Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
When a President is elected in the United States it is not the popular vote that matters but winning a victory in the Electoral College. This raises a variety of mathematical questions. One issue stems from the fact that in essence the Electoral College is a "weighted voting game" because usually the winner of the popular vote in a state wins all of the Electoral College votes for that state. Furthermore, the Electoral College to some extent distorts the way candidates campaign. If a candidate thinks there is no chance of winning the popular vote, say in New York State, why would that candidate spend time and money to campaign in New York? This reality gives undue influence to the results of polls, which are often unreliable, and more importantly means that two voters in different states often don't have equal importance in their role in electing the President.
The five towns in a certain New York State 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?
a. Do the weights above reflect the "power" or "influence" of the players?
b. 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?