Centrist_bias.mw

'''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

<table border>
    <tr>
        <th>voters</th>
        <th>position</th>
        <th>distance from mean</th>
        <th>nearest winner</th>
        <th>distance from winner</th>
    </tr>
    <tr align="right">
        <td>15%</td>
        <td>0.00</td>
        <td>0.50</td>
        <td>0.25</td>
        <td>0.25</td>
    </tr>
    <tr align="right">
        <td>20%</td>
        <td>0.25</td>
        <td>0.25</td>
        <td>0.25</td>
        <td>0.00</td>
    </tr>
    <tr align="right">
        <td>30%</td>
        <td>0.50</td>
        <td>0.00</td>
        <td>either</td>
        <td>0.25</td>
    </tr>
    <tr align="right">
        <td>20%</td>
        <td>0.75</td>
        <td>0.25</td>
        <td>0.75</td>
        <td>0.00</td>
    </tr>
    <tr align="right">
        <td>15%</td>
        <td>1.00</td>
        <td>0.50</td>
        <td>0.75</td>
        <td>0.25</td>
</table>

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.