How it works, precisely
For each list, compute the series votes/1, votes/2, votes/3… Seats go to the largest quotients across all lists, until they run out.
This highest-average rule slightly favours large lists, systematically and knowingly: it is a political choice in favour of governability, not a computational artefact.
An eligibility threshold (5 % in Germany, 3 % for French European elections) removes very small lists before allocation, to avoid fragmentation.
A worked example
One hundred votes, five seats, three lists, D'Hondt method.
| List | Votes | ÷1 | ÷2 | ÷3 |
|---|---|---|---|---|
| A | 45 | 45 | 22.5 | 15 |
| B | 35 | 35 | 17.5 | 11.7 |
| C | 20 | 20 | 10 | 6.7 |
- The five largest quotients across all lists: 45 (A), 35 (B), 22.5 (A), 20 (C), 17.5 (B).
- Final allocation: A 2 seats, B 2 seats, C 1 seat.
- A gets 40 % of the seats with 45 % of the votes; C gets 20 % of the seats with 20 % of the votes.
With so few seats, proportionality is necessarily coarse — the number of seats, far more than the formula, determines how fine the representation can be.
Where it comes from
The Belgian jurist Victor d'Hondt published his method in 1878; in 1899 Belgium became the first country to apply it to national elections. The formula was in fact already known: Thomas Jefferson had proposed it in 1792 to apportion House seats among the American states.
Rival variants have existed just as long: Sainte-Laguë (1910), equivalent to the Webster method of 1832, treats smaller parties more favourably and remains the reference in Scandinavia and New Zealand.
The largest-remainder method, known as Hamilton's, was abandoned in the United States after the Alabama paradox: in 1880 it was found that raising the total number of seats from 299 to 300 COST Alabama a seat. The United States has used the Huntington-Hill method since 1941.
Where it is used
- Parliamentary elections in most European democracies.
- European elections, and French regional elections for the proportional share.
- Composing a board or an association committee.
- Sharing budgets or slots between groups in proportion to support.
Limits and pitfalls
- Faithfully reflects opinions
- Gives minorities a place
- Few wasted votes
- No clear single winner
- Can force coalitions
- The threshold excludes the smallest
Frequently asked questions
D'Hondt or Sainte-Laguë?
D'Hondt (dividing by 1, 2, 3…) slightly favours large lists and makes majorities easier. Sainte-Laguë (by 1, 3, 5…) is fairer to small ones. The choice is political and must be made before the vote, never after.
Why don't my seat percentages match the votes?
Because a seat is indivisible. With five seats the finest possible granularity is 20 %: no formula can do better. The gap narrows as the number of seats grows.
Can it be used with a handful of people?
Yes, to share resources — slots, a budget, places. To choose between options, use approval or Condorcet instead.