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