I really like the proposed calibration game! One thing I’m curious about is whether real-world evidence more often looks like a likelihood ratio or like something else (e.g. pointing towards a specific probability being correct). Maybe you could see this from the structure of priors+likelihoodratios+posteriors in the calibration game — e.g. check whether the long-run top-scorers likelihood ratios correlated more or less than their posterior probabilities.
(If someone wanted to build this: one option would be to start with pastcasting and then give archived articles or wikipedia pages as evidence. Maybe a sophisticated version could let you start out with an old relevant wikipedia page, and then see a wikipedia page much closer to the resolution date as extra evidence.)
I really like the proposed calibration game! One thing I’m curious about is whether real-world evidence more often looks like a likelihood ratio or like something else (e.g. pointing towards a specific probability being correct). Maybe you could see this from the structure of priors+likelihoodratios+posteriors in the calibration game — e.g. check whether the long-run top-scorers likelihood ratios correlated more or less than their posterior probabilities.
(If someone wanted to build this: one option would be to start with pastcasting and then give archived articles or wikipedia pages as evidence. Maybe a sophisticated version could let you start out with an old relevant wikipedia page, and then see a wikipedia page much closer to the resolution date as extra evidence.)
Interesting point, agreed that this would be very interesting to analyze!