Deriving the Huntington-Hill Number The Huntington-Hill number is derived by using the apportionment principle. Let PA = population of state A
a = number of representatives from state A
Pb = 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.
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