What apportionment method does the U.S. House of Representatives use?

The U.S. House of Representatives uses the Huntington-Hill method (also called the Method of Equal Proportions) since 1941. It assigns each state a priority score for each additional seat: Priority = Population ÷ √(n(n+1)), where n is the current number of seats. Seats are assigned in order of priority until all 435 are distributed. Each state is guaranteed at least 1 seat regardless of population. The method slightly favors smaller states compared to Webster's method.

What is the Alabama Paradox in apportionment?

The Alabama Paradox (discovered in 1880) is a counterintuitive problem with the Hamilton method: when the total number of seats increases, a state can actually lose a seat. Example: with 299 seats, Alabama gets 8 seats; with 300 seats total, Alabama gets only 7. This paradox led to the abandonment of the Hamilton method for U.S. Congressional apportionment and adoption of divisor methods (Jefferson, Webster, Huntington-Hill) that are paradox-free — increasing total seats never causes a state to lose representation under divisor methods.

How is apportionment used in business cost allocation?

In cost accounting, apportionment distributes shared costs (overhead, facilities, IT, HR) among cost centers using a fair allocation base. Common bases: headcount (for HR costs), revenue (for executive salaries), square footage (for facilities), compute hours (for IT). The Hamilton method applies directly: Total shared cost × (Department's base ÷ Total base) = Department's allocated cost. If the total must equal exactly the shared cost, fractional cents are allocated by largest-remainder to ensure the sum ties out.

What is the difference between a quota method and a divisor method in apportionment?

Quota methods (Hamilton) calculate exact quotas first, then round. They satisfy the quota property (each group gets either the floor or ceiling of its exact quota) but may exhibit paradoxes. Divisor methods (Jefferson, Webster, Huntington-Hill) adjust a common divisor until the rounded quotas sum to the target total. They're paradox-free but may violate the quota property (a group might get a seat count outside its exact quota floor/ceiling). Webster's method violates the quota property least often and is considered the most proportionally fair divisor method.

Apportionment Calculator: Hamilton, Jefferson, and Webster Methods Explained

Calculate proportional seat or unit allocation from population or weight data. Understand the Hamilton, Jefferson, and Webster apportionment methods and where each is used.

Related Calculators

Apportionment Calculator
Apportion a total amount among four recipients in proportion to their weights and review each recipient's percentage share.

What Is Apportionment?

Apportionment is the process of distributing a fixed number of discrete units (seats, delegates, representatives) proportionally among groups based on population or other weights. The challenge: exact proportional allocation is rarely a whole number, so rounding methods must be applied.

Exact quota = (Group's population ÷ Total population) × Total seats

The Hamilton Method (Largest Remainder)

Calculate exact quota for each group
Give each group the floor (round down) of its exact quota
Remaining seats are given to groups with the largest remainders

This is the most intuitive method and is used in many proportional voting systems.

Worked Example — 10 Seats Among 4 States

State	Population	Exact Quota	Floor	Remainder	Final (Hamilton)
Alpha	35,000	3.50	3	0.50	4
Beta	25,000	2.50	2	0.50	3
Gamma	22,000	2.20	2	0.20	2
Delta	18,000	1.80	1	0.80	1
Total	100,000	10.00	8		10

Remaining 2 seats go to Alpha (0.50) and Beta (0.50) — tied remainders; Delta's 0.80 > Beta's 0.50 → wait, Delta 0.80 is actually highest! Corrected:

Remaining 2 seats → Delta (0.80) and Alpha (0.50): | State | Final | |-------|-------| | Alpha | 4 | Beta | 2 | Gamma | 2 | Delta | 2 |

Comparison of Methods

Method	Bias	Where Used
Hamilton (Largest Remainder)	Can produce Alabama Paradox	Puerto Rico legislature
Jefferson (D'Hondt)	Favors larger parties/states	Many European elections
Webster (Sainte-Laguë)	Most proportional overall	Nordic countries, Germany
Adams	Favors smaller parties/states	Theoretical; rarely used
Huntington-Hill	Currently used in U.S. House	U.S. Congressional apportionment

The Huntington-Hill method (used for the U.S. House of Representatives since 1941) uses the geometric mean of consecutive integers as rounding thresholds, slightly favoring smaller states compared to Webster.

Business Applications

Apportionment applies beyond legislatures: - Allocating overhead costs among departments by headcount or revenue - Distributing insurance premiums among business units - Dividing partnership distributions by ownership percentage - Allocating server capacity among project teams by usage

Frequently Asked Questions

What apportionment method does the U.S. House of Representatives use?: The U.S. House of Representatives uses the Huntington-Hill method (also called the Method of Equal Proportions) since 1941. It assigns each state a priority score for each additional seat: Priority = Population ÷ √(n(n+1)), where n is the current number of seats. Seats are assigned in order of priority until all 435 are distributed. Each state is guaranteed at least 1 seat regardless of population. The method slightly favors smaller states compared to Webster's method.
What is the Alabama Paradox in apportionment?: The Alabama Paradox (discovered in 1880) is a counterintuitive problem with the Hamilton method: when the total number of seats increases, a state can actually lose a seat. Example: with 299 seats, Alabama gets 8 seats; with 300 seats total, Alabama gets only 7. This paradox led to the abandonment of the Hamilton method for U.S. Congressional apportionment and adoption of divisor methods (Jefferson, Webster, Huntington-Hill) that are paradox-free — increasing total seats never causes a state to lose representation under divisor methods.
How is apportionment used in business cost allocation?: In cost accounting, apportionment distributes shared costs (overhead, facilities, IT, HR) among cost centers using a fair allocation base. Common bases: headcount (for HR costs), revenue (for executive salaries), square footage (for facilities), compute hours (for IT). The Hamilton method applies directly: Total shared cost × (Department's base ÷ Total base) = Department's allocated cost. If the total must equal exactly the shared cost, fractional cents are allocated by largest-remainder to ensure the sum ties out.
What is the difference between a quota method and a divisor method in apportionment?: Quota methods (Hamilton) calculate exact quotas first, then round. They satisfy the quota property (each group gets either the floor or ceiling of its exact quota) but may exhibit paradoxes. Divisor methods (Jefferson, Webster, Huntington-Hill) adjust a common divisor until the rounded quotas sum to the target total. They're paradox-free but may violate the quota property (a group might get a seat count outside its exact quota floor/ceiling). Webster's method violates the quota property least often and is considered the most proportionally fair divisor method.

Last updated 8/20/2026