Seat Allocation Formula

A seat allocation formula is the algorithm an electoral system uses to translate raw inputs—party vote shares, district populations, or both—into whole-number seat assignments. Because seats cannot be fractional, every formula must resolve rounding in a defined way, and the choice of method materially shapes which parties benefit.

Formulas fall into two broad families:

• Highest-averages (divisor) methods. Vote totals are repeatedly divided by a sequence of divisors, and seats go to the largest resulting quotients. The D'Hondt method (divisors 1, 2, 3, …) tends to favour larger parties and is used for European Parliament elections in several EU member states, as well as in Spain's Congress of Deputies. The Sainte-Laguë method (divisors 1, 3, 5, …) is more proportional for mid-sized parties and is used in Germany's Bundestag elections (since 2009), New Zealand, Norway, and Sweden.
• Largest-remainder (quota) methods. A quota—such as the Hare quota (votes ÷ seats) or Droop quota—is calculated, each party receives a seat for every full quota, and leftover seats go to those with the largest fractional remainders. Hare-largest-remainder is associated with the Alabama paradox identified in U.S. apportionment debates in the 1880s, where adding a seat can cause a unit to lose one.

Seat allocation formulas also govern legislative apportionment among territories. The U.S. House of Representatives has used the method of equal proportions (Huntington–Hill) since the 1941 apportionment act to distribute 435 seats among the states based on census data.

Formulas often interact with electoral thresholds (e.g., Germany's 5% hurdle) and district magnitude: small districts mechanically reduce proportionality regardless of the formula chosen. Delegates analysing election outcomes should therefore identify the formula, the threshold, and the district structure together rather than in isolation.