Voting Activity (2017)

Prepared by:

Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451


web page:

The five towns in a certain county have populations of 900,000, 500,000, 500,000, 400,000, and 200,000. Is it reasonable for the legislature of this county to have 5 representatives who cast 9, 5, 5, 4, and 2 votes, respectively, where for action to be taken a "bill" needs to get 13 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 13 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 5 votes while player 5 casts 2 votes. Together players 2 and 3 cast 10 votes.

[ 13; 9, 5, 5, 4, 2]

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?