Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
The five towns in a certain county have populations of 1,500,000, 1,000,000, 900,000, 600,000, and 100,000. Is it reasonable for the legislature of this county to have 5 representatives who cast 15, 10, 9, 6, and 1 votes, respectively, where for action to be taken a "bill" needs to get 21 votes to pass?
The situation for a voting body of the kind above is sometimes called a weighted voting game. It can be represented by the notation below where 21 is the quota for a bill to be passed, the players are named 1 to 5 and their votes are shown from left to right. Thus, player 3 casts 9 votes while player 5 casts 1 vote.
Comment: Can the United States Electoral College be thought of as a weighted voting game? How many players are there? What are the weights of the players in this game?
What are the pros and cons of using weighted voting games as a tool for action in a democracy? Can you give examples of weighted voting games that are currently in use? What are the consequences of increasing the quota to 22, 23, etc. for votes where more than a simple majority is required?