Weighted voting is a concept in which voters with different numbers of votes or influences determine the outcome of an election. The more votes someone holds, the more weight she gets in deciding the result. A simple example is a shareholder meeting where 51% of votes are required to settle a decision. Five shareholders hold 15%, 25%, 10%, 30%, and 20% of the total shares. Each of the shareholders gets a weightage corresponding to the shares they hold.
A: 15%
B: 25%
C: 10%
D: 30%
E: 20%
In the above example, Player D gets the highest weight, and Player C has the lowest. Quota is the minimum weight required to pass the election. And in our case, the quota is 51%.
If q represents the quota, w1, w2, etc., denotes the weight of player 1, player 2, etc., then the shorthand notation of the voting system is written as:
[q: w1, w2, w3, w4, w5]
In our example, it is
[51: 15, 25, 10, 30, 20]
Dictator: When one entity has a weight equal to or more than the quota. There is no dictator in [51: 15, 25, 10, 30, 20], but the third entity is a dictator in [51: 10, 20, 52, 18]. A dictator can pass or block any resolution, and nobody can win a vote without the dictator.
A player has veto power if her support is necessary to reach the quota. In [10: 6, 5, 4], player 2 and player 3 can only get the quota with support from player 1. Player 1 has veto power. On the other hand, player 2 or player 3 has no veto power. No one has veto power in [10, 6, 5, 7].
A player is a dummy if her vote is never essential for a group to reach quota. Player 3 is a dummy in [10: 7, 4, 2].
