The Sainte-Laguë index (SLI) measures an election’s disproportionality, the adherence to the

one person, one vote "One man, one vote" or "one vote, one value" is a slogan used to advocate for the principle of equal representation in voting. This slogan is used by advocates of democracy and political equality, especially with regard to electoral reforms like ...

principle of equal representation. This index assumes if the fraction of voters matches the fraction of seats, then perfect proportionality is achieved. Gallagher, Michael. "Proportionality, disproportionality and electoral systems." Electoral studies 10.1 (1991): 33-51. 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. 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 A political party is an organization that coordinates candidates to compete in a particular area's elections. It is common for the members of a party to hold similar ideas about politics, and parties may promote specific ideological or p ...

. The first part of the equation illustrates the derivation of the equation as the squared difference to the ideal

seats-to-votes ratio The seats-to-votes ratio, also known as the advantage ratio, is a measure of equal representation of voters. The equation for seats-to-votes ratio for a political party ''i'' is: : \mathrm = s_i/v_i, where \mathrm is fraction of votes cast for t ...

, 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 The Webster method, also called the Sainte-Laguë method (), is a highest averages apportionment method for allocating seats in a parliament among federal states, or among parties in a party-list proportional representation system. The Sainte- ...

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 or Pearson's \chi^2 test 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-squa ...

, which some argue gives it better statistical underpinning than the

Gallagher index The Gallagher index measures an electoral system's relative Proportional representation, disproportionality between votes received and seats in a legislature. As such, it measures the difference between the percentage of votes each party gets and ...

. The Sainte-Laguë index, as other proportionality indices, is used in

psephology Psephology (; from Greek ) is the study of elections and voting. Psephology attempts to both forecast and explain election results. The term is more common in Britain and in those English-speaking communities that rely heavily on the British st ...

to compare the proportionality between various elections from various

electoral systems An electoral or voting system is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, nonprofit organizations and inf ...

and countries. The relationship among Sainte-Laguë index and the other indices 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.
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Notes

{{Reflist, 30em Electoral systems Psephology

See also

Notes