What’s “Time-Weighted Probability”? Is that just the average probability across the lifespan of the market? That’s not a quantity which is supposed to be calibrated.
e.g., Imagine a simple market on a coin flip, where forecasts of p(heads) are made at two times: t1 before the flip and t2 after the flip is observed. In half of the cases, the market forecast is 50% at t1 and 100% at t2, for an average of 75%; in those cases the market always resolves True. The other half: 50% at t1, 0% at t2, avg of 25%, market resolves False. The market is underconfident if you take this average, but the market is perfectly calibrated at any specific time.
Yeah, this seems to be a big part of it. If you instead switch it to the probability at market midpoint, Manifold is basically perfectly calibrated, and Kalshi is if anything overconfident (Metaculus still looks underconfident overall).
What’s “Time-Weighted Probability”? Is that just the average probability across the lifespan of the market? That’s not a quantity which is supposed to be calibrated.
e.g., Imagine a simple market on a coin flip, where forecasts of p(heads) are made at two times: t1 before the flip and t2 after the flip is observed. In half of the cases, the market forecast is 50% at t1 and 100% at t2, for an average of 75%; in those cases the market always resolves True. The other half: 50% at t1, 0% at t2, avg of 25%, market resolves False. The market is underconfident if you take this average, but the market is perfectly calibrated at any specific time.
Yeah, this seems to be a big part of it. If you instead switch it to the probability at market midpoint, Manifold is basically perfectly calibrated, and Kalshi is if anything overconfident (Metaculus still looks underconfident overall).