Why do this problem?
It is an exercise
in simple probability and combinatorics that provides an intriguing and paradoxical situation for investigation.
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.
How many possible sets of choice can be made in total by the voters?
How many of these sets are intransitive?
See the problems A Dicey Paradox
and Winning Team
and the article Transitivity.