I need 21 and 23 please Can you give a convincing argument to show that, in a we

Question

I need 21 and 23 please Can you give a convincing argument to show that, in a weighted voting system of the form [Q; 1, 2, 2, ..., 2], the first individual will be a dummy if and only if the quota Q is even? Determine the Banzhaf indices of each individual in the weighted voting system [25; 25, 1, 1, 1] without listing all of the winning coalitions. Determine the Banzhaf indices of each individual in the weighted voting system [25; 13, 12, 1, 1, 1, 1] without listing all of the winning coalitions.

Explanation / Answer

There can be 2 cases,

i) Q is odd and

ii) Q is even.

i) Q is odd :

in this case Q is of type 2n+1.

Consider the case where keeping the first person aside, if the remaining '2n' persons vote equally i.e., 'n' vote to a party and other voting to second party. In this case the party who the first has selected wins

ii) Q is even :

Here q is of type '2n'. Keeping the first aside '2n-1' persons have to vote and this cant divided equally between the two . By this we can say there is atleast a difference of two points between the parties and the one point that first person has, can only effect the difference between both of them but it cannot alter the winning party.

So, the vote of first person is never significant when 'Q' is even and if 'Q' is odd his vote plays a vital role when the other '2n' voters vote equally.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.