The A,B,C example you came up with is certainly a strike against average log odds and in favor of average probs.
I have though more about this. I now believe that this invariance property is not reasonable—aggregating outcomes is (surprisingly) not a natural operation in Bayesian reasoning. So I do not think this is a strike agains log-odd pooling.
I have though more about this. I now believe that this invariance property is not reasonable—aggregating outcomes is (surprisingly) not a natural operation in Bayesian reasoning. So I do not think this is a strike agains log-odd pooling.