You could have a market that estimates P(A|B) directly using the reversal mechanism (called-off bets). However, I maintain that this will give identical estimates as the markets I proposed. These things are probabilities, they follow the rules of probability logic.

The point I was trying to illustrate, was not that it is impossible to estimate P(A|B), but rather that P(A|B) is not the quantity that a rational decision maker needs in order to optimize for A.

I agree that using a market that directly estimates P(A|B) might have been a better example, because it avoids readers going in the wrong direction when they try to figure out what is going on. However, changing this will take some non-trivial rewriting of the text. I will try to do that when I have more time on my hands.

Your point about the markets predicting themselves is interesting. I was imagining a democracy informed by prediction markets rather than a pure futarchy. However, if the voters are influenced by the market, it does indeed predict itself to some extent. I don't think this is a major problem, but I will keep thinking about it. I have relatively high confidence that my argument for prediction markets being confounded does not rely on this.