Gallagher Index
Encyclopedia
The Gallagher 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.
result. Note: New Zealand 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 1.11, which is very low by international standards.
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 or Labour parties.
which has better statistical underpinning.
A Gallagher Index listing for 900 elections from 100 countries http://www.tcd.ie/Political_Science/staff/michael_gallagher/ElSystems/Docts/ElectionIndices.pdf
Square root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
of half the sum
SUM
SUM can refer to:* The State University of Management* Soccer United Marketing* Society for the Establishment of Useful Manufactures* StartUp-Manager* Software User’s Manual,as from DOD-STD-2 167A, and MIL-STD-498...
of the squares of the difference between percent of vote and percent of seats for each of the political parties
Political Parties
Political Parties: A Sociological Study of the Oligarchical Tendencies of Modern Democracy is a book by sociologist Robert Michels, published in 1911 , and first introducing the concept of iron law of oligarchy...
.
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
Michael Gallagher (academic)
Michael Gallagher is a political scientist. He is Professor of Comparative Politics and head of the Department of Political Science at the University of Dublin, Trinity College.-Education:...
, who created the index, included 'other' parties as a whole category, and Arend Lijphart
Arend Lijphart
Arend d'Angremond Lijphart is a world renowned political scientist specializing in comparative politics, elections and voting systems, democratic institutions, and ethnicity and politics. He received his PhD in Political Science at Yale University in 1963, after studying at the University of...
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 electionNew Zealand general election, 2005
The 2005 New Zealand general election held on 17 September 2005 determined the composition of the 48th New Zealand Parliament. No party won a majority in the unicameral House of Representatives, but the Labour Party of Prime Minister Helen Clark secured two more seats than nearest rival, the...
result. Note: New Zealand voters have two votes. This list uses the party vote, which determines the proportionality of the House
New Zealand House of Representatives
The New Zealand House of Representatives is the sole chamber of the legislature of New Zealand. The House and the Queen of New Zealand form the New Zealand Parliament....
; the electorate vote determines the local member.
| party | % of votes | % of seats | difference | difference squared |
|---|---|---|---|---|
| Labour New Zealand Labour Party The New Zealand Labour Party is a New Zealand political party. It describes itself as centre-left and socially progressive and has been one of the two primary parties of New Zealand politics since 1935.... |
41.10 | 41.32 | 0.22 | 0.0484 |
| National New Zealand National Party The New Zealand National Party is the largest party in the New Zealand House of Representatives and in November 2008 formed a minority government with support from three minor parties.-Policies:... |
39.10 | 39.67 | 0.57 | 0.3249 |
| NZ First New Zealand First New Zealand First is a political party in New Zealand that was founded in 1993, following party founder Winston Peters' resignation from the National Party in 1992... |
5.72 | 5.79 | 0.07 | 0.0049 |
| Greens Green Party of Aotearoa New Zealand The Green Party of Aotearoa New Zealand is a political party that has seats in the New Zealand parliament. It focuses firstly on environmentalism, arguing that all other aspects of humanity will cease to be of concern if there is no environment to sustain it... |
5.30 | 4.96 | 0.34 | 0.1156 |
| Māori Maori Party The Māori Party, a political party in New Zealand, was formed on 7 July 2004. The Party is guided by eight constitutional "kaupapa", or Party objectives. Tariana Turia formed the Māori Party after resigning from the Labour Party where she had been a Cabinet Minister in the Fifth Labour-led... |
2.12 | 3.30 | 1.18 | 1.3924 |
| United Future | 2.67 | 2.48 | 0.19 | 0.0361 |
| ACT | 1.51 | 1.65 | 0.14 | 0.0196 |
| Progressives New Zealand Progressive Party Jim Anderton's Progressive Party , is a New Zealand political party generally somewhat to the left of its ally, the Labour Party.... |
1.16 | 0.82 | 0.34 | 0.1156 |
