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Table 1 Example of two crowds, each comprised of three estimates

From: How the wisdom of crowds, and of the crowd within, are affected by expertise

Estimate # Error Squared error Squared deviation from average
A
 1 12 144 136.11
 2 − 14 196 205.44
 3 3 9 7.11
  Bias MSE Variance
  0.11 116.33 116.22
B
 1 0 0 0.11
 2 − 2 4 2.78
 3 1 1 1.78
  Bias MSE Variance
  0.11 1.67 1.56
  1. The true value being estimated is 0 (i.e., estimates and errors are equivalent). The two crowds consist of more (a) and less (b) estimate variance. Crowd wisdom (MSE–bias) is equal to the variance of the estimates of the crowd. Crowd wisdom is tautologically less advantageous when variance is small (b)
  2. Bias is the mean of the "Error" column, squared. MSE is the mean of the "Squared error" column. Variance is the mean of the "Squared deviation from average" column