Learning and Pooling, Pooling and Learning

Stewart, Rush T.; Quintana, Ignacio Ojea

doi:10.1007/s10670-017-9894-2

Erkenn

2017

DOI: 10.1007/s10670-017-9894-2

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Learning and Pooling, Pooling and Learning

Rush T. Stewart

Ignacio Ojea Quintana

Abstract: Abstract. We explore which types of probabilistic updating commute with convex IP pooling (Stewart and Ojea Quintana, 2017). Positive results are stated for Bayesian conditionalization (and a mild generalization of it), imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of (precise) externally Bayesian pooling operators due to Wagner (2009). These results strengthen the case that pooling should go by … Show more

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Cited by 3 publications

References 54 publications

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Radical Pooling and Imprecise Probabilities

Quintana

2022

Erkenn

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This paper focuses on radical pooling, or the question of how to aggregate credences when there is a fundamental disagreement about which is the relevant logical space for inquiry. The solution advanced is based on the notion of consensus as common ground (Levi in Synthese 62:3–11, 1985), where agents can find it by suspending judgment on logical possibilities. This is exemplified with cases of scientific revolution. On a formal level, the proposal uses algebraic joins and imprecise probabilities; which is shown to be compatible with the principles of marginalization, rigidity, reverse bayesianism, and minimum divergence commonly endorsed in these contexts. Furthermore, I extend results from previous work by (Stewart & Ojea Quintana in J Philos Logic 47:17–45, 2016; Erkenntnis 83:369–389, 2018) to show that pooling sets of imprecise probabilities can satisfy important pooling axioms.

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Radical Pooling and Imprecise Probabilities

Quintana

2022

Erkenn

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Another Approach to Consensus and Maximally Informed Opinions with Increasing Evidence

Stewart¹,

Nielsen²

2019

Philos. of Sci.

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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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Fusion of Probability Density Functions

et al. 2022

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Learning and Pooling, Pooling and Learning

Cited by 3 publications

References 54 publications

Radical Pooling and Imprecise Probabilities

Radical Pooling and Imprecise Probabilities

Another Approach to Consensus and Maximally Informed Opinions with Increasing Evidence

Fusion of Probability Density Functions

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