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The Gallagher index measures an electoral system's relative disproportionality 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 parties collectively 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 various electoral systems. [3] The Gallagher index is a statistical analysis methodology utilised within political science, notably the branch of psephology.
Michael Gallagher, who created the index, referred to it as a "least squares index", inspired by the sum of squares of residuals used in the method of least 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 the square root of half the sum of the squares of the difference between percent of votes () and percent of seats () for each of the political 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, and Arend Lijphart modified it, excluding those parties. Compared to the Loosemore–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 the Loosemore–Hanby index, Rae index, and the Sainte-Laguë Index.
The first publication of the use of least squares in measuring the dis-proportionality of election outcomes was by Michael Gallagher in 1991: In Michael Gallagher's Electoral Systems web site he offers a PDF download under "Values of Indices" [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] The Special Committee on Electoral Reform (a Parliamentary 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 the 2012 Queensland state election, one of the largest landslides in Australian electoral history. Though Australia and New Zealand have somewhat similar political histories, Australia uses preferential voting in Single-member districts for Commonwealth House of Representative and most state 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 as The Greens or, historically, the Australian Democrats. The 2012 Queensland election had an extremely high Gallagher Index, at 31.16, due to the massive landslide in seats for the victorious LNP. 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 7 political 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 the 2018 Swedish general election was 1.8 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 the modified Sainte-Laguë method in elections to the Riksdag.
The disproportionality of the 2020 Irish general election was 1.96 according to the Gallagher index. The Republic of Ireland uses the single transferable vote (STV) system with Droop quota in elections to the Dáil Éireann.
This table uses the aggregate results of the 2016 elections to the United States House of Representatives. These 435 single-seat elections are winner-take-all, which would tend to create disproportionate results, but this is moderated by the extremely high share of votes obtained by the two major parties—more than 97%, likely in part caused by fears of wasted votes and vote splitting. The Gallagher index ignores the effect of the primaries on the proportionality.
Party | Votes (%) | Seats (%) | Difference | Difference squared | |
---|---|---|---|---|---|
Republican Party | 49.11% | 55.40% | 6.29 | 39.5641 | |
Democratic Party | 48.02% | 44.60% | -3.42 | 11.6964 | |
Libertarian Party | 1.29% | 0.00% | -1.29 | 1.6641 | |
Independents and minor parties | 1.18% | 0.00% | -1.18 | 1.3924 | |
Green Party | 0.39% | 0.00% | -0.39 | 0.1521 | |
Total of differences squared | 54.4691 | ||||
Total / 2 | 27.2346 | ||||
Square root of (Total / 2): Gallagher Index result | 5.22 |
In Michael Gallagher's Electoral Systems web site he offers a PDF download under "Values of Indices." [15] Those Gallagher indices for individual countries are listed below. Only the last available index for each country is shown.
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...
Proportional representation (PR) refers to any type of electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to political divisions among voters. The essence of such systems is that all votes cast – or almost all votes cast – contribute to the result and are effectively used to help elect someone – not just a bare plurality or (exclusively) the majority – and that the system produces mixed, balanced representation reflecting how votes are cast.
Mixed-member proportional representation is a mixed electoral system in which votes are cast for both local elections and also for overall party vote tallies, which are used to allocate additional members to produce or deepen overall proportional representation.
The D'Hondt method, also called the Jefferson method or the greatest divisors method, is an apportionment method for allocating seats in parliaments among federal states, or in proportional representation among political parties. It belongs to the class of highest-averages methods. The D'Hondt method reduces compared to ideal proportional representation somewhat the political fragmentation for smaller electoral district sizes, where it favors larger political parties over small parties.
First-past-the-post voting is an electoral system wherein voters cast a vote for a single candidate, and the candidate with the most votes wins the election. Analogous systems for multi-winner contests are known as plurality block voting or "block voting" systems; both FPTP and block voting are "plurality" systems in that the winner needs only a plurality of the votes and not an absolute majority. The term first-past-the-post is a metaphor from horse racing of the plurality-voted candidate winning such a race; the electoral system is formally called single-member plurality voting (SMP) when used in single-member districts, and informally called choose-one voting in contrast to ranked voting or score voting.
The Webster method, also called the Sainte-Laguë method, is a highest averages apportionment method for allocating seats in a parliament among federal states, or among parties in a party-list proportional representation system. The Sainte-Laguë method shows a more equal seats-to-votes ratio for different sized parties among apportionment methods.
Electoral reform in New Zealand has been a political issue in the past as major changes have been made to both parliamentary and local government electoral systems.
The Canadian electoral system is based on a parliamentary system of government, modelled on that of the United Kingdom.
Canada holds elections for legislatures or governments in several jurisdictions: for the federal (national) government, provincial and territorial governments, and municipal governments. Elections are also held for self-governing First Nations and for many other public and private organizations including corporations and trade unions. Municipal elections can also be held for both upper-tier and lower-tier governments.
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Michael Gallagher is a political scientist. He is Professor of Comparative Politics and head of the Department of Political Science at the Trinity College Dublin.
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Electoral reform is a change in electoral systems which alters how public desires are expressed in election results.
The Sainte-Laguë index (SLI) measures an election’s disproportionality, the adherence to the one person, one vote principle of equal representation. This index assumes if the fraction of voters matches the fraction of seats, then perfect proportionality is achieved.
The House of Commons Special Committee on Electoral Reform (ERRE) (French: Comité spécial sur la réforme électorale) was a special committee of the House of Commons of Canada established in 2016 during the 42nd Canadian Parliament to investigate reforms to the Canadian electoral system. The formation of "an all-party Parliamentary committee to review... [electoral] reforms" was an election promise by Liberal Party leader Justin Trudeau in the 2015 federal election. After the Liberals won a majority in the election, and Trudeau became Prime Minister of Canada, he indicated the formation of a special committee was a priority in his mandate letter for Minister of Democratic Institutions Maryam Monsef. Shortly after the committee submitted its report to Parliament on December 1, 2016, Monsef was transferred to the position of the Minister of Status of Women and Karina Gould took over the electoral reform file. Shortly after taking her position, Gould announced that the government would no longer be pursuing reform of the electoral system, stating "It has become evident that the broad support needed among Canadians for a change of this magnitude does not exist."
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The seats-to-votes ratio, also known as the advantage ratio, is a measure of equal representation of voters. The equation for seats-to-votes ratio for a political party i is: