Question 14.73

image 43. In 1822, Congressman William Lowndes of South Carolina proposed an apportionment method, which was never used. Lowndes started, as Hamilton did, by giving each state its lower quota. But where Hamilton apportions the remaining seats to the states whose quotas have the largest fractional parts—in other words, the states for which the absolute difference between the quota and the lower quota is greatest—Lowndes gives the extra seats to the states where the percentage difference is greatest, increasing the apportionments of as many states as necessary to their upper quotas to fill the House.

  1. Compared with the Hamilton method, would this method be more beneficial to states with large populations or small populations?
  2. Does the Lowndes method satisfy the quota condition?
  3. Would there be any trouble with paradoxes with the Lowndes method?
  4. Use the method to apportion the 1790 House of Representatives with a 120-seat house. The populations and quotas resulting from the 1790 census are in Table 14.5 on page 580.

43.

(a) Lowndes favors small states.

(b) Yes

(c) Yes

A-35

(d)

State Quota Lower Quota Priority Apportionment
DE 1.843 1 84.30% 2
VT 2.839 2 41.95% 3
NJ 5.959 5 19.18% 6
NH 4.707 4 17.68% 5
GA 2.351 2 17.55% 3
SC 6.844 6 14.07% 7
KY 2.280 2 14.00% 3
RI 2.271 2 13.55% 3
CT 7.860 7 12.29% 8
NC 11.732 11 6.65% 11
MA 15.774 15 5.16% 15
VA 20.926 20 4.63% 20
MD 9.243 9 2.70% 9
PA 14.366 14 2.61% 14
NY 11.004 11 0.04% 11
Totals 120 111 120