IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-00404185.html
   My bibliography  Save this paper

Guilbaud's Theorem : An early contribution to judgment aggregation

Author

Listed:
  • Daniel Eckert

    (Institute of Public Economics - Karl-Franzens-Universität Graz)

  • Bernard Monjardet

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

In a paper published in 1952, the French mathematician Georges-Théodule Guilbaud has generalized Arrow's impossibility result to the "logical problem of aggregation", thus anticipating the literature on abstract aggregation theory and judgment aggregation. We reconstruct the proof of Guilbaud's theorem, which is also of technical interest, because it can be seen as the first use of ultrafilters in social choice theory.

Suggested Citation

  • Daniel Eckert & Bernard Monjardet, 2009. "Guilbaud's Theorem : An early contribution to judgment aggregation," Post-Print halshs-00404185, HAL.
    • Handle: RePEc:hal:journl:halshs-00404185
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00404185
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00404185/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Blau, Julian H., 1979. "Semiorders and collective choice," Journal of Economic Theory, Elsevier, vol. 21(1), pages 195-206, August.
    2. Dietrich, F.K. & List, C., 2006. "Judgment aggregation on restricted domains," Research Memorandum 033, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Donald J. Brown, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 89(3), pages 456-469.
    4. Bernard Monjardet & Jean-Pierre Barthélemy & Olivier Hudry & Bruno Leclerc, 2009. "Metric and latticial medians," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00408174, HAL.
    5. MONGIN, Philippe & DIETRICH, Franz, 2007. "The premiss-based approach to logical aggregation," HEC Research Papers Series 886, HEC Paris.
    6. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
    7. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    8. Bengt Hansson, 1976. "The existence of group preference functions," Public Choice, Springer, vol. 28(1), pages 89-98, December.
    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. Mongin, Philippe & Dietrich, Franz, 2011. "An interpretive account of logical aggregation theory," HEC Research Papers Series 941, HEC Paris.
    2. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
    3. Herzberg, Frederik S., 2008. "Judgement aggregation functions and ultraproducts," MPRA Paper 10546, University Library of Munich, Germany, revised 10 Sep 2008.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wesley H. Holliday & Eric Pacuit, 2020. "Arrow’s decisive coalitions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 463-505, March.
    2. Mongin, Philippe & Dietrich, Franz, 2011. "An interpretive account of logical aggregation theory," HEC Research Papers Series 941, HEC Paris.
    3. Herzberg, Frederik, 2010. "Judgment aggregators and Boolean algebra homomorphisms," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 132-140, January.
    4. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
    5. Susumu Cato, 2018. "Collective rationality and decisiveness coherence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 305-328, February.
    6. Susumu Cato, 2013. "Social choice, the strong Pareto principle, and conditional decisiveness," Theory and Decision, Springer, vol. 75(4), pages 563-579, October.
    7. Susumu Cato, 2012. "Social choice without the Pareto principle: a comprehensive analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 869-889, October.
    8. Franz Dietrich & Christian List, 2013. "Propositionwise judgment aggregation: the general case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 1067-1095, April.
    9. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    10. John Weymark, 1984. "Arrow's theorem with social quasi-orderings," Public Choice, Springer, vol. 42(3), pages 235-246, January.
    11. Crès, Hervé & Gilboa, Itzhak & Vieille, Nicolas, 2024. "Bureaucracy in quest of feasibility," Journal of Mathematical Economics, Elsevier, vol. 114(C).
    12. Daniel Eckert & Bernard Monjardet, 2010. "Guilbaud's 1952 theorem on the logical problem of aggregation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00504959, HAL.
    13. Susumu Cato, 2013. "Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 169-202, June.
    14. Sholomov, Lev A., 2000. "Explicit form of neutral social decision rules for basic rationality conditions," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 81-107, January.
    15. Gardner, Roy, 1979. "Onymous Consistent Voting Systems," ISU General Staff Papers 197903010800001088, Iowa State University, Department of Economics.
    16. Bossert, Walter & Cato, Susumu, 2020. "Acyclicity, anonymity, and prefilters," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 134-141.
    17. Susumu Cato, 2016. "Weak independence and the Pareto principle," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 295-314, August.
    18. Duddy, Conal & Piggins, Ashley, 2022. "Collective choice rules with social maximality," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    19. repec:spo:wpmain:info:hdl:2441/dambferfb7dfprc9m2e02cub3 is not listed on IDEAS
    20. Dietrich, Franz, 2015. "Aggregation theory and the relevance of some issues to others," Journal of Economic Theory, Elsevier, vol. 160(C), pages 463-493.
    21. Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories: An oriented survey," Documents de travail du Centre d'Economie de la Sorbonne 10057, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

    More about this item

    Keywords

    Arrow's theorem; aggregation rule; judgment aggregation; logical connexions; ultrafilter.; simple game; ultrafilter; Agrégation des jugements; jeu simple; liaisons logiques; règle d'agrégation; théorème d'Arrow; ultrafiltre.;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    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:hal:journl:halshs-00404185. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.