+1. Concretely this means converting every probability p into p/(1-p), and then multiplying those (you can then convert back to probabilities)
Intuition pump: Person A says 0.1 and Person B says 0.9. This is symmetric, if we instead study the negation, they swap places, so any reasonable aggregation should give 0.5
Geometric mean does not, instead you get 0.3
Arithmetic gets 0.5, but is bad for the other reasons you noted
Geometric mean of odds is sqrt(1/9 * 9) = 1, which maps to a probability of 0.5, while also eg treating low probabilities fairly
Relevant: When pooling forecasts, use the geometric mean of odds.
+1. Concretely this means converting every probability p into p/(1-p), and then multiplying those (you can then convert back to probabilities)
Intuition pump: Person A says 0.1 and Person B says 0.9. This is symmetric, if we instead study the negation, they swap places, so any reasonable aggregation should give 0.5
Geometric mean does not, instead you get 0.3
Arithmetic gets 0.5, but is bad for the other reasons you noted
Geometric mean of odds is sqrt(1/9 * 9) = 1, which maps to a probability of 0.5, while also eg treating low probabilities fairly