1. 2.4 More Apportionment Algorithms and Paradoxes Ms. Magné Discrete Math

2. Central has 464 sophomores, 240 juniors, and 196 seniors. The 20 seats of the student council are divided among each class according to population. We need to determine how many seats each class gets.

3. Step 1: Find the ideal ratio Ideal Ratio= Ideally, each representative should represent _______ students. Total Population Number of Seats 45

4. Step 2: Find class quota Quota= Sophomore: _________ Junior: _________ Senior: __________ Class Size Ideal Ratio 10.31 5.33 4.36

5. Webster Method Round quotas as if you would round any decimal to a whole number. Find Webster Adjusted Ratio. Any extra seats given to highest WAR, seats can be removed from lowest WAR. Webster Adjusted Ratio= Class Size Arithmetic Mean *Arithmetic Mean- Add two numbers and divide by 2

6. Webster Method Sophomore WAR: ___________ Junior WAR: __________ Senior WAR: ___________ Sophomore Seats: ___________ Junior Seats: _______ Senior Seats: _______ 464 10.5 = 44.19 240 5.5 = 43.64 196 4.5 = 43.56 10 + 1 = 11 5 4

7. Hill Method Round quotas as if you would round any decimal to a whole number. Find Hill Adjusted Ratio. Any extra seats given to highest HAR, seats can be removed from lowest HAR. Hill Adjusted Ratio= Class Size Geometric Mean *Geometric Mean- Multiply 2 numbers and take the square root

8. Hill Method Sophomore HAR: ___________ Junior HAR: ____________ Senior HAR: ___________ Sophomore Seats: ___________ Junior Seats: _______ Senior Seats: _______ 464 √(10*11) 240 196 √(5*6) √(4*5) = 44.24 = 43.82 = 43.83 11 5 4