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Judgments aggregation by a sequential majority procedure

Author

Listed:
  • Peleg, Bezalel
  • Zamir, Shmuel
Abstract
We consider a standard model of judgment aggregation as presented, for example, in Dietrich (2015). For this model we introduce a sequential majority procedure (SMP) which uses the majority rule as much as possible. The ordering of the issues is assumed to be exogenous. The definition of SMP is given in Section 2. In Section 4 we construct an intuitive relevance relation for our model, closely related to conditional entailment, for our model. While in Dietrich (2015), the relevance relation is given exogenously as part of the model, we insist that the relevance relation be derived from the agenda. We prove that SMP has the property of independence of irrelevant issues (III) with respect to (the transitive closure of) our relevance relation. As III is weaker than the property of proposition-wise independence (PI) we do not run into impossibility results as does List (2004) who incorporates PI in some parts of his analysis. We proceed to characterize SMP by anonymity, restricted monotonicity, limited neutrality, restricted agenda property, and independence of past deliberations (see Section 3 for the precise details). SMP inherits the first three axioms from the Majority Rule. The axiom of restricted agenda property guarantees sequentiality. The most important axiom, independence of past deliberations (IPD), says that the choice at time (t+1) depends only on the choices in dates 1,…,t and the judgments at (t+1) (and not on the individual judgments in dates 1,…,t). Also, we use this occasion to point out that Roberts (1991) characterization of choice by plurality voting may be adapted to our model.

Suggested Citation

  • Peleg, Bezalel & Zamir, Shmuel, 2018. "Judgments aggregation by a sequential majority procedure," Mathematical Social Sciences, Elsevier, vol. 95(C), pages 37-46.
    • Handle: RePEc:eee:matsoc:v:95:y:2018:i:c:p:37-46
    DOI: 10.1016/j.mathsocsci.2018.06.004
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    References listed on IDEAS

    as
    1. Dietrich, Franz, 2015. "Aggregation theory and the relevance of some issues to others," Journal of Economic Theory, Elsevier, vol. 160(C), pages 463-493.
    2. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
    3. Franz Dietrich & Christian List, 2007. "Arrow’s theorem in judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 19-33, July.
    4. List, Christian, 2004. "A Model of Path-Dependence in Decisions over Multiple Propositions," American Political Science Review, Cambridge University Press, vol. 98(3), pages 495-513, August.
    5. 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.
    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. repec:hal:pseose:halshs-00978027 is not listed on IDEAS
    8. repec:hal:pseose:halshs-01249513 is not listed on IDEAS
    9. Franz Dietrich & Christian List, 2007. "Judgment Aggregation By Quota Rules," Journal of Theoretical Politics, , vol. 19(4), pages 391-424, October.
    10. 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.
    11. Roberts, Fred S., 1991. "Characterizations of the plurality function," Mathematical Social Sciences, Elsevier, vol. 21(2), pages 101-127, April.
    12. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
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    Cited by:

    1. Maya Bar-Hillel & Cass R. Sunstein, 2019. "Baffling bathrooms: On navigability and choice architecture," Discussion Paper Series dp726, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

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