IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v107y2020icp23-36.html
   My bibliography  Save this article

Quota rules for incomplete judgments

Author

Listed:
  • Terzopoulou, Zoi

Abstract

Suppose that a group of individuals are asked to aggregate their judgments on different—possibly logically interconnected—propositions in order to reach a collective decision. Quota rules are natural aggregation rules requiring that a proposition be collectively accepted if and only if the number of individuals that agree with it exceeds a given threshold. In cases where the individuals may also abstain on some of the issues at stake and report incomplete judgments, there are several ways for determining the relevant threshold, depending on the number of abstentions or the margin between those that agree and those that disagree with a given proposition. In this paper I systematically design quota rules for incomplete inputs, within the framework of judgment aggregation, and explore their formal properties. In particular, I characterise axiomatically three distinct classes of quota rules, extending known results of the literature that so far only applied to complete inputs.

Suggested Citation

  • Terzopoulou, Zoi, 2020. "Quota rules for incomplete judgments," Mathematical Social Sciences, Elsevier, vol. 107(C), pages 23-36.
    • Handle: RePEc:eee:matsoc:v:107:y:2020:i:c:p:23-36
    DOI: 10.1016/j.mathsocsci.2020.07.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489620300652
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2020.07.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. François Maniquet & Massimo Morelli, 2015. "Approval quorums dominate participation quorums," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 1-27, June.
    2. Houy, Nicolas, 2007. "Some further characterizations for the forgotten voting rules," Mathematical Social Sciences, Elsevier, vol. 53(1), pages 111-121, January.
    3. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(1), pages 89-110, April.
    4. Dietrich, Franz & List, Christian, 2007. "Strategy-Proof Judgment Aggregation," Economics and Philosophy, Cambridge University Press, vol. 23(3), pages 269-300, November.
    5. Annick Laruelle & Federico Valenciano, 2011. "Majorities with a quorum," Journal of Theoretical Politics, , vol. 23(2), pages 241-259, April.
      • Laruelle, Annick & Valenciano Llovera, Federico, 2010. "Majorities with a quorum," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    6. Paulo P. Côrte-Real & Paulo T. Pereira, 2004. "The voter who wasn’t there: Referenda, representation and abstention," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 349-369, April.
    7. Zoi Terzopoulou & Ulle Endriss, 2019. "Strategyproof judgment aggregation under partial information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(3), pages 415-442, October.
    8. Charles Pattie & Ron Johnston, 2001. "A Low Turnout Landslide: Abstention at the British General Election of 1997," Political Studies, Political Studies Association, vol. 49(2), pages 286-305, June.
    9. Anand, Paul & Pattanaik, Prasanta & Puppe, Clemens (ed.), 2009. "The Handbook of Rational and Social Choice," OUP Catalogue, Oxford University Press, number 9780199290420.
    10. 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.
    11. Franz Dietrich & Christian List, 2007. "Judgment Aggregation By Quota Rules," Journal of Theoretical Politics, , vol. 19(4), pages 391-424, October.
    12. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
    13. Luís Aguiar-Conraria & Pedro Magalhães, 2010. "Referendum design, quorum rules and turnout," Public Choice, Springer, vol. 144(1), pages 63-81, July.
    14. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
    15. Freixas, Josep & Zwicker, William S., 2009. "Anonymous yes-no voting with abstention and multiple levels of approval," Games and Economic Behavior, Elsevier, vol. 67(2), pages 428-444, November.
    16. Gã„Rdenfors, Peter, 2006. "A Representation Theorem For Voting With Logical Consequences," Economics and Philosophy, Cambridge University Press, vol. 22(2), pages 181-190, July.
    17. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
    18. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
    19. Llamazares, Bonifacio, 2006. "The forgotten decision rules: Majority rules based on difference of votes," Mathematical Social Sciences, Elsevier, vol. 51(3), pages 311-326, May.
    Full references (including those not matched with items on IDEAS)

    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. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    2. Frederik S. Herzberg, 2013. "The (im)possibility of collective risk measurement: Arrovian aggregation of variational preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 69-92, May.
    3. Bozbay, Irem, 2012. "Truth-Seeking Judgment Aggregation over Interconnected Issues," Working Papers 2012:31, Lund University, Department of Economics.
    4. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2014. "The Condorcet set: Majority voting over interconnected propositions," Journal of Economic Theory, Elsevier, vol. 151(C), pages 268-303.
    5. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2011. "Condorcet admissibility: Indeterminacy and path-dependence under majority voting on interconnected decisions," MPRA Paper 32434, University Library of Munich, Germany.
    6. Dietrich, Franz, 2016. "Judgment aggregation and agenda manipulation," Games and Economic Behavior, Elsevier, vol. 95(C), pages 113-136.
    7. Schoch, Daniel, 2015. "Game Form Representation for Judgement and Arrovian Aggregation," MPRA Paper 64311, University Library of Munich, Germany.
    8. Marc Pauly, 2013. "Characterizing referenda with quorums via strategy-proofness," Theory and Decision, Springer, vol. 75(4), pages 581-597, October.
    9. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
    10. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
    11. Bozbay, İrem & Dietrich, Franz & Peters, Hans, 2014. "Judgment aggregation in search for the truth," Games and Economic Behavior, Elsevier, vol. 87(C), pages 571-590.
    12. Franz Dietrich & Christian List, 2021. "Dynamically rational judgment aggregation," Post-Print halshs-03140090, HAL.
    13. García-Bermejo, Juan Carlos, 2013. "A Non-Proposition-Wise Variant of Majority Voting for Aggregating Judgments," Working Papers in Economic Theory 2013/02, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
    14. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
    15. List, Christian, 2007. "Group deliberation and the transformation of judgments: an impossibility result," LSE Research Online Documents on Economics 19273, London School of Economics and Political Science, LSE Library.
    16. Dietrich, Franz, 2015. "Aggregation theory and the relevance of some issues to others," Journal of Economic Theory, Elsevier, vol. 160(C), pages 463-493.
    17. Franz Dietrich, 2014. "Scoring rules for judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 873-911, April.
    18. Klaus Nehring & Marcus Pivato & Clemens Puppe, 2016. "Unanimity overruled: Majority voting and the burden of history," Journal of Theoretical Politics, , vol. 28(4), pages 552-597, October.
    19. Peleg, Bezalel & Zamir, Shmuel, 2018. "Judgments aggregation by a sequential majority procedure," Mathematical Social Sciences, Elsevier, vol. 95(C), pages 37-46.
    20. García-Bermejo, Juan Carlos, 2012. "A Pooling Approach to Judgment Aggregation," Working Papers in Economic Theory 2012/01, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).

    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:eee:matsoc:v:107:y:2020:i:c:p:23-36. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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.