1. Huntington-Hill Method Why was this method chosen to apportion the House?

2. Two ways to Measure Fairness Difference in District Populations among states Representative Share

3. Difference in District Population District Populations—In a perfect system each district would have the same size: p/n (total population divided by house size) This is impossible in a practical sense because districts cannot cross state lines. Thus, we compute the district population for each state. The best apportionment would be the one for which the largest difference in district populations between states is minimal (the smallest.)

4. Representative Share Suppose a state has apportionment a and population p. Then a/p = share of a representative (seat) belonging to each citizen of the state. We calculate this for each state and look at the difference between the largest and the smallest representative shares. The best apportionment method would be the one that minimizes this difference.

5. Is there a way to do both things? Webster’s method will minimize difference in representative share but not difference in district size. Huntington-Hill will do both if we use relative differences instead of absolute differences! So what is a relative difference?

6. Relative vs. Absolute Difference Let A and B be two positive numbers where A > B. The absolute difference is A – B (larger minus smaller). The relative difference is (A – B)/B. (x 100 if you want %) Example: 36 – 25 = 11, while (36 – 25)/25 = 11/25 =.44 or 44%.

7. Why we use H—H For any two states it can be shown that the relative difference in district populations is equal to the relative difference in representative share! The Huntington—Hill method gives the apportionment in which the relative differences in representative share and district populations is as small as possible!

8. An example(1940 apportionment) Michigan 5,256,106 Arkansas 1,949,387 HH gave Michigan 17 seats, Arkansas 7 Webster gave Michigan 18 seats, Ark. 6 Calculate the relative difference in district size for Michigan and Arkansas under each method.

9. Under Webster Mich. 18 dist., avg. pop. = 292,006 Ark. 6 dist., avg. pop. = 324,898 The difference, 324,898—292,006 is 32,892. The relative difference is 32,892/292,006 = 0.1126415

10. Under HH Mich. 17 dist., avg. pop. = 309,183 Ark. 7 dist., avg. pop. = 278,484 Absolute difference = 309,183—278,484 = 30,699 Relative difference = 30,699/278,484 = 0.1102361 This relative difference is smaller than with Webster.

11. Representative Share Michigan(17 seats) 3.234 microseats (millionths of a seat). Arkansas(7 seats) 3.591 microseats Relative difference (in %) = (3.591—3.234) /3.234 x 100 = 11.02% Michigan(18 seats) 3.425 microseats Arkansas(6 seats) 3.078 microseats Relative difference = 11.27%

12. What does is mean? If Michigan had 18 seats and Arkansas 6 seats, then Michigan would be 11.27% better represented than Arkansas. If Michigan had 17 seats and Arkansas 7 seats, then Arkansas would be 11.02% better represented than Michigan, a smaller percentage! Thus HH give a fairer apportionment under this criterion.