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.