How does the largest-remainder rule distribute seats among political parties?

The largest-remainder method (also known as the greatest-remainder formula) distributes legislative seats among political parties through a two-step process based on an electoral quota.1

1. Initial Allocation: First, a quota is established, typically by dividing the total number of votes in a district by the number of available seats. Each party is awarded one seat for every full quota of votes it receives.1
2. Remainder Distribution: If any seats remain unallocated after the initial distribution, they are awarded sequentially to the parties with the largest "remainders"—the leftover votes each party has after subtracting the votes used to secure their initial seats.1

This process continues until all allocated seats in the district have been filled. Compared to largest-average formulas, the largest-remainder method generally provides better representation for minor political parties.1