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Luke_A_Somers comments on Harsanyi's Social Aggregation Theorem and what it means for CEV - Less Wrong Discussion
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I don't see how it's like Simpson's paradox, actually. You want to go to Good Hospital instead of Bad Hospital even if more patients who go to Good Hospital die because they get almost the hard cases. Aggregating only hides the information needed to make a properly informed choice. Here, aggregating doesn't hide any information.
But there are a bunch of other ways things like that can happen.
This very morning I did a nonlinear curvefit on a bunch of repeats of an experiment. One of the parameters that came out had values in the range -1 to +1. I combined the data sets directly and that parameter for the combined set came out around 5.
In a way, this analogy may be even more directly applicable than Simpson's paradox. Even if A and B are complete specifications (unlike that parameter, which was one of several), the interpersonal reactions to other people can do some very nonlinear things to interpretations of A and B.