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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.
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Mathematical Excursions (MindTap C...
4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
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Chapter
Section
BuyFindarrow_forward
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 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.
To determine
(a)
To find::
The fraction for the average constituency of state
Explanation of Solution
As per given question:
  
  
  
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.
Chapter 4 Solutions
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