Highest averages

A highest-averages method never calculates a quota. Instead, it imagines each party holding a notional "average" vote per seat: if a party has 120,000 votes and holds three seats, its current average is 40,000. The next seat goes to whichever party would achieve the highest average by receiving it. In practice, this comparison runs as a sequential division: each party's total vote is divided by 1, then 2, then 3, and so on, and the resulting figures are sorted into a single ranked list. Work through the list awarding seats until the chamber is full.

The denominators are everything. The most familiar sequence — 1, 2, 3, 4… — is the D'Hondt method, developed by the Belgian jurist Victor D'Hondt in the 1870s and now used in more than thirty countries including Spain, Poland and the Netherlands. Because it starts from 1, a party with no seats yet is compared at its full vote, giving larger parties a marginal edge in the final rounding. The effect is small but consistent: across many districts, D'Hondt tends to produce outcomes where large parties do fractionally better than strict proportionality would imply.

Sainte-Laguë, proposed by the French mathematician André Sainte-Laguë in 1910, replaces the sequence with odd numbers — 1, 3, 5, 7… Starting from 1, as D'Hondt does, means the first divisor is the same, but subsequent divisors grow faster, which flattens the advantage of size. Sainte-Laguë is generally considered the least biased of the common divisor methods and is used in Scandinavia and New Zealand. A modified variant, opening with 1.4 instead of 1, briefly raises the threshold a party must clear to earn its very first seat; it has been used in Norway and Sweden as a tool for keeping very small parties below the representation line.

The divisor methods family also includes the Adams method (denominators 0, 1, 2, 3…) which tilts systematically toward small parties, and the Huntington-Hill method used for apportioning the United States House, which uses geometric means as rounding thresholds. Each sequence reflects a deliberate or implicit choice about what "fair" rounding means — and none of them is neutral.