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AlexMennen comments on Harsanyi's Social Aggregation Theorem and what it means for CEV - Less Wrong Discussion
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Oh, I see what you mean. It should be possible to find some affinely transformed product that is also a linear combination if the number of agents is at least half the number of outcomes, but some arbitrary affinely transformed product is only likely to also be a linear combination if the number of agents is at least the number of outcomes.