[extropy-chat] Bayes, betting and derivatives
Eliezer S. Yudkowsky
sentience at pobox.com
Tue Jun 6 18:26:00 UTC 2006
Eugen Leitl wrote:
> Perfect knowledge about the real world doesn't exist. No two bases
> of knowledge are alike. I must be missing something, since I don't
> see this as a problem.
The problem is related to (a) "the winner's curse" in auctions (b)
Aumann's Agreement Theorem.
Aumann's Agreement Theorem: While a Bayesian doesn't know the other
Bayesian's specific evidence, they can guess that the other guy has seen
*some* sort of unspecified evidence that makes them willing to pay more
for the stock, or pay more for the bet in an idea-futures market.
The winner's curse: If everyone has some error in how much they
estimate as the fair price of a good, with the error being e.g. normally
distributed around the true value, then whoever wins an auction will
tend to overpay. When you're guessing a fair price at the start of a
problem, you don't yet have access to the information represented by
everyone else's bids. If, at the start of the problem, you bid your
best guess for a fair price, then as soon as you win, your estimate of a
fair price will go down - this is the winner's curse. Thus, you should
offer less in auctions than you think is the fair price, because what
you are really trying to offer is a fair price *conditional* on everyone
else having offered less than you, because that is the only condition
under which your offer will be accepted.
Thus the only way you can run an idea-futures market with Bayesian
bettors is if they don't have common knowledge of each other's
rationality, or if they deliberately try to bet as if they weren't
taking the other's information-of-pricing into account. In either case,
it isn't a real idea-futures market because you require the participants
to deliberately ignore their profit motive. You might as well employ
some other means of aggregating their information.
Eliezer S. Yudkowsky http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence
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