Gallagher Index

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Gallagher Index

The Gallagher Index (or least squares index

Least squares

The method of least squares or ordinary least squares is used to solve overdetermined systems. Least squares is often applied in statistical contexts, particularly regression analysis....
) 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

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* StartUp-Manager...
of the square

Square (algebra)

In algebra, the square of a number is that number multiplication by itself. To square a quantity is to multiply it by itself.Its notation is a superscripted "2"; a number x squared is written as x?....
s of the difference between percent of vote and percent of seats (as whole numbers) for each of the political parties

Political party

A political party is a political organization that seeks to attain and maintain politics power within government, usually by participating in electoral campaigns....
.

The index weighs the deviations by their own value, creating a responsive index, ranging from 0 to 100.

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Encyclopedia

The Gallagher Index (or least squares index

Least squares

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* StartUp-Manager...
of the square

Square (algebra)

Political party

Michael Gallagher (academic)

Michael Gallagher is a noted United Kingdom political scientists, who lives and works in Ireland. He is Professor of Comparative Politics and head of the Department of Political Science at the Trinity College, Dublin....
, 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, Democracys, and ethnicity and politics....
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 election

New Zealand general election, 2005

The 2005 New Zealand general election took place on 17 September 2005 and determined the composition of the 48th New Zealand Parliament. No single political party or recognised bloc won a majority in the Unicameralism New Zealand Parliament, but the New Zealand Labour Party of Prime Minister of New Zealand Helen Clark secured two more seats t...
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 legislature of New Zealand. The House and the Monarchy in 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 Liberalism, and Progressivism, 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....	39.10	39.67	0.57	0.3249
NZ First New Zealand First New Zealand First is a political party in New Zealand. It had members in the New Zealand House of Representatives for over fifteen years, from the date that Winston Peters, its leader, won his Tauranga electorate seat in 1993....	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 in the New Zealand Parliament of New Zealand. 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
Maori Maori Party The Maori Party, a political party in New Zealand, was formed on 7 July 2004. The party is guided by eight constitutional "kaupapa", meaning in this context the way the party frames the objectives of the organisation....	2.12	3.30	1.18	1.3924
United Future United Future New Zealand United Future New Zealand is a New Zealand political party. With the formation of the 49th New Zealand Parliament after the 2008 election, it will have a single member of the New Zealand Parliament ? party leader Peter Dunne, an electorate MP ? and it has signed a confidence and supply agreement with the National Party, making it, along with...	2.67	2.48	0.19	0.0361
ACT ACT New Zealand The New Zealand centre-right political party ACT New Zealand espouses free market liberal parties points of view in the New Zealand Parliament....	1.51	1.65	0.14	0.0196
Progressives New Zealand Progressive Party The Progressive Party is a political party in New Zealand that is somewhat to the left-wing of its ally the New Zealand Labour Party . It has one seat in New Zealand Parliament, that of leader Jim Anderton....	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 movement/pentecostal Destiny Church, New Zealand. The party described itself as "centre-right"....	0.62	0	0.62	0.3844
Legalise Cannabis Aotearoa Legalise Cannabis Party The Aotearoa Legalise Cannabis Party is a small 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 functioned as a New Zealand political party espousing Christianity values. Although it never won seats in an election, it came close to doing so in 1996 as part of the Christian Coalition and briefly had a member in New Zealand Parliament....	0.12	0	0.12	0.0144
Alliance Alliance (New Zealand political party) The Alliance, in Politics of New Zealand, is a left-wing political party. The party is currently outside parliament, but has previously been a significant presence there....	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....	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 based on the political platform of libertarianism favouring self-government and on limiting the power of the government on the individual....	0.04	0	0.04	0.0016
Direct Democracy Direct Democracy Party of New Zealand The Direct Democracy Party of New Zealand is a New Zealand political party which promotes greater participation by the people in the decision making of government....	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 supports a reduction of the number of Member of Parliament from the current 120 to 99....	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....	0.02	0	0.02	0.0004
Republicans The Republic of New Zealand Party The Republic of New Zealand Party is a small political party in New Zealand. The party is not to be confused with the Republican Movement of Aotearoa New Zealand, which is a non-partisan organisation advocating a republic....	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.

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-square test

Pearson's chi-square test

Pearson's chi-square test is the best-known of several chi-square tests ? Statistics procedures whose results are evaluated by reference to the chi-square distribution....
which has better statistical underpinning.

External links

P Kestelman, ", Voting matters, Issue 10, March 1999.

Gallagher Index

Example of calculating disproportionality

Other indices

See also

External links