Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 13 - Voting and Apportionment - 13.3 Apportionment Method - Exercise Set 13.3: 4

Answer

Using Hamilton's method, each state is apportioned the following number of seats. State A is apportioned 17 seats. State B is apportioned 33 seats. State C is apportioned 67 seats. State D is apportioned 83 seats.

Work Step by Step

Hamilton's method is an apportionment method that involves rounding each standard quota down to the nearest whole number. Surplus seats are given, one at a time, to the states with the largest fractional parts in their standard quotas until there are no more surplus seats. State A's standard quota is 17.25 State A's lower quota is 17 State A's upper quota is 18 State B's standard quota is 33.25 State B's lower quota is 33 State B's upper quota is 34 State C's standard quota is 66.75 State C's lower quota is 66 State C's upper quota is 67 State D's standard quota is 82.75 State D's lower quota is 82 State D's upper quota is 83 Initially, each state is apportioned its lower quota. State A is apportioned 17 seats. State B is apportioned 33 seats. State C is apportioned 66 seats. State D is apportioned 82 seats. We can find the total number of seats which have been apportioned. total = 17 + 33 + 66 + 82 = 198 seats Since there is a total of 200 congressional seats, there are two surplus seats. One surplus seat is given to state C and the other surplus seat is given to state D because they have the largest fractional part (0.75) in the standard quota. Using Hamilton's method, each state is apportioned the following number of seats. State A is apportioned 17 seats. State B is apportioned 33 seats. State C is apportioned 66 + 1 = 67 seats. State D is apportioned 82 + 1 = 83 seats.
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