Bayesian Merging of Opinions and Algorithmic Randomness.
We study the phenomenon of merging of opinions for computationally limited Bayesian agents from the perspective of algorithmic randomness. When they agree on which data streams are algorithmically random, two Bayesian agents beginning the learning process with different priors may be seen as having...
| Published in: | British Journal for the Philosophy of Science Vol. 76; no. 4; pp. 921 - 953 |
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| Format: | Article |
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University of Chicago Press
Dec2025
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| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=189879611&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 189879611 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00070882 BPL jtl: British Journal for the Philosophy of Science issn: 00070882 maglogo: N pubinfo: dt: Dec2025 vid: 76 iid: 4 pid: 415 pub: University of Chicago Press artinfo: ui: 189879611 10.1086/721758 ppf: 921 ppct: 32 formats: tig: atl: Bayesian Merging of Opinions and Algorithmic Randomness. aug: au: Zaffora Blando, Francesca affil: Department of Philosophy. Carnegie Mellon University. Pittsburgh, PA, USA. su: Algorithmic randomness Bayesian analysis Uniformity Stream measurements Computational complexity Bayes' estimation sug: subj: Algorithmic randomness Bayesian analysis Uniformity Stream measurements Computational complexity Bayes' estimation ab: We study the phenomenon of merging of opinions for computationally limited Bayesian agents from the perspective of algorithmic randomness. When they agree on which data streams are algorithmically random, two Bayesian agents beginning the learning process with different priors may be seen as having compatible beliefs about the global uniformity of nature. This is because the algorithmically random data streams are of necessity globally regular: they are precisely the sequences that satisfy certain important statistical laws. By virtue of agreeing on which data streams are algorithmically random, two Bayesian agents can thus be taken to concur on which global regularities they expect to see in the data. We show that this type of compatibility between priors suffices to ensure that two computable Bayesian agents will reach inter-subjective agreement with increasing information. In other words, it guarantees that their respective probability assignments will almost surely become arbitrarily close to each other as the number of observations increases. Thus, when shared by computable Bayesian learners with different subjective priors, the beliefs about uniformity captured by algorithmic randomness provably lead to merging of opinions. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2025 holdings: @attributes: islocal: N |
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