[extropy-chat] Probability of identity - solution?

[Robin Hanson]

At 05:33 PM 10/13/2006, Eliezer S. Yudkowsky wrote:
> > After many repetitions you could compare the frequencies you
> > see in your history to the probabilities you had assigned.    Or you
> > could make bets based on your probabilities and see whether such bets
> > win or lose on average.   These two related methods make clear that
> > probabilities are not arbitrary value choices - they can be right or wrong.
>
>The bizarre thing about these situations, as they work in our thought
>experiments, is that, on most assumptions you care to make about where
>the subjective probability mass goes (or as I sometimes say, where the
>realness-fluid flows, bearing in mind that we are almost certainly
>talking about some kind of phlogiston that isn't the actual solution) -
>anyway, regardless of which assumption you make, after N repetitions of
>the experiment, nearly all of your subjective probability mass is in a
>set of observers who, by applying induction, would end up with the
>assumption you started with - that is, under your assumption, all the
>probability mass would end up in observers who, given their experienced
>history, would strongly suspect your assumption - which is to say, after
>N repetitions of the experiment, then "you", wherever you are, would be
>almost certain of the answer.
>But an outside observer would have no idea where most of the
>"probability mass" had gone, so they can't learn anything by performing
>the experiment from outside - you would have to be inside it.

I'm not yet convinced that this claim is true, that there are no outside
observations that can prefer one account to another.   But I haven't thought
about this enough yet to be very confident about any such claim either way.


Robin Hanson  rhanson at gmu.edu  http://hanson.gmu.edu
Associate Professor of Economics, George Mason University
MSN 1D3, Carow Hall, Fairfax VA 22030-4444
703-993-2326  FAX: 703-993-2323