Gallagher Index

From Freepedia

The Gallagher Index (or least squares) can be used to measure the disproportionality of electoral systems, in particular majoritarian systems. The index involves taking the square root of half the sum of the squares of the difference between percent of vote and percent of seats (as whole numbers) for each of the political parties.

<math>LSq = \sqrt{ \frac{1}{2}\Sigma ( V-S ) ^2}</math>

The Gallagher Index weighs the deviations by their own value, creating a responsive index. The lower the index value of a country is the lower the amount of disproportionality is in this country and vice versa. Michael Gallagher, who originally created the index, included 'other' parties as a whole category, Arend Lijphart modified it and excluded those parties.

Example of calculating disproportionality

This table is using the New Zealand general election, 2005 result:

Party	Percentage of votes	Percentage of seats	Difference	Difference squared
Labour	41.10	41.32	0.22	0.0484
National	39.10	39.67	0.57	0.3249
NZ First	5.72	5.79	0.07	0.0049
Greens	5.30	4.96	0.34	0.1156
Maori	2.12	3.30	1.18	1.3924
United Future	2.67	2.48	0.19	0.0361
ACT	1.51	1.65	0.14	0.0196
Progressive	1.16	0.82	0.34	0.1156
Destiny	0.62	0	0.62	0.3844
Legalise Cannabis	0.25	0	0.25	0.0625
Christian Heritage	0.12	0	0.12	0.0144
Alliance	0.07	0	0.07	0.0049
Family Rights	0.05	0	0.05	0.0025
Democrats	0.05	0	0.05	0.0025
Libertarianz	0.04	0	0.04	0.0016
Direct Democracy	0.03	0	0.04	0.0016
99MP	0.03	0	0.03	0.0009
OneNZ	0.02	0	0.02	0.0004
Republicans	0.02	0	0.02	0.0004
TOTAL				2.4711
HALVED				1.23555
SQUARE ROOT				1.11