In SimonM’s comment, we’re talking about probabilities directly. Forecasting. Usually that means what we care about is calibration or a proper scoring rule, so the natural scale is [0,1] or log-odds. Now the correct heuristic is “arithmetic mean” (of log-odds of probability).
Not sure what you mean by this. A proper scoring rule incentivizes the same results that deciding what odds you’d be indifferent to betting on at (against a gambler whose decisions carry no information about reality) does.
Not sure what you mean by this. A proper scoring rule incentivizes the same results that deciding what odds you’d be indifferent to betting on at (against a gambler whose decisions carry no information about reality) does.