D'Hondt Method Calculator | Proportional Representation Seat Allocation (D'Hondt, Sainte-Laguë, Modified Sainte-Laguë, Adams, Hare and Droop), Quotient Table, Votes Needed for One More Seat, Last Seat and Runner-Up, Method Comparison, and Best-Loser Ratio for Japan's List Revival
The D'Hondt Method Calculator answers questions such as “how many seats do these votes give?”, “which party won the last seat?”, “how many more votes would have won another seat?” and “who is revived on the list by best-loser ratio?”. Enter the votes for each party (list) and the number of seats: it builds the table of quotients (votes divided by 1, 2, 3 and so on), hands out seats to the largest quotients and colours which seat went to which party. You can switch to Sainte-Laguë (1, 3, 5…), modified Sainte-Laguë (1.4, 3, 5…), the Adams method (0, 1, 2…) used to apportion Japan's single-member districts among prefectures, and the Hare and Droop largest remainder methods, and compare all six methods side by side. It shows the last seat and the runner-up, flags ties that would be settled by lot, works out how many more votes each party needed to be sure of one more seat, measures the gap between vote share and seat share (Gallagher index) and supports an electoral threshold. Fractional votes (apportioned ballots) are accepted and an election results table can be pasted in at once. For dual candidacy in Japan's House of Representatives it ranks candidates sharing a list position by best-loser ratio (own votes ÷ district winner's votes), drops district winners and candidates below one tenth of the valid votes, and shows who is elected from the list and the cut-off ratio.
Enter parties and votes
Enter the votes for each party (group or list) and the number of seats to fill. Fractional votes from apportioned ballots (for example 12345.678) are accepted.
Paste an election results table
Write “party name, votes” on each line (separated by a tab, comma or space). You can paste two columns copied from a spreadsheet or an election results page as they are.
Allocation method
Divide the votes by 1, 2, 3, 4… and give seats to the largest quotients. Used for the proportional seats of both houses of Japan's Diet, sharing out committee places in local assemblies, and in many European countries. Slightly favours large parties.
Seat allocation
Result of allocating 10 seats with D'Hondt.
Total votes
100,000
Last seat (seat 10)
Party B
Quotient 8,333.33
Runner-up (next seat)
Party A
Quotient 6,800
Gallagher index
7.94
Gap between vote and seat shares (smaller is more proportional)
| Party | Votes | Vote share | Seats | Seat share | Votes for +1 seat |
|---|---|---|---|---|---|
| Party A | 34,000 | 34% | 4 | 40% | 7,667 votes |
| Party B | 25,000 | 25% | 3 | 30% | 9,001 votes |
| Party C | 18,000 | 18% | 2 | 20% | 7,001 votes |
| Party D | 13,000 | 13% | 1 | 10% | 3,667 votes |
| Party E | 6,000 | 6% | 0 | 0% | 2,334 votes |
| Party F | 4,000 | 4% | 0 | 0% | 4,334 votes |
“Votes for +1 seat” is how many more votes the party would need, with every other party's votes unchanged, to be sure of one more seat without a draw.
The upper pale bar is vote share and the lower solid bar is seat share.
Quotient table (votes ÷ divisor)
Shaded cells are winning quotients and the small number is the seat order. Quotients down to the 10th largest win a seat.
| Party | ÷1 | ÷2 | ÷3 | ÷4 | ÷5 | ÷6 |
|---|---|---|---|---|---|---|
| Party A | 34,0001 | 17,0004 | 11,333.337 | 8,5009 | 6,800 | 5,666.67 |
| Party B | 25,0002 | 12,5006 | 8,333.3310 | 6,250 | 5,000 | 4,166.67 |
| Party C | 18,0003 | 9,0008 | 6,000 | 4,500 | 3,600 | 3,000 |
| Party D | 13,0005 | 6,500 | 4,333.33 | 3,250 | 2,600 | 2,166.67 |
| Party E | 6,000 | 3,000 | 2,000 | 1,500 | 1,200 | 1,000 |
| Party F | 4,000 | 2,000 | 1,333.33 | 1,000 | 800 | 666.67 |
The results are estimates based on the numbers you enter. Check the official results from the election administration commission. In Japan's House of Councillors the proportional seats use an open list: candidates are elected in order of personal votes, after any priority-slot candidates.
ABOUT
About D'Hondt Method Calculator | Proportional Representation Seat Allocation (D'Hondt, Sainte-Laguë, Modified Sainte-Laguë, Adams, Hare and Droop), Quotient Table, Votes Needed for One More Seat, Last Seat and Runner-Up, Method Comparison, and Best-Loser Ratio for Japan's List Revival
The D'Hondt Method Calculator is a free tool that allocates proportional representation seats with the D'Hondt method from each party's votes and the number of seats, and shows the quotient table and the order in which seats are won. It also compares Sainte-Laguë, Adams and the largest remainder methods (Hare and Droop), works out how many more votes each party needed for one more seat, and ranks list revival by best-loser ratio in Japan's House of Representatives. Use it to check election-night results, study how the D'Hondt method works, or share out committee places and officer posts among groups.
