I think there's a big problem with this counter example. Which is that you're selecting for one thing and judging whether or not you were biased based on anothe

I think there's a big problem with this counter example. Which is that you're selecting for one thing and judging whether or not you were biased based on another. > Now suppose that we select without bias or inaccuracy all the applicants that have an 80% or better chance of graduation. This is subtly different than selecting for the highest graduation rate possible because it's binary, you want a group with >80% chances not a group with the best chances. Imagine if instead of the distributions you had group A was composed of people with a 100% chance of graduation and B was composed of people with an 80% chance of graduation. Our process does nothing to distinguish between those people because that extra 20% chance of graduation doesn't matter. This brings me to what I think is the fundamental problem with your criticism, it's not clear to me what it means for a group in your example to over perform. If you select a group with the goal of 80% of them graduating it doesn't make sense to call 90% of them graduating an over performance. That only makes sense if your goal up front is to maximize the graduation rate. I think if you rerun your example but instead assume an unbiased strategy that selects for the highest graduation rate possible you'll find that pg's essay makes a lot more sense.