Voting Activity (2018)

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? Twice in recent years the winner of the popular vote for the American president did not win the election.

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?