Robin, on second thought, there’s a better answer to your question. Namely, the reason that BVD (bias variance decomposition) is offered as support for majoritarianism is the assumption that adopting the average of the group estimates is in fact what majoritarianism advises; otherwise BVD would contradict majoritarianism by suggesting a superior alternative, namely, adopting the average of group estimates, instead of whatever it is majoritarianism does advise. And if majoritarianism does advise adopting the group average, then I can offer a superior alternative to it in the scenario given; namely, use an estimate from a randomly selected student. And if majoritarianism is said, after the fact, to give whatever advice we painstakingly deduced to be best—so that someone suggests that majoritarianism doesn’t command averaging the estimates in this case, only after we worked out from nonmajoritarian reasons that averaging was a bad idea—then I’d like to know what the use is of a philosophy whose recommendations no one can figure out in advance. And also, what happened to the idea that the average opinion was likely to be true, not just useful?
Robin, on second thought, there’s a better answer to your question. Namely, the reason that BVD (bias variance decomposition) is offered as support for majoritarianism is the assumption that adopting the average of the group estimates is in fact what majoritarianism advises; otherwise BVD would contradict majoritarianism by suggesting a superior alternative, namely, adopting the average of group estimates, instead of whatever it is majoritarianism does advise. And if majoritarianism does advise adopting the group average, then I can offer a superior alternative to it in the scenario given; namely, use an estimate from a randomly selected student. And if majoritarianism is said, after the fact, to give whatever advice we painstakingly deduced to be best—so that someone suggests that majoritarianism doesn’t command averaging the estimates in this case, only after we worked out from nonmajoritarian reasons that averaging was a bad idea—then I’d like to know what the use is of a philosophy whose recommendations no one can figure out in advance. And also, what happened to the idea that the average opinion was likely to be true, not just useful?