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Mathematical Excursions (MindTap C...

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

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Section
BuyFindarrow_forward

Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 4.3, Problem 4ES
Textbook Problem
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Calculate, if possible, the l3anzhaf power index for each voter. Round to the nearest hundredth.

{ 10 : 7 , 6 , 4 }

To determine

Calculate. if possible. the Banzhaf power index for each voter. Round to the nearest hundredth. (10:7,6,4).

Explanation of Solution

Given Information:

Banzhaf Power indices

Concept used:

  BPI(v)=Number of times voter v is a critical voterNuner of times any voter is a critical voter

Calculation:

Consider three people A,B,and C and the weighted system is {6:7,6,4}.

Therefore,

Winning coalition Number of Votes Critical Voters
  {A,B}  13  {A,B}
  
  {A,C}  11  {A,C}
  {B,C}  10  {B,C}
  {A,B,C}  15None

In above table we look in critical voters' column and find that A is

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Chapter 4 Solutions

Mathematical Excursions (MindTap Course List)
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