Question

A voter who has a weight that is greater than or equal to the quota is called a dictator. In a weighted voting system, the dictator has all the power. A voter who is never a critical voter has no power and is referred to as a dummy. This term is not meant to be a comment on the voter's intellectual powers. It just indicates that the voter has no ability to influence an election.

Identify any dictator and all dummies for the given weighted voting system. (Select all that apply.)

{20: 10, 6, 4, 3}

Dictators:

1. the person with 10 votes

2. the person with 6 votes

3. the person with 4 votes

4.the person with 3 votes

5. none of these

Dummies:

1.the person with 10 votes

2.the person with 6 votes

3.the person with 4 votes

4. the person with 3 votes

5. none of these

Answer 1

The given weighted voting system is - {20: 10, 6, 4, 3}

Dictators -

A dictator would need all the 20 votes. And as there is no one with 20 votes, so we can say that only a coalition would work and thus there is no dictator.

Thus, the correct option is: (5) None of these

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Dummies -

Dummies are those whose votes don't matter. Only option to them is to join the dictator or existing coalition in order to form winning coalition. Note that in the given condition, the weight-10 voter, weight-6 voter and weight-4 voter would have the veto because they meet the quota of 20 and coalition of all the voters has only 3 extra votes which is less than what they have.

So, the only dummy voter is - (4) the person with 3 votes.

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