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Least squares index
The least squares index (LSq) was devised in the summer of 1989 as a measure of the amount of disproportionality generated by an election outcome, by which is meant the disparity, if any, between the distribution of votes at the election and the allocation of seats. There are various ways in which this could be measured and they do not all produce identical rankings of a particular seat allocation; in other words, an allocation that minimises disproportionality (i.e. is the most proportional) according to one measure will not necessarily be the most proportional by another measure. The construction of the index owed much to the work of contemporary electoral systems scholars and also to an article published in 1911 by the French mathematician André Sainte-Laguë. The index was outlined in an article (download HERE; pdf file, 2.7 mb) published in 1991.
More information about the least squares index and about the effective number of parties, a measure of fragmentation, can be found on the accompanying site, which contains
(i) the values of the index for over 900 elections in over 90 countries;
(ii) a downloadable file explaining in detail how to calculate the value of the index for any given election outcome;
(iii) a downloadable file enabling users to calculate the value of the index themselves for any election outcome.
There is also much more information in the book The Politics of Electoral Systems, paperback edition (Oxford University Press, 2008).
Translations
(Unfortunately, some characters, eg those with an accent, an umlaut or equivalent, are impossible to reproduce accurately in this format; the attached file LSqTrans.pdf (40kb), viewable or downloadable here, shows how the translations should look.)
| Language | Translation |
| English | least squares index |
| Albanian | Indeksi i katroreve me te vegjel |
| Danish | mindste kvadraters indekset |
| Dutch, Afrikaans | de kleinste kwadraten index |
| Estonian | vahimruudu naitaja |
| Finnish | pienin neliosumman hakemisto |
| French | l'indice des moindres carrés |
| German | Index der kleinsten Quadrate |
| Bahasa Indonesia | indéks kuadrat-kuadrat yang kecil sekali |
| Irish | Innéacs na nÍoschearnóg |
| Italian | l'indice di minimi quadrati |
| Norwegian | minst rutene indeksen |
| Polish | indeks najmniejszych kwadratów |
| Portuguese | o mínimos quadrados índice |
| Spanish | el índice de mínimos cuadrados |
| Swedish | minsta kvadratmetoden index |
Another concept widely used in the analysis of electoral systems is the effective threshold.
Some political photographs.
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Last updated 15 May, 2012 4:08 PM