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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: 10, 6, 5, 4, 24. (a) What is the smallest value

Chapter 2, Problem 4

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QUESTION:

Consider the weighted voting system 3q: 10, 6, 5, 4, 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 two-thirds of the votes are required to pass a motion? (d) What is the value of the quota if more than twothirds of the votes are required to pass a motion?

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QUESTION:

Consider the weighted voting system 3q: 10, 6, 5, 4, 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 two-thirds of the votes are required to pass a motion? (d) What is the value of the quota if more than twothirds 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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