General Divisor Methods

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

The United States Constitution states that representatives in the House of Representatives "shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State, excluding Indians not taxed" (14th amendment, section 2). The Constitution further places a ceiling on the number of total representatives at 1 per 30,000 of total population and states that every state shall have at least one member in the House of Representatives (Article I, section 2). The Constitution does not specify, however, how to deal with the issue of rounding in the resulting computations.

[more]

Numerous methodologies have been suggested and employed over American history. Many are examples of "general divisor methods", which solve the problem , where the is the population of state , is the total number of seats in the House of Representatives, and is some rounding function that maps a real number to an integer. This Demonstration shows how these different rounding methodologies affect the representation of 13 imaginary states for 10 different scenarios and for between 50 and 500 possible seats. It also checks to make sure that the total number of votes held by the states under each of the methodologies in fact equals the desired number of total votes. A bar chart shows the relative population of each of the 13 states for each dataset.

[less]

Contributed by: Seth J. Chandler (March 2011)
Open content licensed under CC BY-NC-SA

Details

An article on general divisor methods may be found in: E. Park, "The Mathematics of Apportionment," University of Chicago Law School Roundtable, 7, 2000 pp. 227-235. This Demonstration draws significantly on his work.

The "floor" method is essentially that of Thomas Jefferson and was used from 1790 through 1830. The "round" method is essentially that proposed by Daniel Webster and was used in 1840 and again with minor variation in 1910 and 1930. The geometric method is roughly what is used today.

Permanent Citation

Seth J. Chandler

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send