I understand the difference between a casino game and a Dutch book
situation.
What I meant was that the same psychological/cognitive traits that
lead humans to get screwed in casinos in simple situations, lead us
to make inaccurate probability estimates that make us vulnerable to
dutch books in more complex situations.
Let me try to explain this more carefully....
In any one dutch book situation, a human will assign a subjective
probability to the outcome that the dutch book is about. That's fine.
But, what if there are a million complex dutch book situations, with
complex interdependencies between them. The human will assign a
subjective probability to each of them. But if the human does not
properly understand the interdependencies, then the human will not
assign the subjective probabiities to them in a consistent, coherent
way. Thus, an agent that more fully understood the interdependencies
better could beat the human on some dutch book situation defined as a
complex Boolean combination of the initial million dutch book
situations. Because the human's subjective probability for the
combinational dutch book would not be consistent with his subjective
probabilities for its component dutch books, given the actual
interdependencies between the components, which the human is not
smart enough to fully understand.
And the same thing holds for any modest-resources AGI or narrow-AI
system. There are too many interdependencies in the world for a
plausibly-large mind to feasibly manage and reason-on-the-basis-of
them all. So we are bound to be incoherent sometimes, in assigning
subjective probabilities to complex situations involving multiple
interdependencies.
In order to avoid this, we are tuned to recognize certain kinds of
interdependencies that were historically important to us. But, this
tuning was pretty damn crude, and led our brains to evolve the
various "heuristics and biases" that have been documented in the
psychology literature in the last few decades. Which are exemplified
e.g. in human behavior in casinos...
-- Ben G
On Feb 7, 2007, at 11:28 AM, gts wrote:
On Wed, 07 Feb 2007 10:57:04 -0500, Ben Goertzel <[EMAIL PROTECTED]>
wrote:
The dramatic probabilistic incoherency of humans is demonstrated
by human behavior in casinos.
You mean something more stringent than me by the word incoherency,
then. Human betting behavior in casinos is stupid but it is not
incoherent in the De Finetti sense as I understand it.
It's easy to prove incoherence: one need only show how a dutch book
can be made against the allegedly incoherent person. Vulnerability
to dutch books is how incoherence is defined under the theory.
Casino gamblers are stupid in so much as they place bets with
unfavorable odds, but they do not by virtue of those stupid bets
make themselves vulnerable to dutch books. One sometimes wins
against unfavorable odds but it is never possible to beat a dutch
book. In fact casinos do not even offer such betting situations.
-gts
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