- 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 system s. The index involves taking thesquare root of half thesum 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} sum_{i=1}^n ( V_i-S_i ) ^2}
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-knownLoosemore-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 thePearson's chi-square test which has better statistical underpinning.:mathrm{SLI} = sum {(S-V)^2 over V}See also
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 0-19-925756-6External links
* P Kestelman, [http://www.votingmatters.org.uk/ISSUE10/P6.HTM Quantifying Representativity] ", "Voting matters", Issue 10, March 1999.
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