Fairness (A) and the Recharge Round

In the last post, I suggested that the strength of a fairness (A) claim can be assessed according to the the source of the expectation that it is based on, and according to the reliance placed on those expectations.

Let’s explore some of the possibilities in a particular context. There’s a 64-team double-elimination tournament. The winner of the upper bracket is defeated by the winner of the lower bracket in one game. There is no recharge round – the upper bracket winner does not get another chance to win the title. Is this fair?

From a fairness (C) perspective, there may be a reasonably clear answer: in a low-luck game like tennis, it is fairer to have a recharge round, but in a high-luck game like baseball it is fairer not to have one. But this result is not well known – the matter is more likely to be resolved by appealing to fairness (A). How strong is the fairness (A) claim that there should have been a recharge round?

In this post, I’ll discuss the source of the expectations, and in the next I’ll discuss reliance.

If the tournament organizers announced in advance that there would (or would not) be a recharge round, any expectation to the contrary is a weak one. For most people, this should settle the question – the fair result is for the organizers to go ahead and do whatever it is that they said they were going to do. And, as a dispute about the recharge round is otherwise likely, it is incumbent on tournament organizers to make such an announcement. If the matter is decided after the players or teams involved are known to the organizers, the aggrieved party is likely to suspect that favoritism played a part.

But perhaps the organizers didn’t think to announce in advance whether there would be a recharge round. There might still be reasonable expectations one way or the other.

Let’s say that there was not explicit mention of any recharge round, but that the organizers posted a bracket sheet. If there is a space on the bracket for an “if needed” recharge round, that’s a pretty strong indication that there should be one. And if there is no recharge on the bracket, and particularly if the first meeting of the upper and lower bracket winners is labeled “championship game”, there’s a reasonable implication that there will be no recharge.

The source of a fairness (A) expectation is sometimes just the experience of having played similar tournaments. If recharges are common in tourneys for a particular game or sport, it’s reasonable for people to assume that they’ll be played even if there’s no specific announcement to that effect. Likewise, where recharges are not usually played, fairness (A) might be offended by including one.

For many people, the presence of a recharge round is inherent in the very name “double elimination”. If a team can lose only once and still not win the title, well, then it wasn’t really a double elimination, was it? For this very reason, directors who prefer to dispense with a recharge often avoid using the term “double elimination”. That can be problematical, however, as there’s no alternative term that’s as readily understood. Some directors speak of an event as a “modified double elimination” when the only modification they have in mind is not playing a recharge round.

3 thoughts on “Fairness (A) and the Recharge Round”

  1. What happened to the end of this post? Did it get eaten?

    It’s just wrong not to have a recharge round – the losers’ bracket is supposed to be second-tier, not equal status to the winners’ bracket. There’s just something wrong with the idea that the losers’ bracket champion can win the whole tournament with one more game.

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  2. I have no idea what happened, but I’ll clean it up a little. Thanks for bringing this to my attention.

    I don’t agree that dispensing with a recharge is just wrong, but I won’t quarrel with you. The point is that we’re talking about fairness (A) here, the fairness of expectations, and you have a strong expectation in favor of recharge – strong enough that you might still feel aggrieved even if it was announced in advance that there would be no recharge.

    I’m not sure I ever had your intuition that recharge was essential, but if I ever did the feeling has been eroded away to nothing by some of the work I’ve done, particularly the experiments showing that a recharge is often in derogation of fairness (C). There are also a number of non-fairness reasons to avoid recharges. But that’s the whole point – when we disagree about fairness, it’s often because we’re appealing to different aspects of fairness.

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