## Congressional Apportionment## What is Congressional Apportionment?Article 1, Section 2 of the United States constitution requires the federal government to conduct a census of its population every ten years for the purpose of apportioning U.S. House of Representatives seats among the states. Each state is given a number of seats roughly equal to their population, with every state guaranteed at least one seat. Since the number of U.S. House seats is fixed at 435, a new apportionment results in some states gaining congressional seats and some states losing congressional seats.Note that while the fairness issue is often referred to as "one-man, one-vote," the constitutional principle is strictly speaking, "one-person, one unit of representation." ## How Have Congressional Seats Been Apportioned to States?From the Census Bureau:Since the first apportionment following the 1790 census, there have been five basic methods used to apportion the House of Representatives.
Following the 1990 census, two lawsuits concerning apportionment issues
were filed in federal courts. The U.S. Supreme Court held that the method
of equal proportions was constitutional; that the Congress had properly
exercised its apportionment authority; and that the inclusion of U.S.
federal military and civilian personnel, and their dependents, in the
apportionment populations of the states was constitutional. These cases
were ## The Alabama ParadoxConsider a hypothetical nation composed of 14 people living in 3 states, A, B, and C such that the population is distributed as follows{A = 6, B = 6, and C = 2}. Using the Hamilton method, increasing the number of seats from 10 to 11 will result in state C losing a seat.
This is called the Alabama Paradox because in 1880, the Clerk of the U.S. House discovered that increasing the size of the House of Representatives from 299 to 300 members would result in Alabama losing a seat. The actual calculation is archived here. ## The Apportionment Impossibility ResultIn 1982, mathematicians Michel Balinski and Peyton Young proved in their bookFair Representation: Meeting the Ideal of One Man, One Vote (this is a Google Books link to the second edition published in 2001) that any apportionment formula could not satisfy three properties:- The quota rule: A state receives either of the integer number of seats closest to its fair share of seats.
- The Alabama Paradox does not exist.
- The Population Paradox does not exists, whereby if the population size of A increases and the size of B decreases, no seats will be transferred from A to B.
John P. Mayberry. 1978. "Quota Methods for Congressional Apportionment Are Still Non-Unique." Proc. Natl. Acad. Sci. 75(8): 3537-39.## What Are the Alternatives?A nice analysis of the proposed alternatives is available in a 2001 Congressional Research Service Report: David C. Huckabee. 2001. "The House of Representatives Apportionment Formula: An Analysis of Proposals for Change and Their Impact on States." Congressional Research Service Report RL31074. ## SimulationsHere are simulations that may be of interest: ## The Current Formula: Method of Equal ProportionsAn Excel spreadsheet with the current formula is available here. Follow these steps to calculate apportionment under different population scenarios:- Turn on Macros
- Select the tab "State List"
- Select all (Cntl-a)
- Copy
- Paste Special - Values
- Point to cell A1 (upper left-hand corner)
- On the control panel at the top, select View-Macros (this may vary with Excel version)
- Select the Macro "Trans" and select run. This will create a tab "Sheet 1."
- Sort on Column C from largest to smallest
- Each of the 50 states gets 1 district. Start numbering the first row in D1 with a 51. Set D2 as a formula "D1+1" and copy and paste this formula for the D column.
- Scroll down to row 385 and you will see which state is on the cusp of gaining or losing a seat.
- Select all of the data in columns A, B, and C and Copy.
- Select tab "Sheet 2"
- Paste these data into the corresponding columns in the tab "Sheet 2"
- View the tab "Congressional". The counts of districts are in Column E. Note that there are comparison counts for the 2000 apportionment, and a projection based on the 2008 and 2009 census population estimates. These estimates are on the tab "NST_EST2009_ALLDATA". The data in "State List" are generated from Column O. Change the formula here to try out different population scenarios.
## General Divisor Methods SimulatorA simulator for general divisor methods is here. (Requires installing the free Mathematica Player.) |