;; Diversity Prediction Theorem ;; I've recently seen in various places the Diversity Predition Theorem, variously expressed as: ;; Crowd Error = Average Error - Diversity ;; The Crowd Beats the Average ;; Being different is as important as being good ;; Encourage Diversity ;; I'm not going to argue with a mathematical tautology, but I'm a bit sceptical about the ;; happy feelings induced by this law. ;; Consider: (defn diversity-theorem [truth predictions] (let [square (fn[x] (* x x)) mean (/ (reduce + predictions) (count predictions)) avg-sq-diff (fn[a] (/ (reduce + (for [x predictions] (square (- x a)))) (count predictions)))] {:average-error (avg-sq-diff truth) :crowd-error (square (- truth mean)) :diversity (avg-sq-diff mean)})) ;; We have a thing whose real value is 49, and some experts who guess the value fairly accurately ;; Their average guess is really close! (diversity-theorem 49 '(48 47 51)) ;-> {:average-error 3, :crowd-error 1/9, :diversity 26/9} ;; We make our population of experts more diverse: (diversity-theorem 49 '(48 47 51 42)) ;-> {:average-error 29/2, :crowd-error 4, :diversity 21/2}

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## Tuesday, August 13, 2013

### Diversity Prediction Theorem

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Hello! I shared your code on Rosetta Code. Thank you for posting it!

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