For November’s evening meeting, Eric led us through an interesting exploration of past and present methods of determining how many congressional seats to apportion to states of various populations.
The meeting began with the following warm up:
An adult education program is hiring 37 teachers to teach at 3 different sites. Each teacher can work at one site only.
Site A: 1500 students/year
Site B: 1000 students/year
Site C: 100 students/year
How many teachers should go to each site?
After discussing our different decisions and methods on the warm up, Eric presented the following image and we spent some time sharing what we noticed and wondered.
We also took a look at the following data.
We then began to explore some methods for apportioning congressional seats. We started with the Hamilton Method.
Hamilton Method
Exercise 1: For the 3 states given, apportion a number of congressional seats N, with N=37.
- Determine the divisor by dividing the total country population by the number of representatives. total populationseats= ______________ (keep at least 2 decimal places)
- Calculate the “quota” for each state by dividing the state’s population by the divisor. Keep at least 2 decimal places.
- Separate the integer part and the decimal part of the quota. The integer part is the initial number of seats given to this state.
- Total the integer parts of the quota. If the total is the same as the number of total seats available, you’re done.
- Additional seats to apportion are given to states with the highest decimal part, one at a time until they are gone.
| State | Pop. | Quota | Integer part | Decimal part | Additional Seats | Final # of Seats |
| A | 1500 | |||||
| B | 1000 | |||||
| C | 100 | |||||
| Total: | Total: |
We continued with the Jefferson method, Adams method, and the method that is currently used for the House of Representatives, the Huntington-Hill method.
After discussing thoughts and opinions about all the methods we looked at, we discovered there’s still plenty more to explore! All methods are included in the attached word document. Try them out for yourself!
