Textbook Problem

Deriving the Huntington-Hill Number The Huntington-Hill number is derived by using the apportionment principle. Let P_A = population of state A

a = number of representatives from state A

P_b = population of state B

b = number of representatives from state B

Complete the following to derive the Huntington-Hill Number.

a. Write the fraction that gives the average constituency of state A when it receives a new representative.

b. Write the fraction that gives the average constituency of state B without a new representative.

c. Express the relative unfairness of apportionment by giving state A the new representative in terms of the fractions from parts a and b.

d. Express the relative unfairness of apportionment by giving state B the new representative.

e. According to the apportionment principle, state A should receive the next representative instead of state B if the relative unfairness of giving the new representative to state A is less than the relative unfairness of giving the new representative to state B. Express this inequality in terms of the express ions in parts c and d.

f. Simplify the inequality and you will have the Huntington-Hill number.