When aggregating data, selection of aggregation method always depends upon the answer to the question “for what purpose?”
If you include one extreme outlier prediction, it can radically shift the geometric mean of a bunch of moderate ones. Is this a desirable property for your purposes?
For example: if three people all predict that Ms Green will win something versus Dr Blue with 1:1 odds, and I predict that Dr Blue has one in a million chance, then the arithmetic mean of probabilities says that between us, we think that Dr Blue has about 38% chance. Geometric mean of odds says that we think Dr Blue has 3% chance. Is either of these more useful to you for some purpose than the other?
When aggregating data, selection of aggregation method always depends upon the answer to the question “for what purpose?”
If you include one extreme outlier prediction, it can radically shift the geometric mean of a bunch of moderate ones. Is this a desirable property for your purposes?
For example: if three people all predict that Ms Green will win something versus Dr Blue with 1:1 odds, and I predict that Dr Blue has one in a million chance, then the arithmetic mean of probabilities says that between us, we think that Dr Blue has about 38% chance. Geometric mean of odds says that we think Dr Blue has 3% chance. Is either of these more useful to you for some purpose than the other?