Discrete Math Project: Apportion Congress
Name___________________Date_______Pd__
Back when our Founding Fathers were writing the Constitution, one of the great debates was over
the houses of Congress. Some people thought that each state should receive the same number of votes,
while others thought that the states’ representation should be based on the state’s population. Ultimately,
as you are aware, our Founding Fathers decided to use a bicameral (two-house) Congress. Each state
would receive two votes in the Senate and a number of votes pertaining to the state’s population in the
House of Representatives (out of a total of 435). This method was deemed most fair
Suppose the U.S. Congress decides to abolish the bicameral system and instead implement a
unicameral (one house) system. The new Congress would have 535 seats. (100 from the old Senate and
435 from the old House of Representatives). Additionally, Washington D.C., as well as Puerto Rico will
receive representation in the new Congress. Seats will be apportioned to each of the 52 geographical
regions based on the region’s population. It is your job to apportion these seats! Yeah!
To complete this project successfully, you must:
1) Refer to the most recent population estimates from the U.S. Census Bureau and calculate the
Standard Divsor for one representative in Congress and each region’s quota.-________/10 points
2) Apportion the 535 seats of Congress based on ONE of the four apportionment algorithms
discussed in class. (Your apportionment might not seem fair- some states may not even receive
representation!)-_________/50 points
3) Decide if you want to make any qualitative changes or implement any rules (minimum seats per
state, etc.) to your apportionment to make sure that all regions are happy with their representation.
Explain why you have decided to make the changes.-________/20 points
4) Explain why you chose the apportionment algorithm that you did in part 2. Why was it the best
choice? Do you feel that it is more fair than the other methods? Why or why not?__________/10 points
5) Show all of your work NEATLY and include this piece of paper with your work when you turn it
in._________/10 points
**This project will count as a TEST GRADE and will be due Friday, May 30th. If you would like to
receive an automatic 10% extra credit added on to your grade, use two DIFFERENT apportionment
methods!