The Voting Paradox

Three people, A, B and C go to a restaurant. They are told that their dinners will be half price if the all order the same thing, and they all agree to do so. The choices are chicken and steak. The three vote, and steak wins 2 to 1. So steak is chosen.

However, the waitress then informs the group that a third option exists: Ham. The group votes again, listing the three choices in order of preference. The results are: SCH, CHS and HSC. The textbook claims that this means you will select chicken because: “In the original steak/chicken choice you chose steak. However, we now see that ham is preferred to steak. Thus steak is out. However, in comparing chicken with ham, chicken is prefered to ham, so ham is out. Yes, you finish up selecting chicken!” This is obvious nonsense, since all members of the group would not agree to order chicken at that point. The person who voted for steak would make known that in comparing chicken with steak, steak is preferred. What has resulted is not a paradox but a simple tie, no different from what would happen if each person voted simply for their preferred meal and the votes came out: Chicken, Ham, Steak.

Various methods of voting can result in various “undesired” outcomes. Example: In 1992, Bill Clinton won the sufficient electoral college votes to become President. However, it is speculated that this occurred only because the conservative vote was split between George Bush and Ross Perot. If Perot had not run, George Bush might very well have won the election.

Under a parliamentary system, the final membership could wind up with 101 seats Liberal, 99 seats Conservative, and 4 seats Reform. Whenever the liberals and conservatives disagree in a vote, the Reform party wields power completely disproportionate to its representation.