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.