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    Home/Original/inverse
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    Inverse View

    It is not the case that Bayesian conditioning is the probabilistic counterpart of logical public announcements when new information is accepted as irrevocably true by all agents.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Bayesian conditioning requires a prior probability over the entire possibility space, but logical public announcements can introduce wholly novel propositions with no prior.
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    • 2.When an announcement concerns an event outside the agent's prior sigma-algebra, conditionalization is undefined, while the logical submodel operation remains well-formed.
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    • 3.Therefore the two operations diverge precisely at the limit cases that matter most epistemically, revealing a structural asymmetry the claim conceals.
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    Reason for 2 of 2
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    • 1.Jeffrey conditionalization, not simple Bayesian conditioning, is the correct probabilistic model for evidence that shifts credences without certainty, as Richard Jeffrey argued in 'The Logic of Decision'.
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    • 2.Public announcements in dynamic epistemic logic install hard certainty (probability 1), but empirical evidence routinely fails to warrant such certainty, making the logical model an idealization that Bayesian practice does not uniformly endorse.
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    • 3.If Bayesian conditioning and public announcements only align under the special assumption of probability-1 updating, the claimed 'counterpart' relation holds only for a narrow, non-representative class of epistemic updates.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Hard information is accepted as irrevocably true by all agents.
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    • 2.Computing beliefs after a public announcement means recomputing in the submodel consisting of all states where the received information was true.
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    • 3.Recalculating probabilities in Bayesian update uses exactly the same mechanism as recomputing in that submodel.
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