Tiebreaker for the Olympic Games (Gamification Post #6)
Here’s a fun thought problem on a Monday afternoon, concerning the tie for third place in the US Olympic Trials. What is the better way to solve the tie for the one remaining spot on the team, toss a coin or run it off again? The competitors are being allowed to choose. According to my colleague at Saint Louis University, Eric Miller, the rules of games can tell us something about fair judging:
My claim is that the officials have a permission to use either method. What they’ve done is avoid deciding by delegating the decision over what method to use to the runners themselves: another permission (though of a different type). Judges don’t often have the option of delegating in this manner. But either method, coin toss or run off, is (in my view) equally supported by reason (and equally unsupported). The problem for judges (and other institutional decision-makers) lies in the fact that we normally want them to provide reasons, and, moreover, reasons that both support the winners and disfavor the losers. That is not possible where there are ties (or incomparabilities or incommensurabilities).
What do you think is the best way to break the tie?