Centrist bias

Centrist bias is a political spectrum statistic that measures the tendency for elected candidates to be near the mean voter.

Definition
The centrist bias of a set of winning candidates with respect to a given political spectrum is equal to Pearson's correlation coefficient between the distance of a voter from the mean voter and the distance of that voter from the nearest winning candidate.

Example
Assume a one-dimensional political spectrum with the voter distribution


 * 15% at position 0
 * 20% at position 0.25
 * 30% at position 0.5
 * 20% at position 0.75
 * 15% at position 1

If the candidate set {0.25, 0.75} is elected, then

To compute the centrist bias, we consider the (distance from mean, distance from winner) pairs:


 * (0.50, 0.25) with frequency 30%
 * (0.25, 0.00) with frequency 40%
 * (0.00, 0.25) with frequency 30%

The correlation, and thus the centrist bias, is zero.