Question 1171046:
A weighted voting is an electoral system in which the voters do not have the same amount of
influence over the result of an election. Each voting system can be described using the form
{q: w1, w2, w3, w4,…,wn}
where q is the quota, w are the weights and n is the number of voters. The weights are listed in
numerical order, starting with the highest weight.
Problem:
1. Calculate, if possible, the Banzhaf power index for each voter. Round to the nearest hundredth.
a. {8: 4, 3, 2}
b. {15: 8, 6, 4}
c. {20: 7, 3, 2, 1}
d. {10: 7, 5, 1, 1}
e. {12: 14, 12, 4, 3, 1}
f. {5: 1, 1, 1, 1, 1, 1}
g. {21: 21, 7, 3, 3, 1, 1}
h. {12: 6, 6, 4, 3, 1}
i. {80: 60, 40, 30, 25, 5}
j. {85: 50, 40, 25, 5}
Which, if any, of the voting systems is a dictatorship?
Which, if any, of the voting systems is a veto power system?
Which, if any, of the voting systems is a null system?
Which, if any, of the voting systems is a one-person, one-vote system?
Answer by ikleyn(52898)   (Show Source):
You can put this solution on YOUR website! .
I look and read attentively your posts on this subject.
It is with great satisfaction I see that you take my instructions seriously and follow them.
I am glad to see your progress in improving the problem's formulation step by step.
You just included the introduction describing the voting system, and it is a good progress.
The progress is good, but still is not enough.
As the next steps, you should include three things:
1) The description/(definition) of the Banzhaf power index,
2) the criterions of the dictatorship system, veto-power system, null-system
and
3) a methodology on how calculate the index based on the data.
After that (and only after that) your problem, finally, will achieve a high status
of a Math problem, and will be ready a) for the solution, and b) to offer it to the others.
I wish you to successfully make your further steps on the way of your progress (!)
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