1. Warm Up – 3/10 - Monday
State A B C D E
Population
(millions)
12.4
3.6 9
3.7
5.3
A nation contains the five states with the above
populations. Congress assigns seats based on a
state’s population. There are 50 seats in Congress.
Find the standard divisor.
Find the Hamilton Apportionment.

2. Apportionment Methods
Method #1: Hamilton’s method
Find the standard divisor.
Give each state its lower quota.
Give leftovers to states with highest residues.
Method #2: Jefferson’s Method
Find the standard divisor, test apportionment
If not all seats are given out, test different divisors until you find a complete apportionment.

3. Hamilton Method Paradoxes
Alabama Paradox: It is possible for a state to lose a seat just because more seats get added to congress.
Population Paradox: It is possible for a state that is growing in population to lose a seat to a state growing not as fast or not at all.

4. Problems with Jefferson Method

5. Problems with Jefferson
When you look at state B’s standard quota, they have a lower quota of 138 and an upper quota of 139. They receive 140 seats thus we have an upper quota violation!

6. Hamilton and Jefferson Method CW

7. Adam’s Method

8. Adam’s Method

9. Example #1
If there are 250 seats in Congress, find the Adam’s apportionment of the seats.
Find the standard quotas for each state.
Find a suitable divisor for our apportionment.

10. Example #1 - Solution

11. Adam’s Method HW