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Another Approach to Consensus and Maximally Informed Opinions with Increasing Evidence

Stewart, Rush and Nielsen, Michael (2018) Another Approach to Consensus and Maximally Informed Opinions with Increasing Evidence. [Preprint]

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Abstract

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.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Stewart, Rushrush.stewart@lrz.uni-muenchen.de0000-0003-2777-5263
Nielsen, Michaelmn2683@columbia.edu
Keywords: Conditionalization; consensus; convergence; imprecise probabilities; Jeffrey conditioning; learning; merging of opinions
Subjects: Specific Sciences > Mathematics > Epistemology
General Issues > Confirmation/Induction
Specific Sciences > Probability/Statistics
Depositing User: Dr. Rush Stewart
Date Deposited: 15 Jul 2018 23:04
Last Modified: 16 Jul 2018 19:14
Item ID: 14872
Subjects: Specific Sciences > Mathematics > Epistemology
General Issues > Confirmation/Induction
Specific Sciences > Probability/Statistics
Date: 2018
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/14872

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