Consider the weighted voting system 3q: 7, 5, 34. Find the smallest value of q for which

Chapter 2, Problem 7

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QUESTION:

Consider the weighted voting system 3q: 7, 5, 34. Find the smallest value of q for which (a) all three players have veto power. (b) P2 has veto power but P3 does not.

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QUESTION:

Consider the weighted voting system 3q: 7, 5, 34. Find the smallest value of q for which (a) all three players have veto power. (b) P2 has veto power but P3 does not.

ANSWER:

Step 1 of 6

The player is said to have veto power if all of the other players combined do not have enough votes to reach the quota. Let's denote the cumulative number of votes of all players with , the quota with , and the weight of the certain player with . If

 

the player with the weight  has veto power because the quota can not be fulfilled.

 

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