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Mathematical Excursions (MindTap C...

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

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BuyFindarrow_forward

Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 4.3, Problem 8ES
Textbook Problem
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Calculate, if possible, the l3anzhaf power index for each voter. Round to the nearest hundredth.

{ 3 : 1 , 1 , 1 , 1 }

To determine

Calculate, if possible, the Banzhaf power index for each voter. Round to the nearest hundredth.

  {3:1,1,1,1}

Explanation of Solution

Given Information:

The weighted system is {3:1,1,1,1}

Concept used:

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

Calculation:

Winning coalition Number of Votes Critical voters
  {A,B,C}  3  {A,B,C}
  {A,B,D}  3  {A,B,D}
  {A,C,D}  3  {A,C,D}
  {B,C,D}  3  {B,C,D}
  {A,B,C,D}  4None

In above table we look in Critical voters' column and find that A is a critical voter 3 times, B is a critical voter is 3 times, C is a critical voter is 3 times, and D is a critical voter 3 times therefore

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Chapter 4 Solutions

Mathematical Excursions (MindTap Course List)
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