This discussion reminds me of a scene in
The Twelve Tasks of Asterix where he is about to race the best Olympic runner in the world, and he jokes that they also have races in their village but it's not that exciting because everyone drinks the magic potion, so they all finish at the same time and have the winner be decided by lottery. Guess that's another (slightly unsatisfying) hypothetical solution to the problem ;). Useful as a thought experiment though
https://www.youtube.com/watch?v=qHCPot1j0ug&t=14m30s