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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 4.1, Problem 35ES

Textbook Problem

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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.

To determine

**(a)**

**To find::**

The fraction for the average constituency of state

As per given question:

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To determine

**(b)**

**To find::**

The average constituency of state

To determine

**(c)**

**To find::**

The relative unfairness of apportionment by given state

To determine

**(d)**

**To find::**

The relative unfairness of apportionment by giving state

To determine

**(e)**

**To find::**

The inequality in terms of the expressions in parts

To determine

**(f)**

**To find::**

The inequality of the Huntington-Hill number.

Mathematical Excursions (MindTap Course List)

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