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The rarity of consistent aggregators

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  • Baharad, Eyal
  • Neeman, Zvika
  • Rubinchik, Anna

Abstract

We demonstrate that the inconsistency associated with judgment aggregation, known as the “doctrinal paradox”, is not a rare exception. There are n individuals who have opinions about k propositions. Each opinion expresses the degree of belief or conviction and thus belongs to the unit interval [0,1]. We work with an arbitrary proposition aggregator that maps opinions about k propositions into an overall opinion in [0,1] and an arbitrary individual opinions aggregator mapping opinions of n individuals into a single judgement from a unit interval. We show that for any typical proposition aggregator, the set of individual opinion aggregators that are immune to the paradox is very small, i.e., is nowhere dense in the space of uniformly bounded functions. In addition, we offer several examples of judgement aggregation for which the paradox can be avoided.

Suggested Citation

  • Baharad, Eyal & Neeman, Zvika & Rubinchik, Anna, 2020. "The rarity of consistent aggregators," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 146-149.
    • Handle: RePEc:eee:matsoc:v:108:y:2020:i:c:p:146-149
    DOI: 10.1016/j.mathsocsci.2019.09.007
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    References listed on IDEAS

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    1. 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.
    2. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 529-565, June.
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    4. 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.
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    7. Franz Dietrich & Christian List, 2017. "Probabilistic opinion pooling generalized. Part two: the premise-based approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 787-814, April.
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    9. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
    10. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
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    Keywords

    Aggregation of opinions; Doctrinal paradox;

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