   # Three voters. A. B. and C, make decisions by using the weighted voting system { 6 : 5 , 4 , 1 } . In the case of a tie, a fourth voter. D. casts a single vote to break the tie. For this voting scheme, determine the Banzhaf power index for each voter, including voter D. ### 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, Problem 10T
Textbook Problem
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## Three voters. A. B. and C, make decisions by using the weighted voting system { 6 : 5 , 4 , 1 } . In the case of a tie, a fourth voter. D. casts a single vote to break the tie. For this voting scheme, determine the Banzhaf power index for each voter, including voter D.

To determine

Determine the Banzhaf power index for each voter, including voter D.

### Explanation of Solution

Given Information:

Three voters, A,B and C make decisions by using the weighted voting system {6:5,4,1} in the case of a tie, a fourth voter, D, casts a single vote to break the tie.

Concept used:

Calculation:

In above table look in critical voter's column and find that A is a critical voter 4 times, B is a critical voter is 2 times, and C is a critical voter is 2 times, and D is critical voter 2 times, therefore,

Formula of Banzhaf power index of a voter v, symbolized by BPI(v) is given by

BPI(v)=number of times voter v is a critical voternuner of times any voter is a critical voter

BPI(A)=44+2+2+2=410=0

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