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: 38

Answer

Hamilton's method to allocate congressional seats uses the standard divisor to find the standard quota for each state. Then each state is initially assigned their lower quota. If there are surplus seats to be apportioned, the surplus seats are apportioned one at a time to the states which have the largest decimal part in the standard quota. In Jefferson's method, a modified divisor is used which is slightly less than the standard divisor. This modified divisor is used to find each state's modified quota. Then each state's modified quota is rounded down to the nearest whole number. In Adams's method, a modified divisor is used which is slightly more than the standard divisor. This modified divisor is used to find each state's modified quota. Then each state's modified quota is rounded up to the nearest whole number.

Work Step by Step

Hamilton's method, Jefferson's method, and Adams's method are three methods which can be used to allocate congressional seats to each state. Hamilton's method to allocate congressional seats uses the standard divisor to find the standard quota for each state. Then each state is initially assigned their lower quota. If there are surplus seats to be apportioned, the surplus seats are apportioned one at a time to the states which have the largest decimal part in the standard quota. In Jefferson's method, a modified divisor is used which is slightly less than the standard divisor. This modified divisor is used to find each state's modified quota. Then each state's modified quota is rounded down to the nearest whole number. In Adams's method, a modified divisor is used which is slightly more than the standard divisor. This modified divisor is used to find each state's modified quota. Then each state's modified quota is rounded up to the nearest whole number.
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