The Sainte-Laguë index (SLI)Gallagher, Michael. "Proportionality, disproportionality and electoral systems." Electoral studies 10.1 (1991): 33-51.
/ref>Goldenberg, Josh, and Stephen D. Fisher. "The Sainte-Laguë index of disproportionality and Dalton’s principle of transfers." Party Politics 25.2 (2019): 203-207.
/ref> measures an election’s disproportionality, the adherence to the

one person, one vote "One man, one vote", or "one person, one vote", expresses the principle that individuals should have equal representation in voting. This slogan is used by advocates of political equality to refer to such electoral reforms as universal suffrage ...

principle of equal representation. This index assumes if the fraction of voters matches the fraction of seats, then perfect proportionality is achieved. Equation for Sainte-Laguë index: :

\mathrm = \sum_^n =\sum_^n

, where

V_i

is fraction of votes and

S_i

is fraction of seats for each of the political parties. The first part of the equation illustrates the derivation of the equation as the squared difference to the ideal seats-to-votes ratio, then weighted equally for each voter. The larger the Sainte-Laguë index is, the larger the disproportionality and the smaller the Sainte-Laguë index is, the more proportional the election. Michael Gallagher stated that the Sainte-Laguë index (SLI) constructed from and minimized by the Sainte-Laguë method is "at the theoretical level is probably the soundest of all the measures." The Sainte-Laguë index is closely related to the

Pearson's chi-squared test Pearson's chi-squared test (\chi^2) is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many chi-squared tests (e.g ...

, which gives it better statistical underpinning than the Gallagher index. The Sainte-Laguë index, as other proportionality indices, is used in

psephology Psephology (; from Greek el, ψῆφος, psephos, pebble, label=none) or political analysis is a branch of political science, the "quantitative analysis of elections and balloting". As such, psephology attempts to explain elections using the ...

to compare the proportionality between various elections from various

electoral systems An electoral system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. Electoral systems are used in politics to elect governments, while non-political elections m ...

and countries. The relationship among Sainte-Laguë index and the other indexes varies depending if the election disproportionality affects smaller or larger parties more. Arredondo, Verónica, et al. "New indexes for measuring electoral disproportionality." Rect@: Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA 21.2 (2020): 161-178.
/ref>

Notes

{{Reflist, 30em Electoral systems Psephology