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: 36

Answer

After we guess at a modified divisor $d$, we use this modified divisor to find the modified quota for each group. Then each group's modified quota is rounded down to the nearest whole number. If the sum of these whole numbers is equal to the number of apportioned items, then the modified divisor $d$ satisfies the method.

Work Step by Step

When we use Jefferson's method, we need to guess at a modified divisor $d$. Finding a modified divisor which satisfies the method may require some trial and error. After we guess at a modified divisor $d$, we use this modified divisor to find the modified quota for each group. Then each group's modified quota is rounded down to the nearest whole number. If the sum of these whole numbers is equal to the number of apportioned items, then the modified divisor $d$ satisfies the method.
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