The Math Anxiety Club Elections
The Math Anxiety Club, which has 37 members,
needs to elect a president. Four club members agree to be candidates:
Alice, Boris, Carmen, and Don. Assume that each member of the
club orders the candidates by preference. The table below gives
the number of members with each of these preference rankings.
The question you have to decide is: who
should win the election? Another way to put the question is this:
what is the proper way of counting these votes? Some possible
answers would be:
-look at the first place rankings only
-give points for the various ranks, and
add up the points
-look at what happens when each candidate
runs against one of the others
-do an "election with runoff"
What happens when you try these methods?
How does one decide which method to use?
A different question about voting:
Suppose you have a committee composed of
five people, each of which tends to make the right decision about
3/4 of the time. Does having the five people vote to decide increase
or decrease the likelihood of making the right decision?
"Math Anxiety Club" data taken from Excursions in Modern Mathematics, by Peter Tannenbaum and Robert Arnold. (Prentice-Hall, 1992)