Open Thread, June 16-30, 2013

Nissa Seru

If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

I just found this nice quote on The Last Conformer which is supposed to prove that betting on major events is qualitatively different from betting on coinflips:

I wouldn't even offer bets on this kind of probability because that would just invite better informed people to take my money.

It seems to me that the problem exists for coinflips as well. If I flip a coin and don't show you the result, your beliefs about the coin are probably 50/50. But if I offer you to bet at 50/50 odds that the coin came up heads, you'll probably refuse, because I know which way the coin came up and you don't.

According to the Dutch book argument for rationality, we are supposed to accept either side of any bet offered at the odds corresponding to our beliefs. In my example, that idea breaks down, because getting the offer is evidence that you shouldn't take the bet. But then how do we formulate the Dutch book argument?

Omega appears and tells you you've been randomly selected to have the opportunity to take or leave a randomly chosen bet.

3pengvado13y

The selection effect you mention only applies to offering bets, not accepting them. If Alice announces her betting odds and then Bob decides which side of the bet to take, Alice might be doing something irrational there (if she didn't have a bid-ask spread), but we can still talk about dutch books from Bob's perspective. If you want to eliminate the effect whereby Bob updates on the existence of Alice's offer before making his decision, then replace Alice with an automated market maker (setup by someone who expects to lose money in exchange for outsourcing the probability estimate). Or assume some natural process with a naturally occurring payoff ratio that isn't determined by the payoff frequencies nor by anyone's state of knowledge.