Sainte-Laguë method
The Sainte-Laguë method of the highest average (also known as Webster's method or divisor method with standard rounding) is one way of allocating seats proportionally for representative assemblies with party list voting systems. It is named after French mathematician André Sainte-Laguë. The Sainte-Laguë method is closely related to d'Hondt method, although without the latter's favoritism for larger parties.
The Sainte-Laguë method is used in New Zealand, Norway, Sweden, Denmark, Bosnia and Herzegovina, Latvia, Kosovo, Hamburg and Bremen.
See the article on highest averages method for a comparison with the d'Hondt method.
Example
The Sainte-Laguë method is a divisor method, like the d'Hondt method, but with a different divisor. After all the votes have been tallied, successive quotients are calculated for each list. The formula for the quotient is V/(2s+1), where V is the total number of votes that list received, and s is the number of seats that party has been allocated so far, initially 0 for all parties. (The d'Hondt method uses V/(s+1) as the formula). Whichever list has the highest quotient gets the next seat allocated, and their quotient is recalculated given their new seat total. The process is repeated until all seats have been allocated.
| Party A | Party B | Party C | Party D | Party E | |
| Votes | 340,000 | 280,000 | 160,000 | 60,000 | 15,000 |
| Seat 1 | 340,000 | 280,000 | 160,000 | 60,000 | 15,000 |
| Seat 2 | 113,333 | 280,000 | 160,000 | 60,000 | 15,000 |
| Seat 3 | 113,333 | 93,333 | 160,000 | 60,000 | 15,000 |
| Seat 4 | 113,333 | 93,333 | 53,333 | 60,000 | 15,000 |
| Seat 5 | 68,000 | 93,333 | 53,333 | 60,000 | 15,000 |
| Seat 6 | 68,000 | 56,000 | 53,333 | 60,000 | 15,000 |
| Seat 7 | 48,571 | 56,000 | 53,333 | 60,000 | 15,000 |
| Total Seats | 3 | 2 | 1 | 1 | 0 |
Sainte-Laguë and Webster
The Sainte-Laguë method is equivalent to the Webster method in that they always give the same results, but the method of calculating the apportionment is different. The latter uses a quota, as in the Largest remainder method but the quotas are rounded off instead of down to the nearest integer, and the quota is adjusted as necessary to make the number of seats work out if there are too many seats.
Modified Sainte-Laguë method
Some countries, e.g. Sweden and Denmark, replaces the first divisor with 1.4. This gives slightly larger preference to the larger parties.