On Feb 9, 2007, at 11:01 AM, gts wrote:
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.
As Pei and Eliezer and I have all tried to explain in this thread
already ----- yes, the coherence constraint is unfulfillable in
general by any modest-resources mind!
Eliezer even gave a nice argument as to why the **conjunction
fallacy** , a probabilistic error of very simple form, is unavoidable
by any modest-resources mind
The problem is that when confronted with a host of complex,
interdependent propositions S to bet on, the modest-resources mind is
not going to be able to figure out all the interdependencies so as to
set the prices on all the different wagers in a consistent way. So a
smarter mind, more cognizant of the interdependencies, is going to be
able to defeat it by making a judicious selection of which bets to
pose it.
This problem is quite independent of which philosophy one uses to
analytically "justify" probability theory.
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.
But you're thinking about one bet, only. Think about a large set of
interdependent bets, where House knows the dependencies better than
Gambler or Meta-gambler, and where House gets to choose which bets to
pose and Gambler/Meta-gambler must take all the bets House poses
(though Gambler/Meta-gambler get to set the prices).
Then, House will get rich due to its superior understanding of the
dependencies. Just as the house gets rich in the traditional dutch-
book horse-racing arrangements, due to its superior understanding of
dependencies relative to the bettors.
In other words, due to Gambler/Meta-gambler's limited understanding
of the real dependencies, House can arrange a dutch book situation
based on a combination of de Finetti style wagers (or other kinds of
wagers).
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.
This is incorrect, I believe. Coherency requires one to be
reasonably consistent in one's assignment of probabilities to various
interdependent outcomes, otherwise a dutch book can be made against one.
-- Ben
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