Voting Paradox
Why do this
problem?
It is an
exercise in simple probability and combinatorics that provides
an intriging and paradoxical situation for investigation.
Possible approach
The class could name 3 candidates to rank in order. Then everyone
could write down their order of choice. You could then take 3 at a
time and the class could discuss whether those three are transitive
or not. After discussing several sets of 3 rankings they should be
able to make conjectures about when the set will be transitive and
when it will be intransitive.
Key question
How many possible sets of choice can be made in total by the
voters?
How many of these sets are intransitive?
Possible support
See the problems
A Dicey Paradox and
Winning Team and the article
Transitivity.