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 1990 U.S. Census; 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, WA would lose a Representative to MA), 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.

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.

STATE | REP | POPULATION | N | PRIORITY | STATE | REP | POPULATION | N | PRIORITY |
---|---|---|---|---|---|---|---|---|---|

CA | 52 | 29760021 | 1 | 21043513 | CO | 6 | 3294394 | 1 | 2329488 |

NY | 31 | 17990455 | 1 | 12721173 | CT | 6 | 3287116 | 1 | 2324342 |

TX | 30 | 16986510 | 1 | 12011276 | OK | 6 | 3145585 | 1 | 2224264 |

FL | 23 | 12937926 | 1 | 9148495 | OR | 5 | 2842321 | 1 | 2009824 |

PA | 21 | 11881643 | 1 | 8401590 | IA | 5 | 2776755 | 1 | 1963462 |

IL | 20 | 11430602 | 1 | 8082656 | MS | 5 | 2573216 | 1 | 1819538 |

OH | 19 | 10847115 | 1 | 7670069 | KS | 4 | 2477574 | 1 | 1751909 |

MI | 16 | 9295297 | 1 | 6572768 | AR | 4 | 2350725 | 1 | 1662214 |

NJ | 13 | 7730188 | 1 | 5466068 | WV | 3 | 1793477 | 1 | 1268180 |

NC | 12 | 6628637 | 1 | 4687154 | UT | 3 | 1722850 | 1 | 1218239 |

GA | 11 | 6478216 | 1 | 4580790 | NE | 3 | 1578385 | 1 | 1116087 |

VA | 11 | 6187358 | 1 | 4375123 | NM | 3 | 1515069 | 1 | 1071316 |

MA | 10 | 6016425 | 1 | 4254255 | ME | 2 | 1227928 | 1 | 868276 |

IN | 10 | 5544159 | 1 | 3920312 | NV | 2 | 1201833 | 1 | 849824 |

MO | 9 | 5117073 | 1 | 3618317 | NH | 2 | 1109252 | 1 | 784360 |

WI | 9 | 4891769 | 1 | 3459003 | HI | 2 | 1108229 | 1 | 783636 |

TN | 9 | 4877185 | 1 | 3448691 | ID | 2 | 1006749 | 1 | 711879 |

WA | 9 | 4866692 | 1 | 3441271 | RI | 2 | 1003464 | 1 | 709556 |

MD | 8 | 4781468 | 1 | 3381008 | MT | 1 | 799065 | 1 | 565024 |

MN | 8 | 4375099 | 1 | 3093662 | SD | 1 | 696004 | 1 | 492149 |

LA | 7 | 4219973 | 1 | 2983972 | DE | 1 | 666168 | 1 | 471052 |

AL | 7 | 4040587 | 1 | 2857126 | ND | 1 | 638800 | 1 | 451700 |

KY | 6 | 3685296 | 1 | 2605898 | VT | 1 | 562758 | 1 | 397930 |

AZ | 6 | 3665228 | 1 | 2591708 | AK | 1 | 550043 | 1 | 388939 |

SC | 6 | 3486703 | 1 | 2465471 | WY | 1 | 453588 | 1 | 320735 |

PR | 0 | 3522037 | 1 | 2490456 | DC | 0 | 606900 | 1 | 429143 |

ALL 50 STATES | 435 | 248102973 | 50 | 4962059 |