Social:Gallagher index

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Short description: Measure of electoral disproportionality
Comparison of Gallagher indices of various countries since 1945

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 ([math]\displaystyle{ V_i }[/math]) and percent of seats ([math]\displaystyle{ S_i }[/math]) for each of the political parties ([math]\displaystyle{ i=1,\ldots,n }[/math]).[4]

[math]\displaystyle{ \mathrm{LSq} = \sqrt{ \frac{1}{2} \sum_{i=1}^n ( V_i-S_i ) ^2} }[/math]  [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. 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.

History

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)."

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.[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]

Examples of calculating disproportionality

Canada

In the 2015 Canadian federal election, the Gallagher index was 12.02, where 0 would be a perfectly proportional election outcome.[12]

Template:Gallagher index

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. 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. Template:Gallagher index

EU

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. Template:Gallagher index

Sweden

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.

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. The Gallagher index ignores the effect of the primaries on the proportionality. Template:Gallagher index

Countries

This is a dynamic list and may never be able to satisfy particular standards for completeness. You can help by expanding it with reliably sourced entries.

In Michael Gallagher's Electoral Systems web site he offers a PDF download under "Values of Indices." [14] Those Gallagher indices for individual countries are listed below. Only the last available index for each country is shown.

Country Year Gallagher Index
 Albania 2021 4.57
 Algeria 2017 8.57
 Andorra 2019 6.89
 Angola 2022 4.32
 Antigua and Barbuda 2018 30.32
 Argentina 2021 6.75
 Armenia 2021 10.74
 Australia 2022 16.72
 Austria 2019 1.85
 Bahamas 2021 25.01
 Barbados 2022 28.92
 Belgium 2019 3.92
 Belize 2020 23.51
 Bermuda 2020 19.02
 Bhutan 2018 30.81
 Bosnia and Herzegovina 2022 5.30
 Bolivia 2020 2.60
 Botswana 2019 12.26
 Brazil 2022 3.53
 Bulgaria 2022 4.02
 Burkina Faso 2022 4.11
 Canada 2021 13.39
 Cabo Verde 2021 3.54
 Chile 2021 9.58
 Colombia 2022 4.60
 Costa Rica 2022 8.26
 Croatia 2020 7.47
 Cyprus 2021 6.44
 Czech Republic 2021 10.34
 Denmark 2022 1.13
 Dominican Republic 2020 7.32
 El Salvador 2021 3.16
 Estonia 2019 5.28
 EU 2019 7.87
 Faeroe Islands 2019 1.66
 Fiji 2022 4.75
 Finland 2019 3.55
 France 2022 12.81
 Gambia 2022 7.93
 Georgia 2020 8.68
 Germany 2021 3.48
 Ghana 2020 2.64
 Greece 2023 9.80
 Greenland 2021 2.75
 Grenada 2022 7.97
 Guatemala 2019 12.00
 Guinea 2020 2.14
 Guinea-Bissau 2019 9.33
 Honduras 2021 6.41
 Hungary 2022 11.76
 Guyana 2020 0.52
 Iceland 2021 3.96
 India 2019 16.06
 Indonesia 2019 4.51
 Iraq 2010 5.17
 Ireland 2020 2.22
 Israel 2022 4.40
 Italy 2022 12.37
 Jamaica 2020 20.62
 Japan 2021 11.43
 Kosovo 2021 3.26
 Latvia 2022 10.65
 Lesotho 2022 6.03
 Liberia 2017 15.18
 Liechtenstein 2021 5.62
 Lithuania 2020 9.49
 Luxembourg 2018 5.57
 Malawi 2019 8.56
 Malaysia 2022 6.99
 Malta 2022 2.24
 Mauritius 2019 12.96
 Mexico 2021 8.80
 Moldova 2021 8.44
 Monaco 2023 10.37
 Mongolia 2020 28.19
 Montenegro 2020 1.71
 Morocco 2021 4.18
 Mozambique 2019 2.45
 Namibia 2019 0.98
 Nepal 2022 6.02
 Netherlands 2021 1.31
 New Zealand 2020 4.15
 Niger 2021 8.10
 North Cyprus 2022 7.78
 North Macedonia 2020 3.27
 Northern Ireland 2022 7.80
 Norway 2021 3.65
 Panama 2019 14.96
 Paraguay 2018 10.79
 Peru 2021 14.02
 Poland 2019 6.60
 Portugal 2022 7.85
 Romania 2020 6.14
 Saint Kitts and Nevis 2022 15.97
 Saint Lucia 2021 28.97
 Saint Vincent and the Grenadines 2020 10.37
 San Marino 2019 1.91
 Sao Tome and Principe 2022 7.04
 Scotland 2021 7.03
 Senegal 2022 2.73
 Serbia 2022 3.90
 Seychelles 2020 15.33
 Sierra Leone 2018 9.36
 Singapore 2020 21.67
 Slovakia 2023 7.44
 Slovenia 2022 11.49
 South Africa 2019 0.47
 South Korea 2020 13.65
 Spain 2019 6.36
 Sri Lanka 2020 4.54
 Suriname 2020 8.70
 Sweden 2022 0.64
 Switzerland 2019 2.46
 Taiwan 2020 10.91
 Thailand 2019 3.81
 Timor-Leste 2018 2.42
 Trinidad and Tobago 2020 3.55
 Turkey 2018 3.15
 Uganda 2021 14.90
 Ukraine 2019 10.62
 United Kingdom 2019 15.02
 United States 2020 1.44
 Uruguay 2019 1.73
 Wales 2021 9.36
 Zambia 2021 5.21