| Destiny Destiny New Zealand Destiny New Zealand was a Christian political party in New Zealand centred on the charismatic/pentecostal Destiny Church. The party described itself as "centre-right". It placed a strong focus on socially conservative values and argued that the breakdown of the traditional family was a primary... |
0.62 | 0 | 0.62 | 0.3844 |
| Legalise Cannabis Aotearoa Legalise Cannabis Party The Aotearoa Legalise Cannabis Party is a political party in New Zealand. It is dedicated to removing or reducing restrictions on the use of cannabis and similar substances... |
0.25 | 0 | 0.25 | 0.0625 |
| Christian Heritage Christian Heritage New Zealand The Christian Heritage Party of New Zealand was a New Zealand political party espousing Christian values... |
0.12 | 0 | 0.12 | 0.0144 |
| Alliance Alliance (New Zealand political party) The Alliance is a left-wing political party in New Zealand. It was formed in 1991, and was influential in the 1990s, but has since declined and has no representation in parliament. It suffered a major setback after Jim Anderton, the party's leader, left the party in 2002, taking several of the... |
0.07 | 0 | 0.07 | 0.0049 |
| Family Rights New Zealand Family Rights Protection Party The New Zealand Family Rights Protection Party was a political party in New Zealand. It was primarily based around Pacific Islanders, and claims that the established political parties do not give sufficient consideration to the concerns of Pacific Islanders in New Zealand.The party was approved for... |
0.05 | 0 | 0.05 | 0.0025 |
| Democrats New Zealand Democratic Party The New Zealand Democratic Party for Social Credit is a small leftist political party in New Zealand. It is based around the ideas of Social Credit, an economic theory which also attracted some degree of support in Canada and Australia... |
0.05 | 0 | 0.05 | 0.0025 |
| Libertarianz Libertarianz Libertarianz is a political party in New Zealand that advocates libertarianism, favouring self-government and limiting the power of the government over the individual. Ayn Rand's philosophy of Objectivism is a major influence on the party... |
0.04 | 0 | 0.04 | 0.0016 |
| Direct Democracy Direct Democracy Party of New Zealand The Direct Democracy Party of New Zealand was a political party in New Zealand that promoted greater participation by the people in the decision-making of government. The party's leader was Kelvyn Alp.... |
0.03 | 0 | 0.04 | 0.0016 |
| 99MP 99 MP Party The 99 MP Party was a small New Zealand political party that contested the 2005 General Election. It supported a reduction of the number of Members of Parliament from 120 to 99.-History:... |
0.03 | 0 | 0.03 | 0.0009 |
| OneNZ One New Zealand Party The One New Zealand Party was a small political party in New Zealand. It was partly modeled on the Australian One Nation Party, founded by Pauline Hanson. Its primary focus was on matters such as the Treaty of Waitangi, but its wider platform was broadly paleoconservative or producerist... |
0.02 | 0 | 0.02 | 0.0004 |
| Republicans The Republic of New Zealand Party The Republic of New Zealand Party was a political party in New Zealand. The party's registration was cancelled at its own request in 2009... |
0.02 | 0 | 0.02 | 0.0004 |
| total of squares of differences | 2.4711 | |||
| total / 2 | 1.23555 | |||
| square root of (total / 2) | 1.11 | |||
Thus the disproportionality of the 2005 New Zealand election is 1.11, which is very low by international standards.
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
Maori seats
In New Zealand politics, Māori electorates, colloquially also called Māori seats, are a special category of electorate that gives reserved positions to representatives of Māori in the New Zealand Parliament...
. 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 or Labour parties.
Other indices
The Sainte–Laguë Index is considered by Gallagher to be probably the soundest of all the measures. This is closely related to the Pearson's chi-squared testPearson's chi-squared test
Pearson's chi-squared test is the best-known of several chi-squared tests – statistical procedures whose results are evaluated by reference to the chi-squared distribution. Its properties were first investigated by Karl Pearson in 1900...
which has better statistical underpinning.
See also
The Gallagher Index of the results of the Australian 2007 federal election: :Image:Aus07Gallagher.PNGA Gallagher Index listing for 900 elections from 100 countries http://www.tcd.ie/Political_Science/staff/michael_gallagher/ElSystems/Docts/ElectionIndices.pdf
External links
- P Kestelman, Quantifying Representativity", Voting matters, Issue 10, March 1999.