Philosophy of Science (2):236-254 (2018)

Michael Nielsen
University of Sydney
Rush T. Stewart
Ludwig Maximilians Universität, München
Merging of opinions results underwrite Bayesian rejoinders to complaints about the subjective nature of personal probability. Such results establish that sufficiently similar priors achieve consensus in the long run when fed the same increasing stream of evidence. Initial subjectivity, the line goes, is of mere transient significance, giving way to intersubjective agreement eventually. Here, we establish a merging result for sets of probability measures that are updated by Jeffrey conditioning. This generalizes a number of different merging results in the literature. We also show that such sets converge to a shared, maximally informed opinion. Convergence to a maximally informed opinion is a (weak) Jeffrey conditioning analogue of Bayesian “convergence to the truth” for conditional probabilities. Finally, we demonstrate the philosophical significance of our study by detailing applications to the topics of dynamic coherence, imprecise probabilities, and probabilistic opinion pooling.
Keywords Consensus  Convergence  Jeffrey Conditionalization  Imprecise Probabilities  Merging of Opinions
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Reprint years 2019
DOI 10.1086/701954
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References found in this work BETA

Bayes or Bust?John Earman - 1992 - Bradford.
On Indeterminate Probabilities.Isaac Levi - 1974 - Journal of Philosophy 71 (13):391-418.
Games and Decisions: Introduction and Critical Survey.R. Duncan Luce & Howard Raiffa - 1958 - Philosophy and Phenomenological Research 19 (1):122-123.

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Citations of this work BETA

Persistent Disagreement and Polarization in a Bayesian Setting.Michael Nielsen & Rush T. Stewart - 2021 - British Journal for the Philosophy of Science 72 (1):51-78.
Deterministic Convergence and Strong Regularity.Michael Nielsen - 2020 - British Journal for the Philosophy of Science 71 (4):1461-1491.

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