Do I correctly understand that you claim that under some plausible assumptions, the market will converge to P(A|do(B))? Can you state what those assumptions are? The challenge for me is that you go through a set of at least four possible sets of assumptions and give informal arguments for each. But I can’t tell which of these sets of assumptions you believe is realistic, and under which of these you claim market prices will converge to p(A|do(B)). (Feel free to make simplifying assumptions like an infinite number of traders, no market fees, etc.)
Further, when you state that my result is wrong, that would seem to imply that no additional assumptions are needed. Yet all your arguments seem to rely on additional assumptions, which makes me question if my result really is wrong as stated, or rather that you prefer to add some additional assumptions.
Market estimates will converge to the most profitable P(X if A), the one that wins bets vs other versions. And that is the version you want to use when you make decisions.
Sorry to be persistent, but can you confirm that this means you do not claim markets in general converge to p(A|do(B))? That’s my central claim, so when you state that I’m wrong, the obvious interpretation would be that that you believe that central claim is wrong. In your post, you don’t identify what mistake supposedly exists, so I’d like to confirm if you’re actually claiming to refute my central claim or if, rather, you’re arguing that it doesn’t matter.
You say that markets give evidential conditionals while decisions want causal conditionals. For this comment, I’m not taking a position on which conditional we want for decisions. I’m just saying that both trades and the decision advised should use the same conditional, but I’m not saying which one that is.
I respond here: https://www.overcomingbias.com/p/decision-conditional-prices-reflect
Do I correctly understand that you claim that under some plausible assumptions, the market will converge to P(A|do(B))? Can you state what those assumptions are? The challenge for me is that you go through a set of at least four possible sets of assumptions and give informal arguments for each. But I can’t tell which of these sets of assumptions you believe is realistic, and under which of these you claim market prices will converge to p(A|do(B)). (Feel free to make simplifying assumptions like an infinite number of traders, no market fees, etc.)
Further, when you state that my result is wrong, that would seem to imply that no additional assumptions are needed. Yet all your arguments seem to rely on additional assumptions, which makes me question if my result really is wrong as stated, or rather that you prefer to add some additional assumptions.
Market estimates will converge to the most profitable P(X if A), the one that wins bets vs other versions. And that is the version you want to use when you make decisions.
Sorry to be persistent, but can you confirm that this means you do not claim markets in general converge to p(A|do(B))? That’s my central claim, so when you state that I’m wrong, the obvious interpretation would be that that you believe that central claim is wrong. In your post, you don’t identify what mistake supposedly exists, so I’d like to confirm if you’re actually claiming to refute my central claim or if, rather, you’re arguing that it doesn’t matter.
You say that markets give evidential conditionals while decisions want causal conditionals. For this comment, I’m not taking a position on which conditional we want for decisions. I’m just saying that both trades and the decision advised should use the same conditional, but I’m not saying which one that is.
I’m a bit confused. What happens in a concrete example where CDT and EDT normally give a different answer?
For example, would a futarchy one-box (evidential decision theory) or two-box (casual decision theory)?
Thanks, I added a link to the main post on my blog as well.