How to use the proportional seat allocation calculator
- Enter the number of seats to fill.
- Enter one group per line with its name and its votes as a whole number.
- Optionally enter a minimum share of the vote. Groups below it get no seats and their votes are left out.
- Read the seats for each group under three methods, and the quotients that won each seat.
Formula
D'Hondt: divide each group's votes by 1, 2, 3 and so on, and give each seat to the highest result
Sainte-Lague: the same with divisors 1, 3, 5 and so on
Largest remainder: quota = total votes / seats. Each group gets whole quotas, then the largest remainders get the seats left
A tie for the last seat is shown as a warning. The tool gives that seat to the group with more votes, then to the earlier group.
Four groups and 8 seats
With votes of 100, 80, 30 and 20, D'Hondt gives 4, 3, 1 and 0 seats. Sainte-Lague gives 3, 3, 1 and 1 seats, because its odd divisors favor the smaller groups. Largest remainder with the quota of 28.75 votes per seat gives 3, 3, 1 and 1, since the remainders of B and D are the largest. Two groups get different seats depending on the method.
With votes of 60, 30 and 10 and 5 seats, D'Hondt gives 4, 1 and 0 seats, and the last seat is a tie at a quotient of 15 between A and B. The tool shows that tie as a warning. A 5% threshold on 234,000 votes removes a group with 4,000 votes before the count.
Why the method matters
Votes rarely divide into whole seats exactly, so a method has to decide who gets the leftover seats. D'Hondt tends to favor larger groups, Sainte-Lague is more even, and largest remainder depends on the quota that is used. In close counts the choice can change which group gets the last seat, and in some systems that decides who holds a majority.
The second table shows the quotient that won each seat in order. It is the working that checks the result: the highest quotients not yet used take the next seats.
What the tool does not do
Real systems add more rules: districts, compensation seats, modified divisors, party lists and legal thresholds. This page shows the three basic methods side by side for the votes you enter. See the Ranked Choice Voting Calculator for ranked ballots, the Tournament Prize Payout Calculator for another kind of sharing, the Cent-Exact Split Calculator for splitting money, and the Percentage Calculator for shares of the vote.
Assumptions and limits
- Votes are whole numbers and every seat is filled.
- A group needs at least one vote to win a seat.
- The votes shown are examples. Use your own totals.
- The minimum share is measured against all the votes entered.
Frequently asked questions
Which method is the fairest?
It depends on what you value. Sainte-Lague gives the closest match between votes and seats for small groups, and D'Hondt gives a little more to large ones.
Why does the quota show decimals?
It is the total votes divided by the seats, which is rarely a whole number. Largest remainder uses it directly.
How does the minimum share work?
Groups under the share are dropped first, and the seats are shared between the groups that remain using only their votes.
What happens in a tie?
The tool names the groups that tie for the last seat. For the seat itself it picks the group with more votes, then the earlier one in your list.