Weighted voting systems
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Weighted voting systems are based on the idea that not all voters are equal. Instead, it can be desirable to recognize differences by giving voters different amounts of say concerning the outcome of an election. This type of voting system is used in everything from shareholder meetings to the United States Electoral College.
[edit] The Mathematics of Weighted Voting Systems
A weighted voting system is characterized by three things - the players, the weights and the quota. The voters are the players (P1 , P2 . . .PN ). N denotes the total number of players. A player's weight (w) is the number of votes he controls. The quota (q) is the minimum number of votes required to pass a motion. Any integer is a possible choice for the quota as long as it is more than 50% of the total number of votes but is no more than 100% of the total number of votes. Each weighted voting system can be described using the generic form [q: w1 , w2 . . .wN ]. The weights are always listed in numerical order, starting with the highest.[1]
[edit] The Notion of Power
When considering motions, all reasonable voting methods will have the same outcome as majority rules. Thus, the mathematics of weighted voting systems looks at the notion of power: who has it and how much do they have?[2] A player's power is defined as that player's ability to influence decisions.[3]
Consider the voting system [6: 5, 3, 2]. Notice that a motion can only be passed with the support of P1. In this situation, P1 has veto power. A player is said to have veto power if a motion cannot pass without the support of that player. This does not mean a motion is guaranteed to pass with the support of that player.[4]
A dummy is any player, regardless of his weight, who has no say in the outcome of the election. A player without any say in the outcome is a player without power. Dummies always appear in weighted voting systems that have a dictator but also occur in other weighted voting systems.[5]
