ApportionmentApportionment 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.

Standard DivisorThe 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

Standard QuotaThe Standard Quota for a particular

group is found by dividing that group’s population by the standard divisor.

Standard Quota = population of subgroupstandard divisor

Ex: Senior class has 328 students; 328/48 = 6.83 seats in student house

Issue with ApportionmentApportioning 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

The Apportionment ProblemThe 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.

Lower & Upper QuotasSince 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

Hamilton’s MethodThis was Alexander Hamilton’s attempt

to deal with the Apportionment ProblemThere are 3 steps to Hamilton’s Method:

1) Calculate each group’s standard quota2) Round each standard quota down (lower

quota), and give each group that number3) Give the surplus items one at a time to the

groups with the largest decimal parts

For Example…CHS = 1440 studentsSeniors = 328, Juniors = 346, Sophomores =

351, Freshmen = 415Standard divisor = 1440/30 = 48 students per

seat Standard quotas:Seniors = 328/48 =6.83, Juniors = 346/48

=7.21Soph = 351/48 = 7.31, Fresh = 415/48 = 8.65Seniors = 6, Juniors = 7, Soph = 7, Fresh = 8

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 = 7Juniors = 7Sophomores = 7Freshmen = 9

Homework, Homework, Homework; I know you love your homework…

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