His conditional bets include called-off bets, what you call reversal of trades, which is why I thought what he is talking about corresponds to your second market proposal. Your first market proposal doesn’t have called-off bets. Is there some part of your statistical objection which isn’t solved by called-off bets?
I see where you are coming from, in fact this used to be my position: This post was inspired by a talk I gave at the Less Wrong Meetup, where I made the claim that the causality problem is solved by called-off bets (reversals). Jimrandomh called me on it, and he was right: There will still be confounding even when bets are called off/reversed:
Imagine there are two possible worlds: In one of them, Kim is overthrown, in the other he is not. I expect the probability of Hillary being elected will be much higher if he is overthrown. I also expect that the probability of an attack is much higher if Kim is still in office.
If I make a bet on the probability of an attack given that Hillary is elected, and I know that this market will only be settled in the case that she is elected, my estimated probability will incorporate information about the fact that if the market is settled, more likely than not, Kim was overthrown. However, at the time I make the bet, I don’t know whether Kim will be overthrown, so this means my bet incorporates information that causally does not depend on Hillary being elected.
We tried to solve this using the “precommitment” mechanism. In graphical terms, the idea is that this removes all arrows into the election by ensuring that the only cause of who gets to be President is the prediction market itself. My intuition is that it works, but it is certainly something that should be doublechecked by someone with more technical expertise on prediction markets and causality.
Deciding the outcome based on the price in the betting market is the whole point of futarchy. You seem to be saying that prediction markets in absence of futarchy don’t provide good advice on how you should vote. That is an interesting point which I hadn’t considered before your post.
I am still uncomfortable with your example, however. If Kim is overthrown prior to the election, the market rates will adjust based on that information. If he’s overthrown after the election, then there is no causal link between that and the election results, presumably. Prior to his overthrow, the market simply provides the best estimate of the outcome until that result is known. All that means is you shouldn’t make decisions based on outdated estimates that didn’t include all known information.
Yes, the point of futarchy is to make the decision based on the price in the prediction market. What I am saying is that if you want participants to provide their best guesses about which decisions will maximize the outcome, you have to make a credible pre-commitment that the only factor that influences the decision is the prediction market that is currently being traded. You can only make such a commitment for one prediction market per decision (but like you say, the outcome measure can be arbitrarily complex)
I think you are right that once it becomes known whether Kim is overthrown, it is no longer a confounder. Therefore, the bias should be expected to get lower the nearer we get to the decision time point. However, some confounders may be unobservable, or unobserved until the time the decision is made. For instance, if this is not a pure futarchy and there is voting going on, you may gain information from the make-up of the electorate. Imagine there is a referendum on a 70% income tax and Bernie Sanders is running for President. Even if he has no influence on whether the referendum passes, his chances of being elected will be correlated with the outcome of the referendum, and you won’t know which state you are in until you see the exit polls.
I see where you are coming from, in fact this used to be my position: This post was inspired by a talk I gave at the Less Wrong Meetup, where I made the claim that the causality problem is solved by called-off bets (reversals). Jimrandomh called me on it, and he was right: There will still be confounding even when bets are called off/reversed:
Imagine there are two possible worlds: In one of them, Kim is overthrown, in the other he is not. I expect the probability of Hillary being elected will be much higher if he is overthrown. I also expect that the probability of an attack is much higher if Kim is still in office.
If I make a bet on the probability of an attack given that Hillary is elected, and I know that this market will only be settled in the case that she is elected, my estimated probability will incorporate information about the fact that if the market is settled, more likely than not, Kim was overthrown. However, at the time I make the bet, I don’t know whether Kim will be overthrown, so this means my bet incorporates information that causally does not depend on Hillary being elected.
We tried to solve this using the “precommitment” mechanism. In graphical terms, the idea is that this removes all arrows into the election by ensuring that the only cause of who gets to be President is the prediction market itself. My intuition is that it works, but it is certainly something that should be doublechecked by someone with more technical expertise on prediction markets and causality.
Deciding the outcome based on the price in the betting market is the whole point of futarchy. You seem to be saying that prediction markets in absence of futarchy don’t provide good advice on how you should vote. That is an interesting point which I hadn’t considered before your post.
I am still uncomfortable with your example, however. If Kim is overthrown prior to the election, the market rates will adjust based on that information. If he’s overthrown after the election, then there is no causal link between that and the election results, presumably. Prior to his overthrow, the market simply provides the best estimate of the outcome until that result is known. All that means is you shouldn’t make decisions based on outdated estimates that didn’t include all known information.
Yes, the point of futarchy is to make the decision based on the price in the prediction market. What I am saying is that if you want participants to provide their best guesses about which decisions will maximize the outcome, you have to make a credible pre-commitment that the only factor that influences the decision is the prediction market that is currently being traded. You can only make such a commitment for one prediction market per decision (but like you say, the outcome measure can be arbitrarily complex)
I think you are right that once it becomes known whether Kim is overthrown, it is no longer a confounder. Therefore, the bias should be expected to get lower the nearer we get to the decision time point. However, some confounders may be unobservable, or unobserved until the time the decision is made. For instance, if this is not a pure futarchy and there is voting going on, you may gain information from the make-up of the electorate. Imagine there is a referendum on a 70% income tax and Bernie Sanders is running for President. Even if he has no influence on whether the referendum passes, his chances of being elected will be correlated with the outcome of the referendum, and you won’t know which state you are in until you see the exit polls.