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Game Form Representation for Judgement and Arrovian Aggregation

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  • Schoch, Daniel

Abstract

Judgement aggregation theory provides us by a dilemma since it is plagued by impossibility results. For a certain class of logically interlinked agendas, full independence for all issues leads to Arrovian dictatorship. Since independence restricts the possibility of strategic voting, it is nevertheless a desirable property even if only partially fulfilled. We explore a “Goldilock” zone of issue-wise sequential aggregation rules which offers just enough independence not to constrain the winning coalitions among different issues, but restrict the possibilities of strategic manipulation. Perfect Independence, as we call the associated axiom, characterises a gameform like representation of the aggregation function by a binary tree, where each non-terminal node is associated with an issue on which all voters make simultaneous decisions. Our result is universal insofar as any aggregation rule satisfying independence for sufficiently many issues has a game-form representation. One corollary of the game form representation theorem implies that dictatorial aggregation rules have game-form representations, which can be “democratised” by simply altering the winning coalitions at every node.

Suggested Citation

  • Schoch, Daniel, 2015. "Game Form Representation for Judgement and Arrovian Aggregation," MPRA Paper 64311, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:64311
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    File URL: https://mpra.ub.uni-muenchen.de/64311/1/MPRA_paper_64311.pdf
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    References listed on IDEAS

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    1. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
    2. Dietrich, Franz & List, Christian, 2007. "Strategy-Proof Judgment Aggregation," Economics and Philosophy, Cambridge University Press, vol. 23(3), pages 269-300, November.
    3. de Clippel, Geoffroy & Eliaz, Kfir, 2015. "Premise-based versus outcome-based information aggregation," Games and Economic Behavior, Elsevier, vol. 89(C), pages 34-42.
    4. Dietrich, Franz, 2015. "Aggregation theory and the relevance of some issues to others," Journal of Economic Theory, Elsevier, vol. 160(C), pages 463-493.
    5. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    6. 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.
    7. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
    8. 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.
    9. Larsson, Bo & Svensson, Lars-Gunnar, 2006. "Strategy-proof voting on the full preference domain," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 272-287, December.
    10. Herzberg, Frederik & Eckert, Daniel, 2012. "The model-theoretic approach to aggregation: Impossibility results for finite and infinite electorates," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 41-47.
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    More about this item

    Keywords

    Judgment aggregation; Arrow’s theorem; Escape-routes; Game form;

    JEL classification:

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

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