Huntington-Hill method

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The Huntington-Hill method of apportionment assigns seats by finding a modified divisor D such that each constinuency's quotient (population divided by D), when rounded by geometric mean of the lower and upper quota, yields the correct number of seats. When envisioned as a proportional voting system, this is effectively a highest averages method in which the divisors are given by $\sqrt{n(n+1)}$ .

The United States House of Representatives uses this method of apportionment to assign representative seats to each state.

[edit] Example

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. Had Congress used the Equal Proportionment Method to apportion House seats according to state population following the 1790 census, the House of Representatives would have been apportioned as follows (for an 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