Gallagher Index

The Gallagher Index (also known as the Least Squares Index ) is a method of determining the disproportionality of an election result, which is the difference between a party's share of the vote in the election and the percentage of the party's seats in the following legislative period . To do this, take the square root of half the sum of the square of the difference between the share of the vote and the share of seats for each of the political parties .

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

Lsq stands for least square , i.e. the smallest square . n indicates the number of parties, V stands for votes and S for seats (seats in parliament).

The index weights deviations according to their own value, creating a responsive index that ranges from 0 to 100. The lower the index, the lower the disproportionality and vice versa . Michael Gallagher , who compiled the index, included other parties as a separate category. Arend Lijphart modified the index by excluding them.

The index was developed in 1989 and was first published in 1991 in the article Proportionality, Disproportionality and Electoral Systems. published in the journal Electoral Studies . According to Gallagher, the index is based on the work of today's electoral systems scientists and an article by André Sainte-Laguë from 1911.

Calculation using New Zealand as an example

The table uses the results of the 2005 election in New Zealand . New Zealand voters have two votes, and this table shows the party votes that determine the proportionality of the House of Representatives . The second vote determines the local members. (see also parties of New Zealand )

Political party	% of votes	% of seats	difference	Difference in the square
Labor	41.10	41.32	0.22	0.0484
National	39.10	39.67	0.57	0.3249
NZ First	5.72	5.79	0.07	0.0049
Greens	5.30	4.96	0.34	0.1156
Māori	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	1.16	0.82	0.34	0.1156
Destiny	0.62	0	0.62	0.3844
Legalize cannabis	0.25	0	0.25	0.0625
Christian Heritage	0.12	0	0.12	0.0144
Alliance	0.07	0	0.07	0.0049
Family Rights	0.05	0	0.05	0.0025
Democrats	0.05	0	0.05	0.0025
Libertarianism	0.04	0	0.04	0.0016
Direct Democracy	0.03	0	0.04	0.0016
99MP	0.03	0	0.03	0.0009
OneNZ	0.02	0	0.02	0.0004
Republicans	0.02	0	0.02	0.0004
Sum of the square of the differences				2.5336
Sum divided by 2				1.2668
Root of (sum divided by 2)				1.13

Accordingly, the 2005 New Zealand election disproportionality is 1.13, which is a very low value. The Māori Party has the biggest difference, it is significantly above the others. This is due to the New Zealand system of Māori Electorates .

Chart of the Gallagher index for the nationwide elections in Germany between 1919 and 2009

Values ​​for Germany

In a document by Gallagher, which describes the index values ​​for more than 1,050 elections in over 100 countries, Germany is also represented with 27 elections. The highest Gallagher index was in the 1957 federal election with a value of 4.69, followed by the 1990 federal election with 4.63 and the 2002 federal election with 4.61. In the 2013 federal election , the Gallagher index was 7.83, which is a new high. The lowest values ​​are 0.50 for the 1983 Bundestag election , 0.59 for the 1976 Bundestag election and 0.67 for the 1972 Bundestag election . Gallagher states that he viewed the CDU and CSU as individual parties, although different values ​​for n would arise if the CDU / CSU parliamentary group were considered .

Other indices

The Gallagher Index is similar to the Loosemore-Hanby Index , which calculates the sum of the absolute difference between the percentage and the number of seats.

${\displaystyle \mathrm {D} ={{\frac {1}{2}}\sum \left|v_{i}-s_{i}\right|}}$

However, the Gallagher Index is more sensitive to large discrepancies between the percentage and number of seats.

The Sainte-Laguë index is Gallagher as "probably the most solid of all measurements" viewed.

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

This is very close to Pearson's chi-square test , although it has better statistical support.

literature

• Michael Gallagher, Paul Mitchell: The Politics of Electoral Systems . Oxford University Press, 2008, ISBN 978-0-19-923867-5 .
• Michael Gallagher: Proportionality, Disproportionality and Electoral Systems (PDF; 2.8 MB). In: Electoral Studies . 10: 1, 1991. pp. 33-51.

Web links

• Michael Gallagher: Electoral Systems

Individual evidence

1. ↑ ^{a b} Measures of disproportionality (PDF; 147 kB). Retrieved July 29, 2012.
2. ↑ Michael Gallagher: Proportionality, Disproportionality and Electoral Systems ( Memento of the original from March 4, 2016 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. (PDF; 2.8 MB). In: Electoral Studies . 10: 1, 1991. pp. 33-51. Retrieved July 29, 2012. 
3. ↑ Michael Gallagher: Least squares index . Retrieved July 29, 2012.
4. ↑ Michael Gallagher: Election indices (PDF; 264 kB). Pp. 12-35. Retrieved July 19, 2014.
5. ↑ Bruno Simeone: Mathematics And Democracy: Recent Advances in Voting Systems And Collective Choice , Springer, 2006, p. 242, Google Books . Retrieved July 29, 2012.
6. ^ Philip Kestelman: Quantifying Representativity . In: Voting matters . Issue 10, March 1999. Retrieved July 29, 2012.