This is a special post for quick takes by TsviBT. Only they can create top-level comments. Comments here also appear on the Quick Takes page and All Posts page.
Is there a nice way to bet on large-evidence, small-probability differences?
Normally we bet on substantial probability differences, like I say 10% you say 50% or similar. Betting makes sense there--you incentivize having correct probabilities, at least within a few percent or whatever. Is there some way to incentivize reporting the right log-odds, to within a logit or whatever?
One sort of answer might be showing that/how you can always extract a mid-range probability disagreement on latent variables, under some assumptions on the structure of the latent variable models underlying the large-logit small-probability disagreement.
Most high-liquidity securities are this - small movements with large amounts of money riding on them.
I don't think it generalizes, though - different domains or even specific disagreements over probability of an outcome will have different mechanisms for matching counterparties with low-enough transaction costs that a wager is feasible.
I guess that is the generality: every wager is about two parties agreeing that they have a disagreement which will be resolved in the future, and further agreeing that the less-correct party will pay the more-correct p... (read more)