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Quota rules for incomplete judgments

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  • 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
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    References listed on IDEAS

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    1. Houy, Nicolas, 2007. "Some further characterizations for the forgotten voting rules," Mathematical Social Sciences, Elsevier, vol. 53(1), pages 111-121, January.
    2. 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.
    3. Dietrich, Franz & List, Christian, 2007. "Strategy-Proof Judgment Aggregation," Economics and Philosophy, Cambridge University Press, vol. 23(3), pages 269-300, November.
    4. 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.
    5. 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.
    6. Anand, Paul & Pattanaik, Prasanta & Puppe, Clemens (ed.), 2009. "The Handbook of Rational and Social Choice," OUP Catalogue, Oxford University Press, number 9780199290420.
    7. Luís Aguiar-Conraria & Pedro Magalhães, 2010. "Referendum design, quorum rules and turnout," Public Choice, Springer, vol. 144(1), pages 63-81, July.
    8. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
    9. Gärdenfors, Peter, 2006. "A Representation Theorem For Voting With Logical Consequences," Economics and Philosophy, Cambridge University Press, vol. 22(2), pages 181-190, July.
    10. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
    11. 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.
    12. 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.
    13. Annick Laruelle & Federico Valenciano, 2011. "Majorities with a quorum," Journal of Theoretical Politics, , vol. 23(2), pages 241-259, April.
    14. 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.
    15. Franz Dietrich & Christian List, 2007. "Judgment Aggregation By Quota Rules," Journal of Theoretical Politics, , vol. 19(4), pages 391-424, October.
    16. 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.
    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.
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