Why would questions where uninformed forecasters produce uniform priors make logodds averaging work better?
Because it produces situations where more extreme probability estimates correlate with more expertise (assuming all forecasters are well-calibrated).
I don’t understand your point. Why would forecasters care about what other people would do? They only want to maximize their own score.
They wouldn’t. But if both would have started with priors around 50% before they acquired any of their expertise, and it’s their expertise that updates them away from 50%, then more expertise is required to get more extreme odds. If the probability is a martingale that starts at 50%, and the time axis is taken to be expertise, then more extreme probabilities will on average be sampled from later in the martingale; i.e. with more expertise.
This also doesn’t make much sense to me, though it might be because I still don’t understand the point about needing uniform priors for logodd pooling.
If logodd pooling implicitly assumes a uniform prior, then logodd pooling on A vs ¬A assumes A has prior probability 1⁄2, and logodd pooling on A vs B vs C assumes A has a prior of 1⁄3, which, if the implicit prior actually was important, could explain the different results.
Because it produces situations where more extreme probability estimates correlate with more expertise (assuming all forecasters are well-calibrated).
They wouldn’t. But if both would have started with priors around 50% before they acquired any of their expertise, and it’s their expertise that updates them away from 50%, then more expertise is required to get more extreme odds. If the probability is a martingale that starts at 50%, and the time axis is taken to be expertise, then more extreme probabilities will on average be sampled from later in the martingale; i.e. with more expertise.
If logodd pooling implicitly assumes a uniform prior, then logodd pooling on A vs ¬A assumes A has prior probability 1⁄2, and logodd pooling on A vs B vs C assumes A has a prior of 1⁄3, which, if the implicit prior actually was important, could explain the different results.