   # Consider the weighted voting system { q : 8 , 3 , 3 , 2 } , with q an integer and 9 ≤ q ≤ 16 . a. For what values of q is there a dummy? b. For what values of q do all voters have the same power? C. II a voter is a dummy for a given quota, must the voter be a dummy for all larger quotas? ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

#### Solutions

Chapter
Section ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 4.3, Problem 27ES
Textbook Problem
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## Consider the weighted voting system { q : 8 , 3 , 3 , 2 } , with q an integer and 9 ≤ q ≤ 16 .a. For what values of q is there a dummy? b. For what values of q do all voters have the same power?C. II a voter is a dummy for a given quota, must the voter be a dummy for all larger quotas?

To determine

(a)

For what values of q is there a dummy?

### Explanation of Solution

Given Information:

Consider the weighted voting system {q:8,3,3,2}, with q an integer and 9q16.

Concept used:

BPI(v)=Numb

To determine

(b)

For what values of q do all voters have the same power?

To determine

(c)

If a voter is a dummy for a given quota, must the voter be a dummy for all larger quotas?

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