Averaging divides noise by the square root of the number of judgments (100 judgments cut it by 90%) and does nothing to bias, so the gain from a crowd depends on how much of its error is shared; hence, in the authors' words, the wisdom of crowds "works best when judgments are independent". A hundred copies of one model get the square-root cut only on the part of their error that is not common to all of them. On a well-trained base model that part may be small, leaving the ensemble about as wrong as one copy. The quotes are the authors'; the application to model copies is Rio's.

Evidence 3 passages

• groundsSource document

  Averaging is mathematically guaranteed to reduce noise.

• groundsSource document

  Specifically, it divides it by the square root of the number of judgments averaged. This means that if you average 100 judgments, you will reduce noise by 90%.

• groundsSource document

  Because averaging does nothing to reduce bias, its effect on total error, MSE depends on the proportions of bias and noise in it. That is why the wisdom of crowds works best when judgments are independent, and therefore less likely to contain shared biases.

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