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Another Approach to Consensus and Maximally Informed Opinions with Increasing Evidence

Published online by Cambridge University Press:  01 January 2022

Rush T. Stewart  and
Michael Nielsen
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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. Here, we establish a merging result for sets of probability measures 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. Finally, we demonstrate the philosophical significance of our study by detailing applications to the topics of dynamic coherence, imprecise probabilities, and opinion pooling.

Type
Articles
Information
Philosophy of Science , Volume 86 , Issue 2 , April 2019 , pp. 236 - 254
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

We would like to thank Jean Baccelli, Jessica Collins, Robby Finley, Arthur Heller, Simon Huttegger, Isaac Levi, Ignacio Ojea Quintana, Teddy Seidenfeld, Reuben Stern, Greg Wheeler, an audience at the Institute of History and Philosophy of Science and Technology in Paris, and two anonymous referees for generous feedback that helped us to improve the article.

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