I commented on the post as well, but repeating here — I think denominating conditional markets in shares of contracts of the event happening (rather than in $) is more natural and resolves some confusions. i.e. denominate a contract that pays out if A conditional on B in shares of contracts that pay out $1 if B.
Shares of (coin comes up heads, conditional on coin being flipped) will then be traded in currency denominated in shares of (coin is flipped).
If everyone knows the coin will be flipped only if the laser scan comes up estimating the bias at > 0.5, then it’s no surprise if the market is trading at > 0.5, and that really is everyone’s true belief — namely their true belief of the probability of the coin coming up heads conditional on the coin being flipped. (Not their unconditional belief of the probability of the coin coming up heads!)
If instead everyone knows the coin is flipped only if the market is trading at > 0.5, then (probably?) most people’s estimate of the coin’s bias won’t be meaningfully different depending on whether they condition on the coin being flipped or not — it’s not strong evidence of the coin’s bias — and so I expect the price to remain at whatever the market’s prior of the bias was.
But those are two different situations, and I don’t think the first one provides useful intuition for the second one. Setting up the right market is still a skill issue — in your Elon firing example, one would learn more from it by announcing ahead of time that the firing decision itself will be determined only by the results of the market. Then one doesn’t have to worry about “well maybe their conditional probability is really due to some outside factor...”. (Of course making such an announcement might cause both results to trade downward, because the market thinks that’s a dumb way to make firing decisions. That’s why it’s a skill issue. If it seems like a dumb way to make firing decisions, maybe don’t make such an announcement.)
I commented on the post as well, but repeating here — I think denominating conditional markets in shares of contracts of the event happening (rather than in $) is more natural and resolves some confusions. i.e. denominate a contract that pays out if A conditional on B in shares of contracts that pay out $1 if B.
Shares of (coin comes up heads, conditional on coin being flipped) will then be traded in currency denominated in shares of (coin is flipped).
If everyone knows the coin will be flipped only if the laser scan comes up estimating the bias at > 0.5, then it’s no surprise if the market is trading at > 0.5, and that really is everyone’s true belief — namely their true belief of the probability of the coin coming up heads conditional on the coin being flipped. (Not their unconditional belief of the probability of the coin coming up heads!)
If instead everyone knows the coin is flipped only if the market is trading at > 0.5, then (probably?) most people’s estimate of the coin’s bias won’t be meaningfully different depending on whether they condition on the coin being flipped or not — it’s not strong evidence of the coin’s bias — and so I expect the price to remain at whatever the market’s prior of the bias was.
But those are two different situations, and I don’t think the first one provides useful intuition for the second one. Setting up the right market is still a skill issue — in your Elon firing example, one would learn more from it by announcing ahead of time that the firing decision itself will be determined only by the results of the market. Then one doesn’t have to worry about “well maybe their conditional probability is really due to some outside factor...”. (Of course making such an announcement might cause both results to trade downward, because the market thinks that’s a dumb way to make firing decisions. That’s why it’s a skill issue. If it seems like a dumb way to make firing decisions, maybe don’t make such an announcement.)