The Error of Crowds
I've always been annoyed at the notion that the bias-variance decomposition tells us something about modesty or Philosophical Majoritarianism. For example, Scott Page rearranges the equation to get what he calls the Diversity Prediction Theorem:
Collective Error = Average Individual Error - Prediction Diversity
I think I've finally come up with a nice, mathematical way to drive a stake through the heart of that concept and bury it beneath a crossroads at midnight, though I fully expect that it shall someday rise again and shamble forth to eat the brains of the living.
How to use "philosophical majoritarianism"
The majority of people would hold more accurate beliefs if they simply believed the majority. To state this in a way that doesn't risk information cascades, we're talking about averaging impressions and coming up with the same belief.
To the degree that you come up with different averages of the impressions, you acknowledge that your belief was just your impression of the average, and you average those metaimpressions and get closer to belief convergence. You can repeat this until you get bored, but if you're doing it right, your beliefs should get closer and closer to agreement, and you shouldn't be able to predict who is going to fall on which side.
Of course, most of us are atypical cases, and as good rationalists, we need to update on this information. Even if our impressions were (on average) no better than the average, there are certain cases where we know that the majority is wrong. If we're going to selectively apply majoritarianism, we need to figure out the rules for when to apply it, to whom, and how the weighting works.
This much I think has been said again and again. I'm gonna attempt to describe how.
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