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The Gallagher Index (or least squares) can be used to measure the disproportionality of electoral systems (which is to say the difference between the percentage of votes received and the percentage of seats a party gets in the resulting legislature), 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.

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

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 2005 election result (note: New Zealand voters have two votes, this list uses the party vote which determines the proportionality of the House, the electorate vote determines the local member):

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
Māori	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
Progressives	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

Thus the disproportionality of the 2005 New Zealand election is 1.11

Other indicies

The Sainte-Laguë Index is considered by Gallagher to be probably the soundest of all the measures. This is closely related to the Pearson's chi-square test which has better statistical underpinning. :

SLI = \sum {(S-V)^2 \over V}

However the range of values, from zero to infinity, is less useful in practice.

[ Visit the complete Wikipedia entry for Gallagher Index ]

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