In a weighted voting system q w1 w2 wk what are the restri

In a weighted voting system [q : w1, w2, …, wk], what are the restrictions on the possible values of q? Explain each restriction.

For the weighted voting system [9 : 9, 4, 2, 1], describe how much power voter v1 has. Such a voter is called a dictator. Why is this appropriate? Could a system have two dictators? Explain why or why not.

Solution

q(quota) is the minimum amount of weight needed for the proposal of being getting approved by the decision takers or the community holder

The restrictions on quota, that the 1) quota must be less than total number of casting votes,

2) It must be more than half the total number of casting votes

3) The votes for any party can\'t be negative

In the second problem, the quota is 9, i.e. a person with 9 votes can dominate and come in power, since the v1 has 9 votes and hence v1 has the complete control over the voting system

v1 voter is the dictator, since where all parties together come in alliance the governement will be only formed by the v1 members

No, the system can\'t have two dictators, since the quota must be more than half the total votes, hence no two voters can have more than half the total seats