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.
In the scenario I provided, the contracts will be traded at the following prices after the demon reveals his information:
Hillary elected and US nuked: $14.3 (1/7 of $100)
Hillary elected and US not nuked: $28.6 (2/7)
Jeb elected and US nuked: $14.3 (1/7)
Jeb elected and US not nuked: $42.9 (3/7)
Like you said, if people change their votes based on the market, the prices may be distorted by the market predicting itself.
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.
Given how you have set this problem up, what do you think will be the relative prices of the 4 contracts you specified?
In the scenario I provided, the contracts will be traded at the following prices after the demon reveals his information:
Hillary elected and US nuked: $14.3 (1/7 of $100) Hillary elected and US not nuked: $28.6 (2/7) Jeb elected and US nuked: $14.3 (1/7) Jeb elected and US not nuked: $42.9 (3/7)
Like you said, if people change their votes based on the market, the prices may be distorted by the market predicting itself.