How to use D'Hondt Method Calculator | Proportional Representation Seat Allocation (D'Hondt, Sainte-Laguë, Modified Sainte-Laguë, Adams, Hare and Droop), Quotient Table, Votes Needed for One More Seat, Last Seat and Runner-Up, Method Comparison, and Best-Loser Ratio for Japan's List Revival
- 1On the Seat allocation tab, enter the votes for each party (list) and the number of seats to fill. An election results table can be pasted in at once
- 2Choose a method (D'Hondt, Sainte-Laguë and so on) and check each party's seats, vote share and seat share
- 3Use the quotient table to see which party's quotient won each seat, and which party took the last seat and which came next
- 4Check “Votes for +1 seat” to see how many more votes each party needed to be sure of one more seat
- 5Line up all six methods on the Compare methods tab, and work out the list order on the Best-loser ratio tab
Great for
- When you want to check each party's seats from the proportional vote on election night
- When studying civics or politics and you want to see the D'Hondt calculation laid out as a table
- When a council, union or parents' association shares out committee places or officer posts by group size
- When you want to know which party took the last seat and how many votes the runner-up was short
- When you want to compare how small parties fare under D'Hondt and Sainte-Laguë
- When you want to check the order of list revival from dual candidates' best-loser ratios
Good to know
- The D'Hondt method divides each party's votes by 1, 2, 3, 4 and so on and gives the seats, up to the total, to the largest quotients. It is used for the proportional seats of both houses of Japan's Diet and in many European countries. For example, six parties with 34,000, 25,000, 18,000, 13,000, 6,000 and 4,000 votes sharing 10 seats get 4, 3, 2, 1, 0 and 0 seats; the last seat goes to the party with 25,000 ÷ 3 ≈ 8,333.3 and the runner-up is the party with 34,000 ÷ 5 = 6,800.
- Sainte-Laguë divides by 1, 3, 5, 7 and so on, so seats reach small parties more easily than under D'Hondt. In the example above it gives 3, 3, 2, 1, 1 and 0 seats, and the gap between vote share and seat share (Gallagher index) falls from 7.94 under D'Hondt to 6.56. The Adams method (dividing by 0, 1, 2…) first gives one seat to every party with votes, giving 3, 2, 2, 1, 1 and 1 seats.
- The Adams method is used to apportion the single-member districts of Japan's House of Representatives among the prefectures: each prefecture gets its population divided by a common divisor, rounded up. This gives the same result as a divisor method with divisors 0, 1, 2, 3 and so on.
- When the last seat is tied on the same quotient, a real election settles it by drawing lots. This tool flags the tie and lists the party with more votes first. “Votes for +1 seat” is how many more votes a party would have needed, with every other party's votes unchanged, to win one more seat without relying on a draw.
- In the proportional part of Japan's House of Representatives, candidates who also stand in a single-member district can share the same list position, and within that position they are elected in order of best-loser ratio (own votes ÷ the district winner's votes × 100). Candidates who win their district leave the list, and those who received less than one tenth of the valid votes in their district cannot be elected from the list. The House of Councillors uses an open list where candidates are elected in order of personal votes (after any priority-slot candidates), so the best-loser ratio is not used there.
Questions this tool answers
Use D'Hondt Method Calculator | Proportional Representation Seat Allocation (D'Hondt, Sainte-Laguë, Modified Sainte-Laguë, Adams, Hare and Droop), Quotient Table, Votes Needed for One More Seat, Last Seat and Runner-Up, Method Comparison, and Best-Loser Ratio for Japan's List Revival for searches like these:
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- adams method apportionment calculator
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FAQ
- How do you calculate seats with the D'Hondt method?
- Divide each party's votes by 1, 2, 3, 4 and so on, and give the seats to the largest quotients until all are filled. With parties on 34,000, 25,000, 18,000 and 13,000 votes (and two smaller ones) sharing 10 seats, the quotients run 34,000, 25,000, 18,000, 17,000, 13,000, 12,500, 11,333 and so on, and everything down to the 10th, 8,333.3 (25,000 ÷ 3), wins a seat. The result is 4, 3, 2 and 1 seats, and the parties on 6,000 and 4,000 votes get none.
- Does the D'Hondt method favour large parties?
- Slightly, compared with other methods. In the example above D'Hondt gives 4, 3, 2, 1, 0 and 0 seats, while Sainte-Laguë, dividing by 1, 3, 5 and so on, gives 3, 3, 2, 1, 1 and 0, so the party on 6,000 votes also wins a seat. The Gallagher index, which measures the gap between vote share and seat share, is 7.94 for D'Hondt and 6.56 for Sainte-Laguë.
- How do you work out how many more votes would have won another seat?
- Find the number of votes at which the party's next quotient (votes ÷ next divisor) beats the lowest winning quotient of the other parties. In the example above the party on 6,000 votes, with no seats, would have needed 6,000 + 2,334 = 8,334 votes for its quotient to pass 8,333.3 and win a seat. The tool keeps every other party's votes fixed and works out the shortfall for each party.
- What is the best-loser ratio (sekihairitsu) and how is it calculated?
- It is the votes of a candidate who lost a single-member district divided by the votes of the district winner. If the winner had 100,000 votes and the candidate 80,000, the ratio is 80%. When dual candidates share a list position in the proportional part of Japan's House of Representatives, they are elected in order of this ratio.
- When can a candidate not be revived on the list?
- A candidate who wins the single-member district leaves the list. A candidate whose district vote was below one tenth of the valid votes cannot be elected from the list, whatever their position or ratio. For example, in a district with 200,000 valid votes, a candidate with 15,000 votes falls short of 20,000 and cannot be revived.
- What is the difference between the Adams and D'Hondt methods?
- Both divide votes (or population) by a series of divisors, but D'Hondt uses 1, 2, 3 and so on while Adams uses 0, 1, 2 and so on. Under Adams the quotient of a party with no seats is infinite, so every party first gets one seat, and after that seats go to the largest quotients as in D'Hondt. It favours small parties (and less populous prefectures) and is used to apportion Japan's House of Representatives districts among the prefectures.
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