Transcript apportionment3

(Webster)
The following two terms are still needed…
You will find a Modified Divisor
 May be higher, lower, or equal to the Standard Divisor
 More challenging to find than any previous one
These will yield a Modified Quota
 Will round all groups to the nearest whole number
Webster’s Method
 There are a few steps to Webster’s Method:
1) Start with the standard divisor to calculate each
group’s standard quota
2) Round each standard quota to the nearest whole
number (using traditional rounding); the sum of the
whole numbers for all the groups needs to equal the
appropriate number of seats
Webster’s Method
 There are a few steps to Webster’s Method:
3) If the total of all the seats is too low, try a slightly
smaller modified divisor; If the total of all the seats
is too high, try a slightly larger modified divisor
4) Continue until the sum of all the seats adds up to the
appropriate amount
For Example…
 Mathtown = 1693 citizens
 25 seats on town council
 Four districts:
 District 1 = 916 people
 District 2 = 332 people
 District 3 = 244 people
 District 4 = 201 people
 The Standard Divisor
 1693/25 = 67.72 people needed to get a seat
 The Modified Divisor
 Try the standard first before deciding how to modify
For Example…
 Mathtown = 1693 citizens
 25 seats on town council
 Four districts:
 District 1 = 916 people
 District 2 = 332 people
 District 3 = 244 people
 District 4 = 201 people
Standard Quotas:
916/67.72 = 13.526
332/67.72 = 4.903
244/67.72 = 3.603
201/67.72 = 2.968
For Example…
 Mathtown = 1693 citizens
 25 seats on town council
 Four districts:
 District 1 = 916 people
 District 2 = 332 people
 District 3 = 244 people
 District 4 = 201 people
Round to nearest:
916/67.72 = 13.526 (14)
332/67.72 = 4.903 (5)
244/67.72 = 3.603 (4)
201/67.72 = 2.968 (3)
For Example…
 Mathtown = 1693 citizens
 25 seats on town council
 Four districts:
 District 1 = 916 people
 District 2 = 332 people
 District 3 = 244 people
 District 4 = 201 people
Apportionment:
(14)
(5)
(4)
(3)
Adds up to 26…
Try a larger
Modified Divisor
Let’s try 68
For Example…
 Mathtown = 1693 citizens
 25 seats on town council
 Four districts:
 District 1 = 916 people
 District 2 = 332 people
 District 3 = 244 people
 District 4 = 201 people
Modified Quotas:
916/68 = 13.471
332/68 = 4.882
244/68 = 3.588
201/68 = 2.956
For Example…
 Mathtown = 1693 citizens
 25 seats on town council
 Four districts:
 District 1 = 916 people
 District 2 = 332 people
 District 3 = 244 people
 District 4 = 201 people
Modified Quotas:
916/68 = 13.471 (13)
332/68 = 4.882 (5)
244/68 = 3.588 (4)
201/68 = 2.956 (3)
For Example…
 Mathtown = 1693 citizens
 25 seats on town council
 Four districts:
 District 1 = 916 people
 District 2 = 332 people
 District 3 = 244 people
 District 4 = 201 people
Apportionment:
(13)
(5)
(4)
(3)
Adds up to 25…
All is well in the
world!
Notice…they are not always equal
 Mathtown = 1693 citizens
 25 seats on town council
 Four districts:
 District 1 = 916 people
 District 2 = 332 people
 District 3 = 244 people
 District 4 = 201 people
Standard
(13)
(5)
(4)
(3)
Jefferson Adams Webster
(14)
(5)
(3)
(3)
(13)
(5)
(4)
(3)
(13)
(5)
(4)
(3)
Homework… ‘cause you’ve got nothing
better to do!
 P. 761; #15-17