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Math / Excursions in Modern Mathematics: Pearson New International Edition 8 / Chapter 2 / Problem 3

Excursions in Modern Mathematics: Pearson New International Edition | 8th Edition | ISBN: 9781292022048 | Authors: Peter Tannenbaum

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Consider the weighted voting system 3q: 6, 4, 3, 3, 2, 24. (a) What is the smallest

Chapter 2, Problem 3

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QUESTION:

Consider the weighted voting system 3q: 6, 4, 3, 3, 2, 24. (a) What is the smallest value that the quota q can take? (b) What is the largest value that the quota q can take? (c) What is the value of the quota if at least three-fourths of the votes are required to pass a motion? (d) What is the value of the quota if more than threefourths of the votes are required to pass a motion?

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QUESTION:

Consider the weighted voting system 3q: 6, 4, 3, 3, 2, 24. (a) What is the smallest value that the quota q can take? (b) What is the largest value that the quota q can take? (c) What is the value of the quota if at least three-fourths of the votes are required to pass a motion? (d) What is the value of the quota if more than threefourths of the votes are required to pass a motion?

ANSWER:

Step 1 of 5

The weighted distribution is

Let's denote the cumulative number of votes with .

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