So I've talked on and off before about prediction markets. One of the questions one wants to ask is -- are they actually measuring something? I asked this last week.
In a comment to that post, John Armstrong has informed me of this post from the Volokh Conspiracy that shows that yes, they are. At least in the case of certain prediction markets dealing with Major League Baseball, that is. The standard contract here pays $10 if a team wins a particular game. A plot is provided which aggregates all the trades for contracts on MLB games in each ten-cent interval.
Now, let's say the Phillies and the Qankees are playing each other. (Longtime readers may recall that the reason for the Qankees' existence is because their name starts with Q, which is the letter after P. I haven't talked about them for a while, because it's not baseball season.) And let's say that I think the Phillies have a probability of 62.5% of beating the Qankees. Then I will be willing to pay up to $6.25 for the aforementioned contract, since that's the expected payout.
Now, what does it mean that this probability is 62.5%? Well, it means that if lots and lots of games like that one were played, then the Phillies would win about 62.5% of them. (The meaning of "lots and lots" and "about" can be made precise via the law of large numbers.) But that particular game will never be played again, so we can't check if my intuition is right. But we can do the next best thing -- look at all the games where people paid $6.25 for a contract for some team to win $10, and ask if that team won 62.5% of the time.
It turns out that, basically, they do. That's the point of the chart over at Volokh, which is due to Michael Abramowicz, author of the book Predictocracy: Market Mechanisms for Public and Private Decision Making. It's nice to see some evidence that at least in the world of sports -- which seems to be a good test bed for a lot of statistical and economic work, because it's possible to collect basically all the relevant data -- these things appear to actually be measuring probabilities.