Printed from
MyIDEAS: Login to save this article or follow this journal

The doctrinal paradox, the discursive dilemma, and logical aggregation theory

  • Philippe Mongin


Judgment aggregation theory, or rather, as we conceive of it here, logical aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds instead of merely preference judgments. It derives from Kornhauser and Sager’s doctrinal paradox and List and Pettit’s discursive dilemma, two problems that we distinguish emphatically here. The current theory has developed from the discursive dilemma, rather than the doctrinal paradox, and the final objective of the paper is to give the latter its own theoretical development along the line of recent work by Dietrich and Mongin. However, the paper also aims at reviewing logical aggregation theory as such, and it covers impossibility theorems by Dietrich, Dietrich and List, Dokow and Holzman, List and Pettit, Mongin, Nehring and Puppe, Pauly and van Hees, providing a uniform logical framework in which they can be compared with each other. The review goes through three historical stages: the initial paradox and dilemma, the scattered early results on the independence axiom, and the so-called canonical theorem, a collective achievement that provided the theory with its specific method of analysis. The paper goes some way towards philosophical logic, first by briefly connecting the aggregative framework of judgment with the modern philosophy of judgment, and second by thoroughly discussing and axiomatizing the ‘general logic’ built in this framework. Copyright Springer Science+Business Media New York 2012

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Springer in its journal Theory and Decision.

