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Apportionment Methods

Apportionment Methods. Apportionment. Apportionment means distribution or allotment in proper shares. (related to “Fair Division”)

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Apportionment Methods

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  1. Apportionment Methods

  2. Apportionment • Apportionment means distribution or allotment in proper shares. (related to “Fair Division”) • In the context of the Constitution, apportionment means that each state gets a number appropriate to its population. For example, Representatives are apportioned among the states, with the most populous getting the greater share.

  3. Standard Divisor • The Standard Divisor is found by dividing the total population by the number of items to be allocated. • Standard Divisor = Total Population # of Allocated Items Ex: 1440 students at CHS and 30 student house seats; 1440/30 = 48 students per seat

  4. Standard Quota • The Standard Quota for a particular group is found by dividing that group’s population by the standard divisor. • Standard Quota = population of subgroup standard divisor Ex: Senior class has 328 students; 328/48 = 6.83 seats in student house

  5. Issue with Apportionment • Apportioning items is not a challenging problem, because many items can be divided into fractional parts • Apportioning representatives is more challenging because unlike things, people tend to come in whole number increments

  6. The Apportionment Problem • The Apportionment Problem is to determine a method of rounding standard quotas into whole numbers so that the sum of the numbers equals the total number of allocated items.

  7. Lower & Upper Quotas • Since people prefer to be subdivided into whole number increments, the quota numbers will be rounded to a whole number. • The Lower Quota is the standard quota rounded down to the nearest whole number • The Upper Quota is the standard quota rounded up to the nearest whole number

  8. Hamilton’s Method • This was Alexander Hamilton’s attempt to deal with the Apportionment Problem • There are 3 steps to Hamilton’s Method: 1) Calculate each group’s standard quota 2) Round each standard quota down (lower quota), and give each group that number 3) Give the surplus items one at a time to the groups with the largest decimal parts

  9. For Example… • CHS = 1440 students • Seniors = 328, Juniors = 346, Sophomores = 351, Freshmen = 415 • Standard divisor = 1440/30 = 48 students per seat • Standard quotas: • Seniors = 328/48 =6.83, Juniors = 346/48 =7.21 • Soph = 351/48 = 7.31, Fresh = 415/48 = 8.65 • Seniors = 6, Juniors = 7, Soph = 7, Fresh = 8

  10. Final Answer (Hamilton) • Since the total is only 28 representatives, the other 2 will go to the groups with the largest remainders • Final apportionment: • Seniors = 7 • Juniors = 7 • Sophomores = 7 • Freshmen = 9

  11. Homework, Homework, Homework; I know you love your homework… • P. 760-761; #1-5

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