IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v73y2012i3p315-355.html
   My bibliography  Save this article

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

Author

Listed:
  • Philippe Mongin

    ()

Abstract

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

Suggested Citation

  • Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
  • Handle: RePEc:kap:theord:v:73:y:2012:i:3:p:315-355
    DOI: 10.1007/s11238-012-9310-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11238-012-9310-y
    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 below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Philippe Mongin, 2011. "Judgment aggregation," Working Papers hal-00579346, HAL.
    2. Franz Dietrich, 2005. "Judgment aggregation in general logics," Public Economics 0505007, EconWPA.
    3. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
    4. 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.
    5. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
    6. Herzberg, Frederik, 2010. "Judgment aggregators and Boolean algebra homomorphisms," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 132-140, January.
    7. Philippe Mongin & Franz Dietrich, 2010. "Un bilan interprétatif de la théorie de l'agrégation logique," Revue d'économie politique, Dalloz, vol. 120(6), pages 929-972.
    8. 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.
    9. Martin Hees, 2007. "The limits of epistemic democracy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 649-666, June.
    10. Franz Dietrich & Christian List, 2008. "A liberal paradox for judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 59-78, June.
    11. Nehring, Klaus & Puppe, Clemens, 2010. "Justifiable group choice," Journal of Economic Theory, Elsevier, vol. 145(2), pages 583-602, March.
    12. LeBreton, M., 1994. "Arrovian Social Choice on Economic Domains," G.R.E.Q.A.M. 94a37, Universite Aix-Marseille III.
    13. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    14. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
    15. 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.
    16. 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.
    17. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
    18. 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.
    19. Philippe Mongin, 2003. "L'axiomatisation et les théories économiques," Revue économique, Presses de Sciences-Po, vol. 54(1), pages 99-138.
    20. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745.
    21. Franz Dietrich & Christian List, 2007. "Arrow’s theorem in judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 19-33, July.
    22. Nehring, Klaus, 2003. "Arrow's theorem as a corollary," Economics Letters, Elsevier, vol. 80(3), pages 379-382, September.
    23. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    24. Herzberg, Frederik & Eckert, Daniel, 2017. "Impossibility results for infinite-electorate abstract aggregation rules," Center for Mathematical Economics Working Papers 427, Center for Mathematical Economics, Bielefeld University.
    25. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 529-565, June.
    26. Marc Fleurbaey & Philippe Mongin, 2005. "The news of the death of welfare economics is greatly exaggerated," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 381-418, December.
    27. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
    28. 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.
    29. Franz Dietrich & Christian List, 2008. "Judgment aggregation without full rationality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 15-39, June.
    30. MONGIN, Philippe & DIETRICH, Franz, 2007. "The premiss-based approach to logical aggregation," Les Cahiers de Recherche 886, HEC Paris.
    31. Heifetz, Aviad & Mongin, Philippe, 2001. "Probability Logic for Type Spaces," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 31-53, April.
    32. John List & Matti Liski, 2005. "Introduction," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 31(2), pages 121-121, June.
    33. Aki Lehtinen, 2011. "A Welfarist Critique of Social Choice Theory," Journal of Theoretical Politics, , vol. 23(3), pages 359-381, July.
    34. Franz Dietrich & Christian List, 2010. "The impossibility of unbiased judgment aggregation," Theory and Decision, Springer, vol. 68(3), pages 281-299, March.
    35. Elad Dokow & Ron Holzman, 2009. "Aggregation of binary evaluations for truth-functional agendas," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 221-241, February.
    36. 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.
    37. Kornhauser, Lewis A, 1992. "Modeling Collegial Courts. II. Legal Doctrine," Journal of Law, Economics, and Organization, Oxford University Press, vol. 8(3), pages 441-470, October.
    38. Christian List, 2005. "The probability of inconsistencies in complex collective decisions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(1), pages 3-32, May.
    39. List, Christian, 2003. "A possibility theorem on aggregation over multiple interconnected propositions," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 1-13, February.
    40. Franz Dietrich & Christian List, 2007. "Judgment Aggregation By Quota Rules," Journal of Theoretical Politics, , vol. 19(4), pages 391-424, October.
    41. repec:dau:papers:123456789/6413 is not listed on IDEAS
    42. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
    43. Christian List, 2002. "A Model of Path-Dependence in Decisions over Multiple Propositions," Economics Papers 2002-W15, Economics Group, Nuffield College, University of Oxford.
    44. Brennan, Geoffrey, 2001. "Collective coherence?," International Review of Law and Economics, Elsevier, vol. 21(2), pages 197-211, June.
    45. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
    46. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
    47. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    48. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 41-57, June.
    49. N. Lesca, 2010. "Introduction," Post-Print halshs-00640602, HAL.
    50. Klaus Nehring, 2005. "The (Im)Possibility of a Paretian Rational," Economics Working Papers 0068, Institute for Advanced Study, School of Social Science.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Maniquet, François & Mongin, Philippe, 2016. "A theorem on aggregating classifications," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 6-10.
    2. MANIQUET, François & MONGIN, Philippe, 2014. "Judgment aggregation theory can entail new social choice results," CORE Discussion Papers 2014054, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Herzberg, Frederik, 2016. "Respect for experts or respect for unanimity? The liberal paradox in probabilistic opinion pooling," Center for Mathematical Economics Working Papers 513, Center for Mathematical Economics, Bielefeld University.
    4. Herzberg, Frederik, 2017. "Respect for experts vs. respect for unanimity: The liberal paradox in probabilistic opinion pooling," Economics Letters, Elsevier, vol. 151(C), pages 44-47.
    5. Nehring, Klaus & Pivato, Marcus, 2018. "The median rule in judgement aggregation," MPRA Paper 84258, University Library of Munich, Germany.

    More about this item

    Keywords

    Judgment aggregation; Logical aggregation; Doctrinal paradox; Discursive dilemma; General logic; Premiss-based vs. conclusion-based approach; Social choice theory; Impossibility theorems; D 70; D 71; D 79;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D79 - Microeconomics - - Analysis of Collective Decision-Making - - - Other

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. 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 (Rebekah McClure). General contact details of provider: http://www.springer.com .

    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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.