See also

Notes

  1. ↑ Special Committee on Electoral Reform (a Canadian Parliamentary Committee) (December 1, 2016). Report 3: Strengthening Democracy in Canada : Principles, Process and Public Engagement for Electoral Reform (Report). Parliament of Canada. p. 69 (or p. 83 in PDF search). http://www.parl.gc.ca/HousePublications/Publication.aspx?Language=e&Mode=1&Parl=42&Ses=1&DocId=8655791&File=177#50. Retrieved December 26, 2016. "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)." 
  2. ↑ O'Malley, Kady (December 1, 2016). "Read the full electoral reform committee report, plus Liberal and NDP/Green opinions". Ottawa Citizen (Ottawa Citizen). https://ottawacitizen.com/news/politics/read-the-full-electoral-reform-committee-report-plus-liberal-and-ndpgreen-opinions. 
  3. ↑ This is discussed in simple English at "Gallagher Index Made Easy". 2016-12-31. http://gallagherindex.blogspot.ca/. 
  4. ↑ Gallagher 1991, pp. 33–51.
  5. ↑ Gallagher 1991, p. 40.
  6. ↑ Gallagher 1991, p. 41.
  7. ↑ "Election Indices". https://www.tcd.ie/Political_Science/about/people/michael_gallagher/ElSystems/Docts/ElectionIndices.pdf. 
  8. ↑ Cash, Colby (December 2, 2016). "Colby Cosh: Did Maryam Monsef actually read the whole electoral reform report?". National Post. http://news.nationalpost.com/full-comment/colby-cosh-did-maryam-monsef-actually-read-the-whole-electoral-reform-report. 
  9. ↑ Wherry, Aaron (December 1, 2016). "Minister 'disappointed' as electoral reform committee recommends referendum on proportional representation". CBC News. http://www.cbc.ca/news/politics/wherry-electoral-reform-committee-1.3866879. 
  10. ↑ O'Malley, Kady (December 1, 2016). "Read the full electoral reform committee report, plus Liberal and NDP/Green opinions". Ottawa Citizen (Ottawa Citizen). https://ottawacitizen.com/news/politics/read-the-full-electoral-reform-committee-report-plus-liberal-and-ndpgreen-opinions. 
  11. ↑ "Is Canada Fair?". (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.). https://iscanadafair.ca/. 
  12. ↑ The rules for federal elections in Canada require that certain provinces always get a certain quantity of seats – on a province by province basis. If so, then Byron Weber Becker proposed that the Gallagher index for Canada ought to ALSO reflect that. In other words, the Gallagher data should be collected on a province by province basis; and the Gallagher score should be calculated on a province by province basis. Only after that is done, can we then add up all of those provincial scores and then average them out to get the true national "composite Gallagher index" score. If we do that, then the illustrated table calculation of 12 for Canada is incorrect. It should instead show a "composite Gallagher index" of 17.1. Byron Weber Becker developed this "composite" index. See citation here: Special Committee on Electoral Reform (a Canadian Parliamentary Committee) (December 1, 2016). Report 3: Strengthening Democracy in Canada : Principles, Process and Public Engagement for Electoral Reform (Report). Parliament of Canada. p. 69 (or p. 83 in PDF search). http://www.parl.gc.ca/HousePublications/Publication.aspx?Language=e&Mode=1&Parl=42&Ses=1&DocId=8655791&File=177#50. Retrieved December 26, 2016. "...Professor Becker developed the “Gallagher Index Composite” for the Committee’s study..." 
  13. ↑ "European Parliament: Facts and Figures". https://www.europarl.europa.eu/RegData/etudes/BRIE/2022/698880/EPRS_BRI(2022)698880_EN.pdf. 
  14. ↑ "Election Indices". https://www.tcd.ie/Political_Science/about/people/michael_gallagher/ElSystems/Docts/ElectionIndices.pdf. 

References

External links



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