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A Non-Proposition-Wise Variant of Majority Voting for Aggregating Judgments

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  • García-Bermejo, Juan Carlos

    ()
    (Departamento de Análisis Económico (Teoría e Historia Económica). Universidad Autónoma de Madrid.)

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    Abstract

    Majority voting is commonly used in aggregating judgments. The literature to date on judgment aggregation (JA) has focused primarily on proposition-wise majority voting (PMV). Given a set of issues on which a group is trying to make collective judgments, PMV aggregates individual judgments issue by issue, and satisfies a salient property of JA rules—independence. This paper introduces a variant of majority voting called holistic majority voting (HMV). This new variant also meets the condition of independence. However, instead of aggregating judgments issue by issue, it aggregates individual judgments en bloc. A salient and straightforward feature of HMV is that it guarantees the logical consistency of the propositions expressing collective judgments, provided that the individual points of view are consistent. This feature contrasts with the known inability of PMV to guarantee the consistency of the collective outcome. Analogously, while PMV may present a set of judgments that have been rejected by everyone in the group as collectively accepted, the collective judgments returned by HMV have been accepted by a majority of individuals in the group and, therefore, rejected by a minority of them at most. In addition, HMV satisfies a large set of appealing properties, as PMV also does. However, HMV may not return any complete proposition expressing the judgments of the group on all the issues at stake, even in cases where PMV does. Moreover, demanding completeness from HMV leads to impossibility results similar to the known impossibilities on PMV and on proposition-wise JA rules in general.

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    Bibliographic Info

    Paper provided by Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History) in its series Working Papers in Economic Theory with number 2013/02.

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    Length: 23 pages
    Date of creation: Jan 2013
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    Handle: RePEc:uam:wpaper:201302

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    Related research

    Keywords: judgment aggregation; judgment aggregation correspondences; proposition-wise majority voting; holistic majority voting;

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    References

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    1. Franz Dietrich & Christian List, 2008. "Judgment aggregation without full rationality," Social Choice and Welfare, Springer, vol. 31(1), pages 15-39, June.
    2. 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.
    3. Franz Dietrich, 2005. "Judgment aggregation in general logics," Public Economics 0505007, EconWPA.
    4. 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.
    5. Conal Duddy & Ashley Piggins, 2012. "A measure of distance between judgment sets," Social Choice and Welfare, Springer, vol. 39(4), pages 855-867, October.
    6. Franz Dietrich & Christian List, 2004. "Strategy-proof judgment aggregation," Public Economics 0404007, EconWPA, revised 25 Jul 2005.
    7. Dietrich, Franz, 2011. "Scoring rules for judgment aggregation," MPRA Paper 35657, University Library of Munich, Germany.
    8. 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.
    9. Franz Dietrich & Christian List, 2005. "Judgment aggregation by quota rules," Public Economics 0501005, EconWPA.
    10. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
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