>Assuming people know about the assistant, the market will give at least an 80% probability of reinstatement to everything, regardless of how bad it is. (You are guaranteed to make money over time by blindly taking any bet with odds lower than 80%. So people will always bid the odds up to 80% or higher.)
Ironically, this is wrong for the same reason as the point you're making. There's adverse selection. Let's say traders happen to have a close to perfect Scott oracle, so they will be willing to sell you shares of the ones (they think) that Scott would reinstate only at 99%, but will be willing to sell ones (they think) he won't at 50%.
The assistant is calibrated but doesn't have that good of an oracle. Out of every 5 cases he sents Scott, 4 were priced at 99% and get accepted, and the last was priced at 50% and gets rejected. You lose all of your money with a 0% hit rate.
There are more than enough confounding variables, or causal vectors, to break down pure correlations in the real world, which is inconveniently complicated. Which is a problem with prediction markets, esp those which aren't very liquid (ie almost all of them). We also don't know a benchmark of noise for most markets (equity included) which makes relying on % probabilities hard - eg the CEO firing market which is just silly.
I'm surprised you don't consider "the market decides" to be a solution to this. The original idea of decision markets is that the actions are taken on the basis of market prices, and under this structure causality seems like it might be handled just fine.
I don't have a rigorous proof of this - proof is difficult because decision theories tend to have vague "I know it when I see it" definitions to begin with. However, we can at least see that your objections are answered when the market decides. Suppose that the market prices express expectations E[Y|a] and E[Y|b] for some outcome Y and some pair of options {a, b}. You worry that whether a or b is chosen might be informed by some other events or states of the world which, if they transpired or were known to hold, would modify E[Y|a] and E[Y|b]. But if the choice is determined by the closing price of the market, then there obviously cannot be any events or states of the world that inform the choice but not the closing price.
It's not obvious to me that such markets can successfully integrate all of the available information by the time it closes. The closing price can, in general, reflect information about the world not reflected by the price before closing, and the price before closing is trying to anticipate any such developments. It seems like it usually ought to converge, but I can imagine there might be some way to bake self-reference into the market such that it does not converge. Also, once it becomes clear that one choice is preferred to another, there's little incentive to trade the loser, but this might not be much of a problem in practice. If convergence is a problem, adding some randomisation to the choice might help.
Also, there's always a way to implement "the market decides". Instead of asking P(Emissions|treaty), ask P(Emissions|market advises treaty), and make the market advice = the closing prices. This obviously won't be very helpful if no-one is likely to listen to the market, but again the point is to think about markets that people are likely to listen to.
>Assuming people know about the assistant, the market will give at least an 80% probability of reinstatement to everything, regardless of how bad it is. (You are guaranteed to make money over time by blindly taking any bet with odds lower than 80%. So people will always bid the odds up to 80% or higher.)
Ironically, this is wrong for the same reason as the point you're making. There's adverse selection. Let's say traders happen to have a close to perfect Scott oracle, so they will be willing to sell you shares of the ones (they think) that Scott would reinstate only at 99%, but will be willing to sell ones (they think) he won't at 50%.
The assistant is calibrated but doesn't have that good of an oracle. Out of every 5 cases he sents Scott, 4 were priced at 99% and get accepted, and the last was priced at 50% and gets rejected. You lose all of your money with a 0% hit rate.
There are more than enough confounding variables, or causal vectors, to break down pure correlations in the real world, which is inconveniently complicated. Which is a problem with prediction markets, esp those which aren't very liquid (ie almost all of them). We also don't know a benchmark of noise for most markets (equity included) which makes relying on % probabilities hard - eg the CEO firing market which is just silly.
I'm surprised you don't consider "the market decides" to be a solution to this. The original idea of decision markets is that the actions are taken on the basis of market prices, and under this structure causality seems like it might be handled just fine.
I don't have a rigorous proof of this - proof is difficult because decision theories tend to have vague "I know it when I see it" definitions to begin with. However, we can at least see that your objections are answered when the market decides. Suppose that the market prices express expectations E[Y|a] and E[Y|b] for some outcome Y and some pair of options {a, b}. You worry that whether a or b is chosen might be informed by some other events or states of the world which, if they transpired or were known to hold, would modify E[Y|a] and E[Y|b]. But if the choice is determined by the closing price of the market, then there obviously cannot be any events or states of the world that inform the choice but not the closing price.
It's not obvious to me that such markets can successfully integrate all of the available information by the time it closes. The closing price can, in general, reflect information about the world not reflected by the price before closing, and the price before closing is trying to anticipate any such developments. It seems like it usually ought to converge, but I can imagine there might be some way to bake self-reference into the market such that it does not converge. Also, once it becomes clear that one choice is preferred to another, there's little incentive to trade the loser, but this might not be much of a problem in practice. If convergence is a problem, adding some randomisation to the choice might help.
Also, there's always a way to implement "the market decides". Instead of asking P(Emissions|treaty), ask P(Emissions|market advises treaty), and make the market advice = the closing prices. This obviously won't be very helpful if no-one is likely to listen to the market, but again the point is to think about markets that people are likely to listen to.