2.4 More Apportionment Algorithms and Paradoxes

Ms. MagneDiscrete Math

• 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.

Step 1: Find the ideal ratio

Ideal Ratio=

Ideally, each representative should represent _______ students.

Total PopulationNumber of Seats

45

Step 2: Find class quota

Quota=

Sophomore: _________Junior: _________Senior: __________

Class SizeIdeal Ratio

10.315.33

4.36

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

Webster Method

Sophomore WAR: ___________Junior WAR: __________Senior WAR: ___________

Sophomore Seats: ___________Junior Seats: _______Senior Seats: _______

46410.5 = 44.19

2405.5

= 43.641964.5 = 43.56

10 + 1 = 11

54

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

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

1154