Explanation Approach: The number of votes required to pass a resolution is called a quota. A weighted voting system with p voters is described by a set of numbers in the following format. [quota: weight of voter 1, weight of voter 2,….weight of voter p] Ex: [ 20 : 10 , 8 , 6 ] Here the number 20 represents the quota. The remaining numbers are called voter’s weights. Banzhaf power index is used to measure the voting power. A voters Banzhaf power index in a weighted voting system is given as = n u m b e r o f t i m e s t h e v o t e r i s c r i t i t c a l i n w i n n i n g c o a l i t i o n s t h e t o t a l n u m b e r o f t i m e s v o t e r s a r e c r i t i c a l i n w i n n i n g c o a l i t i o n s . Ex: 12 : 1 , 7 , 10 The number of voters = 3 Set of possible coalitions = 2 3 - 1 = 8 - 1 = 7 Here the quota is 12 . List out all possible coalitions one by one. Coalitions Weight Winning ( ≥ quota) { 1 } 1 No { 7 } 7 No { 10 } 10 No { 1 , 7 } 8 No 1 , 10 11 No { 7 , 10 } 17

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Chapter 11.3, Problem 47E

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Whether the statement voter’s weight and the voter’s Banzhaf index is same or not.

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Chapter 11.3, Problem 46E

Chapter 11.3, Problem 48E

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Whether the statement voter’s weight and the voter’s Banzhaf index is same or not.

Solution Summary: The author explains that the number of votes required to pass a resolution is called quota, and Banzhaf power is used to measure the voting power.

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To explain: Whether the statement voter’s weight and the voter’s Banzhaf index is same or not.

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To explain:

Whether the statement voter’s weight and the voter’s Banzhaf index is same or not.