I guess I can potentially see us changing our minds in a year’s time and deciding that arithmetic mean of probabilities is better after all, or that some other method is better than both of these.
This seems very unlikely, I’ll bet your $20 against my $80 that this doesn’t happen.
Thanks both (and Owen too), I now feel more confident that geometric mean of odds is better!
(Edit: at 1:4 odds I don’t feel great about a blanket recommendation, but I guess the odds at which you’re indifferent to taking the bet are more heavily stacked against us changing our mind. And Owen’s <1% is obviously way lower)
This seems very unlikely, I’ll bet your $20 against my $80 that this doesn’t happen.
(I have not read the post)
I endorse these implicit odds, based on both theory and some intuitions from thinking about this in practice.
Thanks both (and Owen too), I now feel more confident that geometric mean of odds is better!
(Edit: at 1:4 odds I don’t feel great about a blanket recommendation, but I guess the odds at which you’re indifferent to taking the bet are more heavily stacked against us changing our mind. And Owen’s <1% is obviously way lower)