2.3 Apportionment Algorithms

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2.3 Apportionment Algorithms

• Ms. Magne?
• Discrete Math

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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.

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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.

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• Step 1 Find the ideal ratio
• Ideal Ratio
• Ideally, each representative should represent
  _______ students.

Total Population
Number of Seats
45
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• Step 2 Find class quota
• Quota
• Sophomore _________
• Junior _________
• Senior __________

Class Size
Ideal Ratio
10.31
5.33
4.36
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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
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Jefferson Method

• Each class gets the number of seats equal to the
  whole number of their Quota. Find the Jefferson
  Adjusted Ratio. Whoevers 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