> The lower certainty would in turn lead to lower rankings for women even without any bias in the data.
This is not true.
Probabilistic-ly speaking, if we are computing P(hiring | gender);
Lower certainty means there is a high variance in prior over women. However, over a large dataset, the "score" would almost certainly be equal to the mean of the distribution, and be independent of the variance.
In simpler words, if there was a frequency diagram of scores for each gender (most likely bell curves), then only the peak of the bell curve would matter. The flatness / thinness of the curve would be completely irrelevant to the final score. The peak is the mean, and the flatness is the uncertainty. Only the mean matters.
This is not true.
Probabilistic-ly speaking, if we are computing P(hiring | gender); Lower certainty means there is a high variance in prior over women. However, over a large dataset, the "score" would almost certainly be equal to the mean of the distribution, and be independent of the variance.
In simpler words, if there was a frequency diagram of scores for each gender (most likely bell curves), then only the peak of the bell curve would matter. The flatness / thinness of the curve would be completely irrelevant to the final score. The peak is the mean, and the flatness is the uncertainty. Only the mean matters.