Sainte-Laguë Method

The Sainte-Laguë method (also called the Webster method in the United States) is a seat-allocation rule used in party-list proportional representation systems. It was described by French mathematician André Sainte-Laguë in 1910 and, independently, by American statesman Daniel Webster in 1832 in the context of US congressional apportionment.

Under the standard version, each party's vote total is successively divided by the odd numbers 1, 3, 5, 7, 9 … The resulting quotients are ranked, and seats are awarded one by one to the highest remaining quotient until all seats in the district are filled. The formula is mathematically equivalent to rounding each party's exact seat share to the nearest whole number while ensuring the total matches the district magnitude.

Compared with the D'Hondt method (which divides by 1, 2, 3, 4…), Sainte-Laguë is generally more favourable to small and mid-sized parties and produces results closer to strict proportionality. Some jurisdictions use a modified Sainte-Laguë, replacing the first divisor 1 with 1.4 to raise the effective threshold and discourage micro-parties; Sweden, Norway, and Denmark have all used this variant at various points.

Countries that have used some form of Sainte-Laguë include Germany (for Bundestag seat distribution from 2009 to 2013, before later reforms), New Zealand (for MMP allocation since 1996), Norway, Sweden, Denmark, Latvia, Kosovo, Bosnia and Herzegovina, and Iraq (since 2013 for Council of Representatives elections).

Because the divisor sequence grows faster than D'Hondt's, a large party gaining additional seats faces a steeper "penalty" quotient, which is why analysts often describe Sainte-Laguë as the more neutral or unbiased of the two leading highest-averages methods. It does not, however, eliminate distortions arising from district magnitude, legal thresholds, or overhang seats in mixed systems.