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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, Problem 23RE
Textbook Problem
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Calculate the Banzhaf power indices for voters A. B. and C in the weighted sting system { 9 : 6 , 5 , 3 } .

To determine

Calculate the BanZhaf power indices for voters A,B and C in the weighted voting system {9:6,5,3}.

Explanation of Solution

Given Information:

Consider three people A,B and C and the weighted system is {9:6,5,3}

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 {9:6,5,3}

Therefore,

Winning Coalition Number of Votes Critical Voters
  {A,B}

  
  11  {A,B}
  {A,C}  12  {A,C}
  {A,B,C}  14  A
  

In above table we l

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Chapter 4 Solutions

Mathematical Excursions (MindTap Course List)
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Ch. 4.1 - Sales Associates The table below shows the number...Ch. 4.1 - Hospital Interns The table below shows the number...Ch. 4.1 - House of Representatives The U.S. House of...Ch. 4.1 - College Enrollment The following table shows the...Ch. 4.1 - Medical Care A hospital district consists of six...Ch. 4.1 - What is the Alabama paradox?Ch. 4.1 - What is the population paradox?Ch. 4.1 - What is the new states paradox?Ch. 4.1 - 15. 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Explain how the pairwise comparison voting...Ch. 4.2 - What does the Condorcet criterion say?Ch. 4.2 - Is there a best voting method? 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