Arin Dube points to a great illustration of the power of prediction markets. Yesterday due to a new scandal the probability that Graham Platner would drop out of the Maine Democratic primary exploded from 9% to 96% (+87 percentage points). At the same time, the probability that the Democrats would win the election jumped by about 9 percentage points, from 54% to 63%. What does this tell you?
The market is signaling that Platner reduces the Democrats’ chances of victory. We can be more precise. If an 87-point increase in the probability of dropping out gets you 9 points of winning, then a 100% chance of dropping out implies a gain of 9/0.87 ≈ 10.3 percentage points.

Thus the market’s best estimate is that Platner is reducing the Democrats’ chance of winning by about 10 percentage points (compared to an unknown replacement). That’s a pretty big number! Democrats should surely use this information to make better decisions.

Now, I have been a bit loose. We have implicitly assumed that the news mainly moved the probability of Platner dropping out, rather than independently changing the Democrats’ general-election prospects. The issue is we are trying to reverse engineer two conditional prices, P(win|drop) and P(win|stay), from one unconditional price, P(win), and its comovement with P(drop). It works pretty well here as an illustration but Robin Hanson’s idea is that we can do better yet by trading the conditionals instead of inferring them.

Hanson’s decision markets would run contracts of the form “pays $1 if Democrats win, conditional on Platner dropping out — bet refunded if he stays.” Plus the mirror contract conditioned on staying. The refund provision makes the price a conditional probability: a trader pricing the first contract doesn’t need any view on whether Platner drops out, only on how the race goes if he does. With this structure we would get cleaner estimates of the conditional probabilities–in this case whether the Democrats do better with Platner in or out–which is exactly what a decision maker needs.

We were able to plausibly reverse engineer our estimate because the market happened to move 87 points in a single day. But a decision market would have posted the number continuously, no scandal required. In other words, with decision markets in play, not just prediction markets, we could have seen how much Platner was costing the Democrats before the latest scandal hit—which is precisely when the information would have been most useful.

It’s been fun to see prediction markets catch on with the public but the world is still decades behind Hanson’s decision markets—let alone futarchy!