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Binary Collective Choice with Multiple Premises

Author

Listed:
  • Masaki Miyashita

    (Department of Economics, Yale University, USA)

Abstract

Imagine a group of individuals facing with a complicated yes-no question whose truth value is logically driven from multiple premises. Their purpose is to make a correct group judgment on the question based on their individual judgments. There are two types of ways to aggregate individual judgments: "the premise driven way" (PDW) and "the conclusion driven way" (CDW). We analyze which way is superior to the other to find a correct answer. In our analysis, we introduce a Boolean algebraic approach to formulate a general class of such judgment aggregation problems. We find that if a decision problem is conjunctive, then PDW is more likely to avoid "false acquittance," while CDW is more likely to avoid "false conviction". If a decision problem is disjunctive, the converse of this result holds. These conditions are sufficient to characterize intrinsic biases of aggregation procedures when an aggregation rule possesses no veto power. We also study the asymptotic properties of aggregation procedures, and find that, as the size of a group goes to infinity, PDW ensures the probability that the voting outcome is correct converges to one, while this holds for CDW only if an additional condition is satisfied.

Suggested Citation

  • Masaki Miyashita, 2017. "Binary Collective Choice with Multiple Premises," Discussion Paper Series DP2017-27, Research Institute for Economics & Business Administration, Kobe University.
  • Handle: RePEc:kob:dpaper:dp2017-27
    as

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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2017-27.pdf
    File Function: First version, 2017
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    References listed on IDEAS

    as
    1. Franz Dietrich & Christian List, 2008. "A liberal paradox for judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 59-78, June.
    2. 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.
    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. de Clippel, Geoffroy & Eliaz, Kfir, 2015. "Premise-based versus outcome-based information aggregation," Games and Economic Behavior, Elsevier, vol. 89(C), pages 34-42.
    5. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    6. repec:cup:apsrev:v:82:y:1988:i:02:p:567-576_08 is not listed on IDEAS
    7. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
    8. repec:cup:apsrev:v:82:y:1988:i:04:p:1231-1244_19 is not listed on IDEAS
    9. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Social choice; Judgment aggregation; Doctrinal paradox; Condorcet jury theorem; Boolean algebra;

    JEL classification:

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

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