Another Approach to Consensus and Maximally Informed Opinions with Increasing Evidence

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

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.

Analytics

Added to PP
2018-06-01

Downloads
344 (#31,315)

6 months
26 (#34,443)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

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.
Distention for Sets of Probabilities.Rush T. Stewart & Michael Nielsen - 2022 - Philosophy of Science 89 (3):604-620.

Add more citations

Similar books and articles

Oracles, Aesthetics, and Bayesian Consensus.Jeffrey A. Barrett - 1996 - Philosophy of Science 63 (Supplement):273-280.
On the Nature of Bayesian Convergence.James Hawthorne - 1994 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:241 - 249.
A Dilemma for the Imprecise Bayesian.Namjoong Kim - 2016 - Synthese 193 (6):1681-1702.
Consensus in Art and Science.Keith Lehrer - 2007 - Vienna Circle Institute Yearbook 13:159-172.
Defeasible Conditionalization.Paul D. Thorn - 2014 - Journal of Philosophical Logic 43 (2-3):283-302.
The Extent of Dilation of Sets of Probabilities and the Asymptotics of Robust Bayesian Inference.Timothy Herron, Teddy Seidenfeld & Larry Wasserman - 1994 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:250 - 259.