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TheGallagher index measures an electoral system's relativedisproportionality between votes received and seats in a legislature.[1][2] As such, it measures the difference between the percentage of votes each party gets and the percentage of seats each party gets in the resulting legislature, and it also measures this disproportionality from all partiescollectively in any one given election. That collective disproportionality from the election is given a precise score, which can then be used in comparing various levels of proportionality among various elections from variouselectoral systems.[3] The Gallagher index is a statistical analysis methodology utilised withinpolitical science, notably the branch ofpsephology.
Michael Gallagher, who created the index, referred to it as a "least squares index", inspired by thesum of squares of residuals used in the method ofleast squares. The index is therefore commonly abbreviated as "LSq" even though the measured allocation is not necessarily a least squares fit. The Gallagher index is computed by taking thesquare root of half thesum of the squares of the difference between percent of votes () and percent of seats () for each of thepolitical parties ().[4]
The division by 2 gives an index whose values range between 0 and 100. The larger the differences between the percentage of the votes and the percentage of seats summed over all parties, the larger the Gallagher index. The larger the index value the larger the disproportionality and vice versa. Michael Gallagher included "other" parties as a whole category, andArend Lijphart modified it, excluding those parties. Compared to theLoosemore–Hanby index, the Gallagher index is more sensitive to large discrepancies.[6] Other indices measuring the proportionality between seat share and party vote share are theLoosemore–Hanby index,Rae index, and theSainte-Laguë Index.
The first publication of the use ofleast squares in measuring the dis-proportionality of election outcomes was by Michael Gallagher in 1991[7] in which he writes: "These [election] indices were originally outlined in Markku Laakso and Rein Taagepera, ‘ “Effective” number of parties: a measure with application to west Europe’,Comparative Political Studies 12:1 (1979), pp. 3–27 (effective number of parties), and Michael Gallagher, ‘Proportionality, disproportionality and electoral systems’,Electoral Studies 10:1 (1991), pp. 33–51 (least squares index)."
The Gallagher index gained considerable attention in Canada in December 2016 in the context of efforts to reform Canada's electoral system.[8][9] TheSpecial Committee on Electoral Reform (aParliamentary Committee) recommended "that the Government should, as it develops a new electoral system, use the Gallagher index in order to minimize the level of distortion between the popular will of the electorate and the resultant seat allocations in Parliament." The committee recommended that "the government should seek to design a system that achieves a Gallagher score of 5 or less."[10][11]
In the 2015 Canadian federal election, the Gallagher index was 12.02, where 0 would be a perfectly proportional election outcome.[12]
| Party | Votes (%) | Seats (%) | Difference | Difference squared | |
|---|---|---|---|---|---|
| Liberal | 39.47% | 54.44% | 14.97 | 224.1009 | |
| Conservatives | 31.89% | 29.29% | -2.6 | 6.76 | |
| New Democratic | 19.71% | 13.02% | -6.69 | 44.7561 | |
| Bloc Québecois | 4.66% | 2.96% | -1.7 | 2.89 | |
| Green | 3.45% | 0.29% | -3.16 | 9.9856 | |
| Other | 0.82% | 0.00% | -0.82 | 0.6724 | |
| Total of differences squared | 289.165 | ||||
| Total / 2 | 144.5825 | ||||
| Square root of (Total / 2):Gallagher Index result | 12.02 | ||||
This table uses for example the2012 Queensland state election, one of the largest landslides in Australian electoral history. Though Australia and New Zealand have somewhat similar political histories,[citation needed] Australia usespreferential voting inSingle-member districts forCommonwealth House of Representative and moststate and territory Legislative Assembly elections, which tends to result in far less proportionality compared to New Zealand's MMP system (or other proportional electoral systems), especially for larger minor parties, such asThe Greens or, historically, theAustralian Democrats. The 2012 Queensland election had an extremely high Gallagher Index, at 31.16, due to the massive landslide in seats for the victoriousLNP. The LNP gained 88% of the seats with less than 50% of the vote. Most recent Australian state and federal elections however score between 10 and 12.
| Party | Votes (%) | Seats (%) | Difference | Difference squared | |
|---|---|---|---|---|---|
| Liberal National | 49.65% | 87.64% | 37.99 | 1443.2401 | |
| Labor | 26.66% | 7.87% | -18.79 | 353.0641 | |
| Katter | 11.53% | 2.25% | -9.28 | 86.1184 | |
| Greens | 7.53% | 0.00% | -7.53 | 56.7009 | |
| Other | 1.47% | 0.00% | -1.47 | 2.1609 | |
| Independent | 3.16% | 2.25% | -0.91 | 0.8281 | |
| Total of differences squared | 1942.1125 | ||||
| Total / 2 | 971.0563 | ||||
| Square root of (Total / 2):Gallagher Index result | 31.16 | ||||
The 7political groups of the European Parliament instead of the 203 political parties[13] allow a concise calculation of disproportionality between votes and seats. The Gallagher index for the European Parliament is 7.87.
