# Gallagher Index

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Gallagher Index

The Gallagher Index (or least squares index) is used to measure the disproportionality of an electoral outcome, that is the difference between the percentage of votes received and the percentage of seats a party gets in the resulting legislature. This is especially useful for comparing proportionality across electoral 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.

$LSq = sqrt\left\{ frac\left\{1\right\}\left\{2\right\} sum_\left\{i=1\right\}^n \left( V_i-S_i \right) ^2\right\}$

The index weighs the deviations by their own value, creating a responsive index, ranging from 0 to 100. The lower the index value the lower the disproportionality and vice versa. Michael Gallagher, who created the index, included 'other' parties as a whole category, and Arend Lijphart modified it, excluding those parties. Unlike the well-known Loosemore-Hanby index, the Gallagher index is less sensitive to small discrepancies.

Example of calculating disproportionality

This table uses 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.

Thus the disproportionality of the 2005 New Zealand election is 1.11.

Other indices

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.:$mathrm\left\{SLI\right\} = sum \left\{\left(S-V\right)^2 over V\right\}$

The Gallagher Index of the results of the

References

* Benoit, K. 2000. 'Which Electoral Formula Is the Most Proportional? A New Look with New Evidence.' "Political Analysis" 8:381-388.
* Gallagher, M. 1991. "Proportionality, Disproportionality and Electoral Systems." "Electoral Studies" 10:33-51.
* Gallagher, M. 1992. 'Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities.' "British Journal of Political Science" 22:469-496.
* Gallagher, M and Mitchell P. (eds). 2005. "The Politics of Electoral Systems" Oxford: Oxford University Press. Appendix B. ISBN 0-19-925756-6

* P Kestelman, [http://www.votingmatters.org.uk/ISSUE10/P6.HTM Quantifying Representativity] ", "Voting matters", Issue 10, March 1999.

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