"Proportional representation" sounds like it describes one thing. It does not. Once a country decides that seats should reflect votes, it still has to pick a rule for converting one into the other — and the rules disagree. Not by much, usually. But parliaments are decided at the margin, and the margin is exactly where these formulas differ.
The two that matter most in practice are d'Hondt and Sainte-Laguë. Both are divisor methods, both are genuinely proportional, and both are in wide use across Europe. Here is what separates them, worked through on a real election rather than a toy example.
How a divisor method works
Forget percentages for a moment. A divisor method allocates seats one at a time. Every party's vote total is repeatedly divided by a sequence of numbers, producing a table of quotients; the highest remaining quotient wins the next seat, and that continues until the seats run out.
The only difference between the two methods is the sequence of divisors:
| Method | Divisors | Effect |
|---|---|---|
| d'Hondt | 1, 2, 3, 4, 5 … | Mildly favours larger parties |
| Sainte-Laguë | 1, 3, 5, 7, 9 … | Closer to pure proportionality; kinder to mid-sized parties |
The intuition behind the difference: under d'Hondt, a party that already holds seats is divided by a number that grows slowly, so its next quotient stays high and it keeps competing for further seats. Under Sainte-Laguë the divisors grow twice as fast, so a large party's quotients fall away sooner and a smaller party overtakes it earlier. Sainte-Laguë is the more faithful mirror of the vote; d'Hondt builds in a small bonus for size, which is often defended as making governing majorities easier to assemble.
The same votes, two parliaments: Kosovo 2026
Kosovo's parliamentary election of 2026 makes an ideal test case. The Assembly has 120 seats, of which 100 are allocated proportionally among lists clearing a 5% threshold and 20 are reserved for national minorities. Four lists cleared the threshold, on 812,324 valid votes in total.
Here is what each formula produces from the actual vote counts, for those 100 seats:
| Party | Votes | Share of the four | d'Hondt | Sainte-Laguë |
|---|---|---|---|---|
| Vetëvendosje (LVV) | 382,865 | 52.37% | 53 | 52 |
| PDK | 157,893 | 21.60% | 22 | 22 |
| LDK | 135,559 | 18.54% | 18 | 19 |
| AAK | 54,731 | 7.49% | 7 | 7 |
One seat moves — from the largest party to the third-largest. That is a small difference, and it is also completely typical: across most real elections the two methods differ by nought to two seats out of a hundred. The bonus d'Hondt gives the leader is real but modest.
Kosovo uses d'Hondt, and the official allocation is 53 / 22 / 18 / 7 — exactly the left-hand column. I mention that because I once had it wrong on this site: an early seat projection for Kosovo used Sainte-Laguë, produced 52 / 22 / 19 / 7, and was quietly one seat off in two places. The votes were right and the arithmetic was right; the statute was not. When a projection disagrees with an official allocation, the formula is the first thing to check.
The last seat, in numbers
Divisor methods feel abstract until you look at the boundary. These are the real quotients around the hundredth seat in Kosovo, under d'Hondt:
| Order | Party | Quotient | Value |
|---|---|---|---|
| 99th seat | LVV | 382,865 ÷ 53 | 7,224 |
| 100th seat — the last one | PDK | 157,893 ÷ 22 | 7,177 |
| 101st — first to miss out | LDK | 135,559 ÷ 19 | 7,135 |
LDK's nineteenth seat missed by 42 quotient points — the equivalent of roughly 800 votes, in an election of over 800,000. Swap in Sainte-Laguë's divisors and that same LDK seat becomes the hundredth and last, at a quotient of 3,664, while the seat that drops out is LVV's fifty-third. Nothing about the electorate changed. The sequence of divisors did.
This is also the honest answer to "which method is fairer". Sainte-Laguë tracks vote share more closely and is the better choice if proportionality is the goal on its own terms. D'Hondt's tilt toward larger parties is a deliberate design decision, not an error — a country that has struggled to form governments may reasonably prefer it. What is not defensible is choosing a method for a given election after seeing the votes, which is why the formula is fixed in electoral law rather than decided by a commission on the night.
Where each is used
Both are common enough that you cannot guess from the region:
- d'Hondt: Kosovo, Poland, Spain, Portugal, the Netherlands, Belgium, Israel, Turkey, Argentina, Brazil, Finland, Croatia, and most of Latin America.
- Sainte-Laguë (usually the modified variant, whose first divisor is 1.4): Sweden, Norway, Denmark, Germany, New Zealand, Latvia, Iraq, Nepal.
The modified variant deserves a note, because it is what Scandinavian countries actually use. Replacing the first divisor 1 with 1.4 makes the first seat harder to win, which suppresses very small parties without needing an explicit legal threshold. It is a threshold implemented as arithmetic instead of as law.
Why the formula is not the biggest lever
It is tempting to conclude that the choice of divisor is what shapes a parliament. Usually it is not — two other design decisions matter more:
- The legal threshold. A 5% barrier can discard several percent of the vote outright before any formula runs. That has a far larger effect than the difference between two divisor sequences.
- District magnitude. How many seats are allocated in each district determines how proportional the outcome can possibly be. Applying any formula in a three-seat district produces a roughly majoritarian result; applying the harshest formula across a 100-seat national district produces a nearly proportional one. Magnitude dominates method.
So when a result looks disproportionate, the divisor is rarely the culprit. Check the threshold and the district sizes first — and then, as I should have done with Kosovo, check what the electoral law actually says.