On Wed, 07 Feb 2007 18:37:52 -0500, Ben Goertzel <[EMAIL PROTECTED]> wrote:
This is simply a re-post of my prior post, with corrected terminology,
but unchanged substance:
Thanks! Very helpful.
Now that you have a better understanding of dutch books, I wonder if you
still feel the De Finetti coherence constraint is as formidable as you may
have first thought. I haven't seen your code but I would be surprised if
Novamente is really incoherent.
Probably you can show that the prices of the bets set by Gambler and
Meta-gambler respectively are consistent and related in such a way that
the House cannot make a dutch book against the Gambler and Meta-Gambler
seen as a team; that is, that the House cannot force Novamente to lose
automatically no matter what is true.
The House might attempt, for example, buying the operational subjective
probability bet (p) from Gambler while simultaneously selling the g bet to
Meta-Gambler, or vice versa, in such a way as to force the team of
Gamblers to lose money. These transactions could perhaps take place at
separate times. For example the House might attempt to buy one bet after n
observations of S and sell the other after n+x observations of S.
This doesn't really add anything practical to the indefinite
probabilities framework as already formulated, it
just makes clearer the interpretation of the indefinite probabilities in
terms of de Finetti style betting games.
Yes, thanks for the illustration.
Note that coherency does not constrain one to be especially accurate in
one's judgemental probabilities. A coherent entity needn't be very smart
about the true state of nature. The coherency constraint merely defines
the outer limits of what one may rationally consider possible.
-gts
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