Volume (Year): 73 (2012)
Issue (Month): 3 (September)
Pages: 315-355

in new window

Handle: RePEc:kap:theord:v:73:y:2012:i:3:p:315-355
Contact details of provider: Web page:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Hartmann, Stephan & Pigozzi, Gabriella & Sprenger, Jan, 2010. "Reliable Methods of Judgement Aggregation," Economics Papers from University Paris Dauphine 123456789/6413, Paris Dauphine University.
  2. Franz Dietrich & Christian List, 2010. "The impossibility of unbiased judgment aggregation," Theory and Decision, Springer, vol. 68(3), pages 281-299, March.
  3. Franz Dietrich & Christian List, 2005. "Arrow's Theorem in Judgement Aggregation," Public Economics 0504007, EconWPA, revised 10 Sep 2005.
  4. Marc Fleurbaey & Philippe Mongin, 2004. "The News of the Death of Welfare Economics is Greatly Exaggerated," Working Papers hal-00242931, HAL.
  5. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
  6. LeBreton, M., 1994. "Arrovian Social Choice on Economic Domains," G.R.E.Q.A.M. 94a37, Universite Aix-Marseille III.
  7. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
  8. Elad Dokow & Ron Holzman, 2009. "Aggregation of binary evaluations for truth-functional agendas," Social Choice and Welfare, Springer, vol. 32(2), pages 221-241, February.
  9. Franz Dietrich & Christian List, 2004. "A liberal paradox for judgment aggregation," Public Economics 0405003, EconWPA.
  10. Heifetz, A. & Mongin, P., 1998. "Probability Logic for Type Spaces," Papers 9825, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  11. Klaus Nehring, 2005. "The (Im)Possibility of a Paretian Rational," Economics Working Papers 0068, Institute for Advanced Study, School of Social Science.
  12. John List & Matti Liski, 2005. "Introduction," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 31(2), pages 121-121, 06.
  13. Philippe Mongin, 2003. "L'axiomatisation et les théories économiques," Revue économique, Presses de Sciences-Po, vol. 54(1), pages 99-138.
  14. Christian List, 2002. "A Possibility Theorem on Aggregation Over Multiple Interconnected Propositions," Economics Series Working Papers 123, University of Oxford, Department of Economics.
  15. Christian List, 2002. "A Model of Path-Dependence in Decisions over Multiple Propositions," Economics Papers 2002-W15, Economics Group, Nuffield College, University of Oxford.
  16. Martin Hees, 2007. "The limits of epistemic democracy," Social Choice and Welfare, Springer, vol. 28(4), pages 649-666, June.
  17. Dietrich Franz & List Christian, 2007. "Judgment aggregation without full rationality," Research Memorandum 023, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  18. Franz Dietrich & Christian List, 2007. "Judgment Aggregation By Quota Rules," Journal of Theoretical Politics, , vol. 19(4), pages 391-424, October.
  19. Daniel Eckert & Bernard Monjardet, 2009. "Guilbaud's Theorem : An early contribution to judgment aggregation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00404185, HAL.
  20. d'Aspremont, Claude & Gevers, Louis, 2002. "Social welfare functionals and interpersonal comparability," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 10, pages 459-541 Elsevier.
  21. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
  22. Christian List & Ben Polak, 2010. "Introduction to Judgment Aggregation," Cowles Foundation Discussion Papers 1753, Cowles Foundation for Research in Economics, Yale University.
  23. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(01), pages 89-110, April.
  24. Mongin, Philippe & Dietrich, Franz, 2010. "Un bilan interprétatif de la théorie de l’agrégation logique," Les Cahiers de Recherche 936, HEC Paris.
  25. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
  26. Kornhauser, Lewis A, 1992. "Modeling Collegial Courts. II. Legal Doctrine," Journal of Law, Economics and Organization, Oxford University Press, vol. 8(3), pages 441-70, October.
  27. Aki Lehtinen, 2011. "A Welfarist Critique of Social Choice Theory," Journal of Theoretical Politics, , vol. 23(3), pages 359-381, July.
  28. Franz Dietrich, 2005. "Judgment aggregation in general logics," Public Economics 0505007, EconWPA.
  29. Dietrich Franz & Mongin Philippe, 2008. "The Premiss-Based Approach to Judgment Aggregation," Research Memorandum 013, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  30. Kirman, Alan P. & Sondermann, Dieter, 1972. "Arrow's theorem, many agents, and invisible dictators," Journal of Economic Theory, Elsevier, vol. 5(2), pages 267-277, October.
  31. Brennan, Geoffrey, 2001. "Collective coherence?," International Review of Law and Economics, Elsevier, vol. 21(2), pages 197-211, June.
  32. Duddy, Conal & Piggins, Ashley, 2013. "Many-valued judgment aggregation: Characterizing the possibility/impossibility boundary," Journal of Economic Theory, Elsevier, vol. 148(2), pages 793-805.
  33. Frederik Herzberg & Daniel Eckert, 2010. "Impossibility results for infinite-electorate abstract aggregation rules," Center for Mathematical Economics Working Papers 427, Center for Mathematical Economics, Bielefeld University.
  34. Franz Dietrich & Christian List, 2010. "Majority voting on restricted domains," LSE Research Online Documents on Economics 27902, London School of Economics and Political Science, LSE Library.
  35. Christian List & Ben Polak, 2010. "Introduction to judgment aggregation," LSE Research Online Documents on Economics 27900, London School of Economics and Political Science, LSE Library.
  36. Herzberg, Frederik, 2010. "Judgment aggregators and Boolean algebra homomorphisms," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 132-140, January.
  37. Conal Duddy & Ashley Piggins, 2009. "Many-valued judgment aggregation: characteriing the possibility/impossibility boundary for an important class of agendas," Working Papers 0154, National University of Ireland Galway, Department of Economics, revised 2009.
  38. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
  39. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer, vol. 31(1), pages 41-57, June.
  40. repec:cup:cbooks:9780521028745 is not listed on IDEAS
  41. MONGIN, Philippe & DIETRICH, Franz, 2007. "The premiss-based approach to logical aggregation," Les Cahiers de Recherche 886, HEC Paris.
  42. MONGIN, Philippe, 1993. "Consistent Bayesian Aggregation," CORE Discussion Papers 1993019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  43. Nehring, Klaus, 2003. "Arrow's theorem as a corollary," Economics Letters, Elsevier, vol. 80(3), pages 379-382, September.
  44. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
  45. Christian List, 2005. "The probability of inconsistencies in complex collective decisions," Social Choice and Welfare, Springer, vol. 24(1), pages 3-32, 05.
  46. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
  47. Dietrich, Franz, 2010. "The possibility of judgment aggregation on agendas with subjunctive implications," Journal of Economic Theory, Elsevier, vol. 145(2), pages 603-638, March.
  48. Nehring, Klaus & Puppe, Clemens, 2010. "Justifiable group choice," Journal of Economic Theory, Elsevier, vol. 145(2), pages 583-602, March.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:kap:theord:v:73:y:2012:i:3:p:315-355. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)

or (Christopher F. Baum)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.