[extropy-chat] Bayes, betting and derivatives

[David Masten]

On Mon, 2006-06-05 at 18:54 -0700, Eliezer S. Yudkowsky wrote:
> Robin Hanson wrote:
> > 
> > Risk-averse Bayesian wannabes would not make pure bets with each other
> > seeking financial gain.   Risk-loving ones might make bets, but only to
> > achieve the risk they want, not because of any disagreement.    Derivatives
> > markets supposedly help people to hedge risk, and not just to make bets.
> > And a patron who wanted to get answers to a question might subsidize
> > a betting market, thereby inducing Bayesian wannabes to bet there.
> 
> Why would Bayesian wannabes with common knowledge of each other's 
> rationality have any expectation of gain in a betting market? 

Because the two Bayesian wannabes have different goals, and different
comparative advantages. Even though they both agree on all the facts of
the matter at hand, they have different subjective valuations of the
bet.

A couple of possible scenarios:
"A" may be looking for insurance against the downside possibility, while
"B" is looking to gain revenue and can handle the downside. Even though
both may agree on the odds, "A" will gladly pay a premium and "B" will
gladly take it.

Another example, "A" wants to cash out and use the cash elsewhere (most
likely to do something where she has a better comparative advantage),
"B" wants to buy a position. Again, "A" will subjectively value the bet
at less than "B" will and therefore they will trade.

>  Why would I ever sell my bet - given the fact that you offer me more
> money than I thought my bet was worth, and I believe you to be
> rational, and I believe you expect to make a profit?  Wouldn't I just
> adjust my estimate of the fair price upward, and then refuse to sell?

Depends. If your objective is to raise cash or otherwise change your
current positions, then you want to trade, not estimate an upward price
and refuse to sell.

Dave