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2.3 Apportionment Algorithms

2.3 Apportionment Algorithms. Ms. Magné Discrete Math. Apportionment is the distribution or allotment in proper shares. Example: Apportionment of seats in the US House of Representatives Seats must be distributed among states according to population.

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2.3 Apportionment Algorithms

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  1. 2.3 Apportionment Algorithms Ms. Magné Discrete Math

  2. Apportionment is the distribution or allotment in proper shares. Example: Apportionment of seats in the US House of Representatives • Seats must be distributed among states according to population. • Hamilton Method was first used and later replaced by the Jefferson Method.

  3. Example • 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.

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

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

  6. Hamilton Method Each class gets the number of seats equal to the whole number of their Quota. Any remaining seats goes to the highest decimal. Sophomore Seats: __________ Junior Seats: __________ Senior Seats: ____________ 10 + 5 + 4 = 19 10 5 4 + 1 = 5

  7. Jefferson Method Each class gets the number of seats equal to the whole number of their Quota. Find the Jefferson Adjusted Ratio. Whoever’s JAR is highest gets extra seat. Jefferson Adjusted Ratio = Class Size Seats + 1

  8. Jefferson Method Sophomore JAR: ___________ Junior JAR: ____________ Senior JAR: ____________ Sophomore Seats: _____________ Junior Seats: ________ Senior Seats: ________ 42.2 40 39.2 10 + 1 = 11 5 4

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