Activity 14.2, Divisor Methods
Name(s): _________________________________
Adam’s Method
The method consists of finding a modified divisor, D, which is larger than the standard divisor, and which produces
smaller modified quotas. These modified quotas are then rounded up, and summed. This total is then compared to the
number of representatives to be allocated. Several values of D might have to be tried until the total agrees with the desired
number of representatives. The four states below are apportioning 11 representatives.
1. Find the standard divisor
Standard divisor = total population / number of representatives = __________________________
2. Choose a Modified Divisor, __________________________
3. Calculate the Modified Quota in the third column. Remember that the modified quota is given by:
modified quota = state's population / modified Divisor
4. In the last column, enter the integer number obtained by rounding up the modified quota.
5. Calculate the sum of the numbers in the last column.
6. If the previous sum is exactly 11, you have succeeded in using Adams' method to apportion representatives.
7. If the sum is not 11, then you WOULD need to try other numbers for the modified divisor until 11 is reached. Here you
don’t need to actually re-calculate, just provide the next
Modified Divisor you would try, _________________________,
along with an explanation of why you chose that Modified Divisor.
State
State
Population
Calcsylvania
230
Lindiana
85
Mathinois
275
Quantifornia
430
Total
Pop =
Modified
Quota
Total Number of
Reps
=
Modified Quota rounded up, aka number
of rep's obtained using Adams' Method
Huntington-Hill Method
The Huntington-Hill method is also called the method of equal proportions, and it is the method currently used to
apportion seats in the U.S. House of Representatives. If q is the modified quota, and q is between integers n and n+1, then
the geometric mean of n and n+1, which is the square-root of n*(n+1), is used to decide whether to round q up or down.
The four states below are apportioning 11 representatives.
If q <= sqrt( n*(n+1) ), then q is rounded down.
If q > sqrt( n*(n+1) ), then q is rounded up.
8. Find the standard divisor
Standard divisor = total population / number of representatives = __________________________
9. Choose a Modified Divisor, __________________________
10. Calculate the Modified Quota in the third column. Remember that the modified quota is given by:
modified quota = state's population / modified Divisor
11. Fill in the Geometric Mean column. Take the square root of the product of the integer part of the modified quota and
the next integer.
12. Fill in the last column with each modified quota rounded up or down, according to the geometric mean, using the
following instructions.
If the modified quota is less than the geometric mean, then enter the integer part of the modified quota. Otherwise, enter
the integer part of the modified quota plus 1 (which is the next largest integer).
13. Calculate the sum of the numbers in the last column.
14. If the previous sum is exactly 11, you have succeeded in using the Huntington-Hill method to apportion
representatives.
15. If the sum is not 11, then you WOULD need to try other numbers for the modified divisor until 11 is reached. Here
you don’t need to actually re-calculate, just provide the next
Modified Divisor you would try, _________________________,
along with an explanation of why you chose that Modified Divisor.
State
State
Population
Calcsylvania
230
Lindiana
85
Mathinois
275
Quantifornia
430
Total
Pop =
Modified Quota
Geometric
Mean
Total Number of
Reps
=
Number of rep's obtained using the
Huntington-Hill Method