Is there a Dutch Book argument saying that the agent (to avoid book) must have credences defined for all the propositions in the event space? All DB proofs I know assume as much, and I am worried you would have to make controversial assumptions about one gambles with no credence?
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Replying to @przcrbll @lastpositivist and
The accuracy argument doesn't require credences be defined over the whole algebra. And the Dutch book theorem relies on similar geometry, so maybe? But certainly many instances of the DB argument can operate on just a partial credence function.
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E.g. if I've fallen for the bank teller fallacy and assigned Pr(Feminist) = 1/2, Pr(Feminist & Bank teller) = 3/4, I can be Dutch booked. Hmmm... now I'm thinking maybe this isn't what you were asking about?
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I think these videos by Richard Pettigrew (
@Wiglet1981) present and prove the Dutch book theorem for (possibly) merely-partially-defined credence functions: http://www.showme.com/sh/?h=EChN7ey and http://www.showme.com/sh/?h=pCb4QXg1 reply 0 retweets 1 like
Thank you!
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