Gallagher index

Comparison of Gallagher indices of various countries since 1945.

The Gallagher index is a statistical analysis methodology utilised within political science (notably the branch of psephology) which "measures an electoral system’s relative disproportionality between votes received and seats allotted 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]

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 (${\displaystyle V_{i}}$) and percent of seats (${\displaystyle S_{i}}$) for each of the political parties (${\displaystyle i=1,\ldots ,n}$).^[4]

${\displaystyle \mathrm {LSq} ={\sqrt {{\frac {1}{2}}\sum _{i=1}^{n}(V_{i}-S_{i})^{2}}}}$  ^[5]

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. Unlike the well-known Loosemore–Hanby index, the Gallagher index is less sensitive to small discrepancies.^[6]

Application in Canada[]

The Gallagher index gained considerable attention in Canada in December 2016 in the context of efforts to reform Canada's electoral system.^[7][8] 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."^[9][10] In the 2015 Canadian federal election, the Gallagher index was 12.02, where 0 would be a perfectly proportional election outcome.^[11]

Examples of calculating disproportionality[]

New Zealand[]

This table uses the New Zealand 2005 election result.^[12] 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.

Thus the disproportionality of the 2005 New Zealand election is 1.13, which is very low by international standards.^[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 have historically been won by either the Māori Party, the Labour Party, or New Zealand First.

Australia[]

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. Most recent Australian state and federal elections however score between 10 and 12.

The 2012 Election for the Australian state of Queensland resulted in a Gallagher Index of 31.16 – the winning party gained over 87% of the seats with just less than 50% of the vote

For comparison, the 2010 Australian Federal Election was more typical of Australian state and federal politics:

The 2010 Australian Federal Election for the Lower House of Parliament. The disproportionality of the lower house in the 2010 election was 11.34 according to the Gallagher Index, mainly between the Labor and Green Parties.

Sweden[]

The disproportionality of the 2018 Swedish general election was 0.63 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.

Republic of Ireland[]

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.

United States[]

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.

Brazil[]

This table uses the results of the 2018 Brazilian general election (Lower House). The 513 seats are contested in statewide districts via open list proportional representation.

Other indices[]

Gallagher stated that the index constructed from and minimized by the Sainte-Laguë method "at the theoretical level is probably the soundest of all the measures."^[14] This is closely related to the Pearson's chi-squared test which has better statistical underpinning.

${\displaystyle \mathrm {SLI} =\sum {(S-V)^{2} \over V}}$

Notes[]

References[]

• Benoit, Kenneth (2000). "Which Electoral Formula Is the Most Proportional? A New Look with New Evidence". Political Analysis. 8 (4): 381–388. doi:10.1093/oxfordjournals.pan.a029822.
• 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 (4): 469–496. doi:10.1017/s0007123400006499.
• Gallagher, Michael; Mitchell, P, eds. (2005). The Politics of Electoral Systems. Oxford: Oxford University Press. Appendix B. ISBN 978-0-19-925756-0.
• Kestelman, Philip (March 1999). "Quantifying Representativity". Voting Matters. 10. Retrieved 10 August 2013.

External links[]

• Gallagher Index Made Easy
• The Gallagher Index: A Measure of Disproportionality
• Various Gallagher Indexes at Wikimedia Commons
• Website: Measuring Unfairness — Calculating Canada's Gallagher Index (This website includes the Gallagher Index in adjustable table format. It initially shows the data for Canada's 2015 federal election, but some variables in some table cells are adjustable by the visitor to the website, and then the rest of the table is automatically adjusted to reflect this visitor's new input).
• A CSV file of Galagher indices of various countries.