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The Bayes Blind Spot of a finite Bayesian Agent is a large set

Gyenis, Zalán and Rédei, Miklós (2016) The Bayes Blind Spot of a finite Bayesian Agent is a large set. In: UNSPECIFIED.

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Abstract

The Bayes Blind Spot of a Bayesian Agent is the set of probability measures on a Boolean algebra that are absolutely continuous with respect to the background probability measure (prior) of a Bayesian Agent on the algebra and which the Bayesian Agent cannot learn by conditionalizing no matter what (possibly uncertain) evidence he has about the elements in the Boolean algebra. It is shown that if the Boolean algebra is finite, then the Bayes Blind Spot is a very large set: it has the same cardinality as the set of all probability measures (continuum); it has the same measure as the measure of the set of all probability measures (in the natural measure on the set of measures); and is a ``fat'' (second Baire category) set in topological sense in the set of all probability measures taken with its natural topology.


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Item Type: Conference or Workshop Item (UNSPECIFIED)
Creators:
CreatorsEmailORCID
Gyenis, Zalángyz@renyi.hu
Rédei, MiklósM.Redei@lse.ac.uk0000-0001-5298-1443
Additional Information: A talk based on this paper was given under the title "Having a Look at What a Bayesian Agent Cannot See (the Bayes Blind Spot)" at the 8th Quadrennial International Fellows Conference in Lund, Sweeden, July 11-13, 2016
Keywords: Probability theory, Bayesianism, conditional probability
Subjects: Specific Sciences > Mathematics
Specific Sciences > Probability/Statistics
Depositing User: Dr Miklos Redei
Date Deposited: 02 Aug 2016 17:44
Last Modified: 02 Aug 2016 17:44
Item ID: 12326
Subjects: Specific Sciences > Mathematics
Specific Sciences > Probability/Statistics
Date: 1 August 2016
URI: https://philsci-archive.pitt.edu/id/eprint/12326

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