Re: Rationality of Disagreement (Was: Status of Superrationality)

From: Hal Finney (hal@finney.org)
Date: Sat May 31 2003 - 21:28:38 MDT

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    Eliezer writes:
    > I can personally attest that, in practice, this is not how meta-rational
    > Bayesian wannabes actually argue.
    > ...
    > Eliezer Yudkowsky: "What's your estimated probability that the $20 bill
    > is yours?"
    > Nick Bostrom: "Fifteen percent."
    > Eliezer Yudkowsky: "Mine is twenty percent."
    > (Calculator referred to.)
    > Eliezer Yudkowsky: "I'll keep the twenty. Here's eight dollars and
    > fifty-seven cents."
    >
    > And that's how it works.

    I'm surprised that your two estimates were so low. At the time of your
    conversation, you said that you both knew that the other didn't think it
    was their $20 bill, and you had both spent some effort to verify this,
    counting the money in your wallets and such. It's strange that you
    each thought that there was an 80 to 85 percent chance that the other
    person had made a mistake about how much money he had paid, even after he
    had gone through the same careful verification procedure that you had.
    I would have expected that the kind of objective, symmetrical reasoning
    required by meta-rationality would lead you to place a greater credibility
    on the statements of the other person.

    I also wonder how you might have each adjusted your probabilities upon
    hearing the estimates of the other. Given that the two probabilities
    have to sum to 1, what you basically have is an estimate by Nick of 85%
    that the bill was Elizer's, and an estimate by Eliezer of 20% for the
    same fact. I believe Robin's result is that upon hearing these estimates,
    each of you would adjust his own estimate, and would now expect that the
    other's adjusted estimate would be about the same as you's. At least,
    you would not be able to predict whether the other person's estimate
    was now greater or less than your updated value.

    It might have made sense for you to have exchanged a few more estimates.
    Chances are you would have converged quickly and been able to split the
    money on that basis.

    Hal

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