If we had a voting profile that represented this tournament, we could use
it to construct a set of dice where any two dice have a third that
beats both, on average.
Here is a betting game you can play with two other friends:
- They each pick a die from the set, and you pick a third.
- You each roll your die.
- If you beat both of theirs, they each give you a dollar.
- If they both beat yours, you give each of them a dollar.
- If you only beat one of theirs, no money is
- Roll again and repeat.