| Party | Votes (%) | Seats (%) | Difference | Difference squared | |
|---|---|---|---|---|---|
| EPP | 20.80% | 24.23% | 3.43 | 11.7649 | |
| S&D | 17.88% | 20.51% | 2.63 | 6.9169 | |
| RE | 12.01% | 14.38% | 2.37 | 5.6169 | |
| G/EFA | 10.04% | 9.85% | -0.19 | 0.0361 | |
| ID | 10.59% | 9.72% | -0.87 | 0.7569 | |
| ECR | 7.17% | 8.26% | 1.09 | 1.1881 | |
| GUE/NGL | 5.16% | 5.46% | 0.3 | 0.09 | |
| NI | 6.52% | 7.59% | 1.07 | 1.1449 | |
| Wasted vote | 9.82% | 0.00% | -9.82 | 96.4324 | |
| Total of differences squared | 123.9471 | ||||
| Total / 2 | 61.9736 | ||||
| Square root of (Total / 2):Gallagher Index result | 7.87 | ||||
The disproportionality of the2022 Swedish general election was 0.64 according to the Gallagher index, which is extremely low by international standards (resulting in almost perfectly proportional seat allocations), due to Sweden's use of themodified Sainte-Laguë method in elections to theRiksdag.
The disproportionality of the2020 Irish general election was 1.96 according to the Gallagher index. The Republic of Ireland uses thesingle transferable vote (STV) system withDroop quota in elections to theDáil Éireann.
This table uses the aggregate results of the2012 elections to the United States House of Representatives. These 435single-seat elections arewinner-take-all, which would tend to create disproportionate results, but this is moderated by the extremely high share of votes obtained by thetwo major parties—more than 96%, likely in part caused by fears ofwasted votes andvote splitting.[citation needed] The Gallagher index ignores the effect of the primaries on the proportionality.
| Party | Votes (%) | Seats (%) | Difference | Difference squared | |
|---|---|---|---|---|---|
| Republican Party | 47.66% | 53.80% | 6.14 | 37.6996 | |
| Democratic Party | 48.77% | 44.20% | -4.57 | 20.8849 | |
| Libertarian Party | 1.11% | 0.00% | -1.11 | 1.2321 | |
| Independents andminor parties | 1.01% | 0.00% | -1.01 | 1.0201 | |
| Green Party | 0.31% | 0.00% | -0.31 | 0.0961 | |
| Others | 1.13% | 0.00% | -1.13 | 1.2769 | |
| Total of differences squared | 62.2097 | ||||
| Total / 2 | 31.1049 | ||||
| Square root of (Total / 2):Gallagher Index result | 5.58 | ||||
The 2024 general election in the United Kingdom was the most disproportional in modern British history.[15] The Liberal Democrats recorded their best ever seat result (72), despite receiving only around half the votes they did in2010,[16] and fewer votes overall than Reform, although the party's seat share was again lower than its share of the vote. Advocacy groupMake Votes Matter found that 58% of voters did not vote for their elected MP. Make Votes Matter spokesman Steve Gilmore,Electoral Reform Society chiefDarren Hughes, Reform UK leader Nigel Farage and the Green Party of England and Wales co-leader Adrian Ramsay were among the figures that called for electoral reform in the wake of the election. The campaigners said it was the "most disproportionate election in [British] history".[17][18]
| Party | Votes (%) | Seats (%) | Difference | Difference squared | |
|---|---|---|---|---|---|
| Labour | 33.70% | 63.23% | 29.53 | 872.0209 | |
| Conservative | 23.70% | 18.62% | -5.08 | 25.8064 | |
| Reform UK | 14.29% | 0.77% | -13.52 | 182.7904 | |
| Liberal Democrats | 12.22% | 11.08% | -1.14 | 1.2996 | |
| Green | 6.39% | 0.46% | -5.93 | 35.1649 | |
| Independents | 1.96% | 0.92% | -1.04 | 1.0816 | |
| Others | 7.74% | 4.92% | -2.82 | 7.9524 | |
| Total of differences squared | 1126.1162 | ||||
| Total / 2 | 563.0581 | ||||
| Square root of (Total / 2):Gallagher Index result | 23.73 | ||||
One tool that has been developed to measure an electoral system's relative disproportionality between votes received and seats allotted in a legislature is the Gallagher Index, which was developed by Michael Gallagher (who appeared before the Committee).
...Professor Becker developed the "Gallagher Index Composite" for the Committee's study...
