apportionment, a FORTRAN90 code which demonstrates some of the methods used to apportion seats in the United States House of Representatives.

Methods that have been proposed include:

  1. Alexander Hamilton's method;
  2. Thomas Jefferson's method;
  3. John Adam's method;
  4. Daniel Webster's method;
  5. The Huntington-Hill method (the method used since 1940);

Article I, Section 2 of the US Constitution:

The House of Representatives shall be composed of Members chosen every second Year by the People of the several States, and the Electors in each State shall have the Qualifications requisite for Electors of the most numerous Branch of the State Legislature.

No Person shall be a Representative who shall not have attained to the Age of twenty five Years, and been seven Years a Citizen of the United States, and who shall not, when elected, be an Inhabitant of that State in which he shall be chosen.

Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers, which shall be determined by adding to the whole Number of free Persons, including those bound to Service for a Term of Years, and excluding Indians not taxed, three fifths of all other Persons. The actual Enumeration shall be made within three Years after the first Meeting of the Congress of the United States, and within every subsequent Term of ten Years, in such Manner as they shall by Law direct. The Number of Representatives shall not exceed one for every thirty Thousand, but each State shall have at Least one Representative; and until such enumeration shall be made, the State of New Hampshire shall be entitled to chuse three, Massachusetts eight, Rhode-Island and Providence Plantations one, Connecticut five, New-York six, New Jersey four, Pennsylvania eight, Delaware one, Maryland six, Virginia ten, North Carolina five, South Carolina five, and Georgia three.

When vacancies happen in the Representation from any State, the Executive Authority thereof shall issue Writs of Election to fill such Vacancies.

The House of Representatives shall chuse their Speaker and other Officers; and shall have the sole Power of Impeachment.


The computer code and data files described and made available on this web page are distributed under the MIT license


apportionment is available in a FORTRAN90 version.

Related Data and Programs:


CENSUS, a dataset directory which contains some US census data for state populations.

KNAPSACK, a FORTRAN77 library which solves a variety of knapsack problems.


  1. Michael Balinski, Hobart Young,
    The Quota Method of Apportionment,
    The American Mathematical Monthly,
    Volume 82, Number 7, August-September 1975, pages 701-730.
  2. Barry Cipra,
    E Pluribus Confusion,
    American Scientist,
    Volume 98, Number 4, July-August 2010, pages 276-279.
  3. Donald Saari,
    Apportionment Methods and the House of Representatives,
    The American Mathematical Monthly,
    Volume 85, Number 10, December 1978, pages 792-802.

Source Code:

Last revised on 26 August 2021.