Voting Paradox
Why do this problem?
It is an exercise in simple probability and combinatorics that provides an intriguing 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 problem Winning Team and the article Transitivity.
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