Apportionment Methods
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Transcript of Apportionment Methods
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…
P. 760-761; #1-5