Question
In the weighted voting system below, the weights represent voters A, B, C, and so on, in that order. Answer parts (a) through (d). \( [17: 16,6,6,6] \) b. How many yoters are there? What are the weights of the voters? A has 16 vote(s). 6 vote(s). C has 6 vote(s). D has 6 vote(s). c. Are there any dictators? Y Yes No
Ask by Conner Lyons. in the United States
Feb 13,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
There are 4 voters: A (16 votes), B (6 votes), C (6 votes), and D (6 votes). No voter is a dictator.
Solution
We are given the weighted voting system [17: 16, 6, 6, 6], where the first number (17) is the quota and the subsequent numbers are the weights assigned, in order, to voters A, B, C, D.
b. How many voters are there? What are the weights of the voters?
There are 4 voters.
• Voter A has 16 votes.
• Voter B has 6 votes.
• Voter C has 6 votes.
• Voter D has 6 votes.
c. Are there any dictators?
A dictator is a voter who can single-handedly determine the outcome (i.e., by voting yes alone they meet or exceed the quota, and by voting no always defeat a proposal regardless of the others).
In this case the quota is 17. Since voter A’s weight is 16 (< 17), even A cannot reach the quota without support. Therefore, no voter has the power to decide the outcome on his or her own.
Answer: No, there are no dictators.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
In this weighted voting system, there are four voters in total: A, B, C, and D. The weights assigned to the voters are as follows: A has 16 votes, while B, C, and D each have 6 votes. This voting setup offers a great balance of influence, highlighting how a few votes can hold significant power in decision-making processes. Determining whether there are any dictators can be quite fascinating! In this case, a dictator is someone whose vote alone can decide an outcome. Voter A, with 16 votes, can effectively dictate the outcome as their votes surpass the majority threshold (which is 17 in this case). So yes, A is indeed a dictator. But don’t worry, the system balances out!
