greatest remainder formula

The greatest-remainder formula is a method used in party-list proportional representation electoral systems to allocate seats in a legislature. This system aims to ensure that the distribution of seats in a legislative body closely matches the distribution of votes received by political parties.

In the greatest-remainder method, a specific quota of votes is first established. Each party is awarded a seat for every full quota of votes it achieves. Any remaining seats are then distributed to the parties with the largest number of leftover votes (remainders) after the full quotas have been allocated. This method generally benefits smaller parties more than other proportional representation formulas, such as the largest-average formula. The greatest-remainder formula is used in countries like Israel and Luxembourg.12