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pedanterrific comments on Apply your knowledge: pick half a number - Less Wrong
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Will they, though? The object is to choose the number closest to half the average. If ten people pick zero, five pick twelve and five pick twenty-five, the average will be 9.25, half of which is 4.625, which is closer to zero than twelve.
(I mean, the people choosing zero will get it wrong, but it's because at least one person - me - thought that far ahead and picked 1. fiddlemath picked 2, presumably due to a different estimate of the ratio of LWers/NPRers in the poll.)
I have a feeling the half-average "should" be in the interval between 0 and 1.
I will be very surprised if the half-average is zero.
I'm guessing there is both literature and mathematical models for this interesting problem, but I'm not going to go ahead and Google it. Not knowing is way more fun.