   # 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. ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

#### Solutions

Chapter
Section ### Mathematical Excursions (MindTap C...

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 PA = population of state Aa = number of representatives from state APb = population of state Bb = number of representatives from state BComplete 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 A when this receives a new representative.

### Explanation of Solution

As per given question:

PA= Population of state A

a= Number of representative from state A

PB= Population of state B<

To determine

(b)

To find::

The average constituency of state B without a new representative.

To determine

(c)

To find::

The relative unfairness of apportionment by given state A which is the new representative in terms of the fractions from parts a and b.

To determine

(d)

To find::

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

To determine

(e)

To find::

The inequality in terms of the expressions in parts c and d.

To determine

(f)

To find::

The inequality of the Huntington-Hill number.

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