The Huntington–Hill method of apportionment assigns seats by finding a modified divisor D such that each constituency's priority quotient (population divided by D ), using the geometric mean

Geometric mean

The geometric mean, in mathematics, is a type of mean or average, which indicates the central tendency or typical value of a set of numbers. It is similar to the arithmetic mean, except that the numbers are multiplied and then the nth root of the resulting product is taken.For instance, the...

 of the lower and upper quota for the divisor, yields the correct number of seats that minimizes the percentage differences in the size of the congressional districts. When envisioned as a proportional

Proportional representation

Proportional representation is a concept in voting systems used to elect an assembly or council. PR means that the number of seats won by a party or group of candidates is proportionate to the number of votes received. For example, under a PR voting system if 30% of voters support a particular...

 voting system

Voting system

A voting system or electoral system is a method by which voters make a choice between options, often in an election or on a policy referendum....

, this is effectively a highest averages method

Highest averages method

The highest averages method is the name for a variety of ways to allocate seats proportionally for representative assemblies with party list voting systems....

 in which the divisors are given by , n being the number of seats a state is currently allocated in the apportionment process (the lower quota) and n+1 is the number of seats the state would have if it is assigned to this state (the upper quota).

The United States House of Representatives

United States House of Representatives

The United States House of Representatives is one of the two Houses of the United States Congress, the bicameral legislature which also includes the Senate.The composition and powers of the House are established in Article One of the Constitution...

 uses this method of apportionment to assign the number of representative seats to each state.

The method is credited to Edward Vermilye Huntington

Edward Vermilye Huntington

Edward Vermilye Huntington was an American mathematician....

 and Joseph Adna Hill

Joseph Adna Hill

Joseph Adna Hill was an American statistician, born at Stewartstown, New Hampshire; he graduated from Harvard University in 1885 and from the University of Halle in 1892...

.

Examples

The U.S. House of Representatives guarantees one seat for each state. So, each state starts off with a divisor D of 1.41 (the square root of the product of one, the number seats currently assigned, and two, the number of seats that would next be assigned). Each state's census population is divided by its D, to produce a priority value for each state. Since all of the D's are equal for this first seat, the state with the largest population would win (California).

Now, California's D would be changed to 2.45 (the square root of two times three), and we would repeat this process. Unless California has about twice the population of any other state, the next largest state would win this second seat. In this case Texas would win the next seat because its population (24 million) divided by its current D (still 1.41) is greater than California's similarly calculated priority value (37 million/2.45) for priority values of 17 million and 15 million, respectively).

This process is repeated until all empty house seats have been exhausted. If the number of U.S. House of Representatives seats were equal in size to the population of the United States, this method would guarantee that the appointments would equal the populations of each state.

Although the U.S. House of Representatives currently uses the Equal Proportionment Method, Congress has not always used it. In fact, George Washington used the presidential veto power for the very first time in order to block apportionment legislation less favorable to his home state of Virginia

Virginia

The Commonwealth of Virginia , is a U.S. state on the Atlantic Coast of the Southern United States. Virginia is nicknamed the "Old Dominion" and sometimes the "Mother of Presidents" after the eight U.S. presidents born there...

. Had Congress used the Equal Proportionment Method (with a divisor of 34,800) to apportion House seats according to state population following the 1790 census

United States Census

The United States Census is a decennial census mandated by the United States Constitution. The population is enumerated every 10 years and the results are used to allocate Congressional seats , electoral votes, and government program funding. The United States Census Bureau The United States Census...

, the House of Representatives would have been apportioned as follows (for a historically accurate House size of 105 seats):

State	Population	Quotas	Lower	Upper	G. Mean	Rnd. Dir.	Seats
Connecticut	236,841	6.81	6	7	6.48	up	7
Delaware	55,540	1.60	1	2	1.41	up	2
Georgia	70,835	2.04	2	3	2.45	down	2
Kentucky	68,705	1.97	1	2	1.41	up	2
Maryland	278,514	8.00	8	9	8.49	down	8
Massachusetts	475,327	13.66	13	14	13.49	up	14
New Hampshire	141,822	4.08	4	5	4.47	down	4
New Jersey	179,570	5.16	5	6	5.48	down	5
New York	331,589	9.53	9	10	9.49	up	10
North Carolina	353,523	10.16	10	11	10.49	down	10
Pennsylvania	432,879	12.44	12	13	12.49	down	12
Rhode Island	68,446	1.97	1	2	1.41	up	2
South Carolina	206,236	5.93	5	6	5.48	up	6
Vermont	85,533	2.46	2	3	2.45	up	3
Virginia	630,560	18.12	18	19	18.49	down	18