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 for each of the political parties.
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 that since New Zealand uses the MMP voting system, 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||% of votes||% of seats||difference|| difference|
|total of squares of differences||2.5336|
|total / 2||1.2668|
|square root of (total / 2)||1.13|
Note that the Māori Party has the highest difference, which is significantly above the others. This is due to New Zealand's system of reserved seats for Māori. The Māori seats are allocated by votes on a separate electoral roll, and while any party can contest these seats, they are generally won by either the Māori Party, the Labour Party, or New Zealand First.
The Sainte-Laguë method is considered by Gallagher to be probably the soundest of all the measures. This is closely related to the Pearson's chi-squared test which has better statistical underpinning.
- Benoit, Kenneth (2000). "Which Electoral Formula Is the Most Proportional? A New Look with New Evidence". Political Analysis. 8: 381–388. doi:10.1093/oxfordjournals.pan.a029822. Retrieved 10 August 2013.
- Gallagher, Michael (1991). "Proportionality, Disproportionality and Electoral Systems". Electoral Studies. 10: 33–51. doi:10.1016/0261-3794(91)90004-c.
- Gallagher, Michael (1992). "Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities". British Journal of Political Science. 22: 469–496. doi:10.1017/s0007123400006499.
- Gallagher, Michael; Mitchell, P, eds. (2005). The Politics of Electoral Systems. Oxford: Oxford University Press. Appendix B. ISBN 0-19-925756-6.
- Kestelman, Philip (March 1999). "Quantifying Representativity". Voting matters. 10. Retrieved 10 August 2013.