28. a. In a weighted voting system, suppose that two voters have the same weight. Must they also have the same Banzhaf power index? b. In a weighted voting system, suppose that voter A has a larger weight than voter B. Must the Banzhaf power index for voter A be larger than the Banihaf power index for voter B? Most voting systems are susceptible to fraudulent practices. In the following exercise, the Hanzhaf power index is used to examine the power shift that occurs when a fraudulent practice is used.

Mathematical Excursions (MindTap C...

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

Chapter
Section

Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 4.3, Problem 28ES
Textbook Problem
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28. a. In a weighted voting system, suppose that two voters have the same weight. Must they also have the same Banzhaf power index?b. In a weighted voting system, suppose that voter A has a larger weight than voter B. Must the Banzhaf power index for voter A be larger than the Banihaf power index for voter B?Most voting systems are susceptible to fraudulent practices. In the following exercise, the Hanzhaf power index is used to examine the power shift that occurs when a fraudulent practice is used.

To determine

(a)

Explain why voter D is a dummy in this system.

Explanation of Solution

Given Information:

Consider four people A,B,CÂ andÂ D and the weighted system is {17:7,7,7,2}.

Concept used:

Voters will be dummy if he has never critical votes.

Calculation:

 Winning Coalition Number of Votes Critical Voters â€ƒâ€ƒ{A,B,C} â€ƒâ€ƒ21
To determine

(b)

Explain an easy way to compute the Banzhaf power indices for this system.

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