The Huntington–Hill method, also known as the Method of Equal Proportions, ensures the smallest percentage difference in the sizes of U.S. Congressional districts among the states by first assigning to each state its Constitutionally mandated at least one Representative and then ranking the states according to the geometric mean between the current population of their Congressional districts and what it would be with one more Representative, with the next Representative going to the highest-ranked state, and finally repeating the process until the desired number of Congressional seats has been apportioned among the states.

The following data come from the U.S. Census Bureau and were released at 2:57:19.55 EST on Tuesday ; the state receiving the next Representative is highlighted.

The census figures have been revised since their initial release (and if the actual apportionment were based on the revised figures, TX would lose a Representative to NJ), and this simulation also estimates the apportionment if Puerto Rico and the District of Columbia were states, and the number of Representatives were permanently increased by 2; just disregard the last two rows to get the 435-representative estimate. It can also be set to see how the representatives would be reapportioned based on the estimated populations as of Monday .

Now you can try another divisor method, including the one proposed by U.S. Senator Daniel Webster in 1832 and used for the Censuses of 1840, 1910, and 1930 (the non-divisor Hamilton method, first proposed by Alexander Hamilton and not shown here, being used from 1850 through 1900 before the apportionment paradoxes became seen as more than flukes, and the 1920s reapportionment not done due to Congressional dispute about enlarging the House); the Jefferson method used from 1790 through 1830; the method proposed by John Quincy Adams but never used; and three other interesting methods of apportionment used in other parts of the world for party-list apportionment following elections but never proposed for the U.S. House of Representatives; and one extra.

As mentioned before, the Huntington–Hill divisor for a state with n Representatives apportioned is √((n+1)n), the geometric mean of n and n+1; the Adams method uses just n, the Jefferson method uses just n+1, the Webster method uses their arithmetic mean (n+½), and the Dean method uses their harmonic mean, which equals their product divided by their arithmetic mean: 2/(1/n+1/(n+1))=(n+1)n/(n+½). The Quadratic method uses their quadratic mean, a.k.a. root-mean-square, which turns out to be a hybrid of the Webster and Huntington–Hill methods: √(½(n²+(n+1)²))=√(n²+n+½). Adams and Huntington–Hill require each state to receive one Representative to start, while the others may need special-case logic to ensure compliance with the Constitution, although in practice, no state has ever had a low-enough population to require a special case.

Allocate more seats: | | | Method:
The Selected Method in the 2010 U.S. Census
STATEREPPOPULATIONNPRIORITYSTATEREPPOPULATIONNPRIORITY
CA5337253956126342525KY6433936713068396
TX3625145561117780597OR5383107412708978
NY2719378102113702387OK5375135112652606
FL2718801310113294534CT5357409712527268
IL181283063219072627IA4304635512154098
PA181270237918981938MS4296729712098196
OH161153650418157540AR4291591812061865
MI14988364016988789KS4285311812017459
GA14968765316850205UT4276388511954362
NC13953548316742605NV4270055111909578
NJ12897189416344087NM3205917911456059
VA11800102415657578WV3185299411310265
WA10672454014754968NE3182634111291418
MA9654762914629873ID2156758211108448
IN9648380214584740HI213603011961878
AZ9641270014534464ME213283611939293
TN9634610514487374NH213164701930885
MO8598892714234811RI210525671744277
MD8577355214082518MT19894151699622
WI8568698614021306DE18979341634935
MN8530392513750441SD18141801575712
CO7502919613556179AK17102311502209
AL7477973613379784ND16725911475594
SC7462536413270626VT16257411442466
LA6453337213205578WY15636261398544
PR0372578912634530DC06017231425482
ALL 50 STATES435308344498506166890