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RichardKennaway comments on 0 And 1 Are Not Probabilities - Less Wrong

34 Post author: Eliezer_Yudkowsky 10 January 2008 06:58AM

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Comment author: RichardKennaway 19 October 2011 08:37:19AM *  2 points [-]

The ("Bayesian") framework explored in these essays replaces the two Cartesian options, affirmation and denial, by a continuum of judgmental probabilities in the interval from 0 to 1, endpoints included, or -- what comes to the same thing -- a continuum of judgmental odds in the interval from 0 to infinity, endpoints included. Zero and 1 are probabilities no less than 1/2 and 99/100 are. Probability 1 corresponds to infinite odds, 1:0. That's a reason for thinking in terms of odds: to remember how momentous it may be to assign probability 1 to a hypothesis."

Richard Jeffrey, "Probability and the art of judgement".

I leave it as an exercise to correctly state the relationships between Eliezer's article, the Jeffrey quote, and the value of P(A|A).

(Note: Jeffrey is not to be confused with Jeffreys, although both were Bayesian probability theorists.)