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Meta-Inductive Probability Aggregation

Author

Listed:
  • Christian J. Feldbacher-Escamilla

    (University of Cologne)

  • Gerhard Schurz

    (University of Duesseldorf)

Abstract

There is a plurality of formal constraints for aggregating probabilities of a group of individuals. Different constraints characterise different families of aggregation rules. In this paper, we focus on the families of linear and geometric opinion pooling rules which consist in linear, respectively, geometric weighted averaging of the individuals’ probabilities. For these families, it is debated which weights exactly are to be chosen. By applying the results of the theory of meta-induction, we want to provide a general rationale, namely, optimality, for choosing the weights in a success-based way by scoring rules. A major argument put forward against weighting by scoring is that these weights heavily depend on the chosen scoring rule. However, as we will show, the main condition for the optimality of meta-inductive weights is so general that it holds under most standard scoring rules, more precisely under all scoring rules that are based on a convex loss function. Therefore, whereas the exact choice of a scoring rule for weighted probability aggregation might depend on the respective purpose of such an aggregation, the epistemic rationale behind such a choice is generally valid.

Suggested Citation

  • Christian J. Feldbacher-Escamilla & Gerhard Schurz, 2023. "Meta-Inductive Probability Aggregation," Theory and Decision, Springer, vol. 95(4), pages 663-689, November.
  • Handle: RePEc:kap:theord:v:95:y:2023:i:4:d:10.1007_s11238-023-09933-z
    DOI: 10.1007/s11238-023-09933-z
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    References listed on IDEAS

    as
    1. 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.
    2. Dietrich, Franz, 2016. "A Theory Of Bayesian Groups," MPRA Paper 75363, University Library of Munich, Germany.
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