On Feb 8, 2007, at 8:59 AM, gts wrote:
On Wed, 07 Feb 2007 20:40:27 -0500, Charles D Hixson
<[EMAIL PROTECTED]> wrote:
I suspect you of mis-analyzing the goals and rewards of casino
gamblers.... I'm not sure whether or not this speaks to the points
that you are attempting to raise, but it certainly calls into
question comments about "stupid bets". Well, the lottery isn't a
casino, so perhaps you are correct, but I would be suspicious
about calculating values based solely on the money.
The point I was making, and it applies equally well to lottery bets
as it does to casino bets, is that such bets are not evidence of
incoherence where incoherence is defined (by De Finetti) as
vulnerability to dutch books.
A dutch book occurs when an incoherent thinker is forced to lose as
a result of his inconsistent judgmental probabilities, no matter
the outcome. Such bets are worse than stupid. :)
I gave an example of a Dutch book in a post to Russell in which an
incoherent thinker assigns a higher probability to intelligent life
on Mars than to mere life on Mars. Since the first hypothesis can
be true only if the second is true, it is incoherent to assign a
higher probability to the first than to the second.
Well, the heuristics and biases literature contains MANY results
showing that people regularly DO make that kind of "conjunction fallacy"
Coherence is basically just common sense applied to probabilistic
reasoning. I'm dismayed to learn from Ben that coherence is so
difficult to achieve in AGI.
AGIs don't need to be as lame as humans, they can certainly avoid the
conjunction fallacy. But Dutch Book scenarios can be quite
complicated, see e.g. the Gambling example at
http://en.wikipedia.org/wiki/Dutch_book
which is only moderately complicated. If you create a similar
example of 10 times the complexity, basically any human may be fooled
unless they do some math or write some code to understand the
probabilities involved...
Ben
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