TheHuntington–Hill method, sometimes calledmethod of equal proportions, is ahighest averages method for assigning seats in alegislature topolitical parties orstates.^[1] Since 1941, this method has been used to apportion the 435 seats in theUnited StatesHouse of Representatives following the completion of each decennialcensus.^[2][3]

The method minimizes therelative difference in the number of constituents represented by each legislator. In other words, the method selects the allocation such that no transfer of a seat from one state to another can reduce the percent error in representation for both states.^[1]

In this method, as a first step, each of the 50 states is given its one guaranteed seat in the House of Representatives, leaving 385 seats to be assigned. The remaining seats are allocated one at a time, to the state with the highestaverage district population, to bring its district population down. However, it is not clear if we should calculate the averagebefore orafter allocating an additional seat, and the two procedures give different results. Huntington-Hill uses acontinuity correction as a compromise, given by taking thegeometric mean of both divisors, i.e.:^[4]

${\displaystyle A_n=\frac{P}{\sqrt{n(n+1)}}}$

whereP is the population of the state, andn is the number of seats it currently holds before the possible allocation of the next seat.

Consider the reapportionment following the 2010 U.S. census: after every state is given one seat:

1. The largest value ofA₁ corresponds to the largest state, California, which is allocated seat 51.
2. The 52nd seat goes to Texas, the 2nd largest state, because itsA₁ priority value is larger than theA_n of any other state.
3. The 53rd seat goes back to California because itsA₂ priority value is larger than theA_n of any other state.
4. The 54th seat goes to New York because itsA₁ priority value is larger than theA_n of any other state at this point.

This process continues until all remaining seats are assigned. Each time a state is assigned a seat,n is incremented by 1, causing its priority value to be reduced.

Unlike theD'Hondt andSainte-Laguë systems, which allow the allocation of seats by calculating successive quotients right away, the Huntington–Hill system requires each party or state have at least one seat to avoid adivision by zero error.^[5] In the U.S. House of Representatives, this is ensured by guaranteeing each state at least one seat;^[5] inparty-list representation, small parties would likely be eliminated using someelectoral threshold, or the first divisor can be modified.

Consider an example to distribute 8 seats between three parties A, B, C having respectively 100,000, 80,000 and 30,000 votes.

Each eligible party is assigned one seat. With all the initial seats assigned, the remaining five seats are distributed by a priority number calculated as follows. Each eligible party's (Parties A, B, and C) total votes is divided by√2  • 1 ≈ 1.41, then by approximately 2.45, 3.46, 4.47, 5.48, 6.48, 7.48, and 8.49. The 5 highest entries, marked with asterisks, range from70,711 down to28,868. For each, the corresponding party gets another seat.

• Edward Vermilye Huntington
• Highest averages method
• Joseph Adna Hill

• Apportionment methods

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