Question 14.81

51. A county has five townships and elects a 301-seat board of supervisors, using the Webster method of apportionment. The populations of the townships are as follows:

Township Population
109,050
55,920
67,770
61,260
7,500
  1. Determine the Webster apportionment.
  2. Determine the district population for each township. Call the township with the greatest district population the “disadvantaged township.”
  3. To make the apportionment more equitable in terms of district population, which township should give a seat to the disadvantaged township?

51.

(a) The total population of this county is 301,500, and the house size is 301. The standard divisor is therefore . The quotas, determined by dividing the township populations by the house size, are shown in the following table. The sum of the rounded quotas (using the Webster rounding) is equal to the house size. Thus, each township’s Webster apportionment is its rounded quota.

Township Population Quota Rounded Quota District Population
109,050 108.87 109 1000.46
55,920 55.83 56 998.57
67,770 67.66 68 996.62
61,260 61.16 61 1004.28
7,500 7.49 7 1071.43

(b) The district populations are shown in the table displayed in part (a). Township is disadvantaged, because its district population is greater than the district population of each of the others by approximately 70.

(c) The following table shows the absolute difference between the district populations of Township and each of the other townships, as well as the difference if a seat were transferred from the other township to Township .

Township Abs Diff Before Transfer Abs Diff After Transfer
70.97 72.22
72.86 79.23
74.81 73.99
67.17 83.50

The table shows that if a seat is taken from

Township and given to Township , the absolute difference in district population will be less.