Sainte-Laguë Index

The Gallagher index "measures an electoral system’s relative disproportionality between votes received and seats allotted in a legislature." As such, it measures the difference between the percentage of votes each party gets and the percentage of seats each party gets in the resulting legislature, and it also measures this disproportionality from all parties collectively in any one given election. That collective disproportionality from the election is given a precise score, which can then be used in comparing various levels of proportionality among various elections from various electoral systems.

Michael Gallagher, who created the index, referred to it as a "least squares index", inspired by the sum of squared residuals used in the method of least squares. The index is therefore commonly abbreviated as "LSq" even though the measured allocation is not necessarily a least squares fit. The Gallagher index is computed by taking the square root of half the sum of the squares of the difference between percent of votes (${\displaystyle V_{i}}$) and percent of seats (${\displaystyle S_{i}}$) for each of the political parties (${\displaystyle i=1...n}$).

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