# Difference between revisions of "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

voters position distance from mean nearest winner distance from winner
15% 0.00 0.50 0.25 0.25
20% 0.25 0.25 0.25 0.00
30% 0.50 0.00 either 0.25
20% 0.75 0.25 0.75 0.00
15% 1.00 0.50 0.75 0.25

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.