divisormethodes

Divisor methods, also known as divisormethodes in some contexts, are a family of apportionment procedures used to allocate a fixed number of seats in a legislature among parties or groups in proportion to their votes, or among regions in proportion to population. Each method starts with a sequence of divisors d1 < d2 < d3 ... and, for each party i with vote total Vi, generates a sequence of quotients Qi(k) = Vi / di for k = 1, 2, ..., where k indicates the number of seats already allocated to that party plus one. The next seat is awarded to the party with the largest current quotient. This process repeats until all seats are assigned.

Common variants include Jefferson (D'Hondt), Webster (Sainte-Laguë), Adams, and Huntington-Hill. In Jefferson, divisors are the natural numbers 1, 2, 3, ...; Webster uses divisors 0.5, 1.5, 2.5, ...; Adams uses divisors 0, 1, 2, ...; Huntington-Hill uses divisors sqrt(k(k+1)) for k seats already allocated. These different sequences produce different allocations and different biases toward larger or smaller parties.

Divisor methods are widely used for national and regional elections in various countries and are often contrasted with quota methods that allocate seats based on exact quotas first. They are valued for computational simplicity and for producing proportional results, but criticized for potential strategic manipulation, sensitivity to rounding rules, and the possibility of paradoxes where changes in total seats or in vote shares yield counterintuitive results.