Elimination system where both opponents can lose

Question

Is there any tournament system that deals with the fact that both opponents can lose? Or is there an easy, non-complicated and fair way of modifying an elimination-like system to deal with it?

Context

I'm doing in historical fencing (HEMA). In this type of fencing, we want to strongly discourage so-called double hits, i.e. a situation in which both opponents hit each other at approximately the same time.

When we do tournaments, there are several options of dealing with double hits. The simplest one is that a double hit is a point for both opponents but that does not discourage the double hits, on the contrary, it encourages it in some situations (one of the opponents is one point from victory while the other one is not).

Another system is that double hits are not counted at all. This is a bit better but it can lengthen the matches.

The last system is that double hits are punished by both opponents losing (either right away or after some amount of double hits). This last option is closest to what we would want - it punishes double hits and can be scaled depending on the experience of the contestants (by the amount of double hits allowed). However it has one major drawback: it works only in round-robin-like tournament systems and any elimination-like system is broken by the fact that both opponents should lose. Hence my question.

Answer 1

You are essentially asking for two contradictory things. You want a single-elimination system where (1) there is a winner of each match, so that there is an opponent for the next round, and (2) there is no winner of the match. You need to decide which factor is more important to you.

Here are the options that I see:

1. If it's most important that there be a winner of the match, then you need to decide on a "tiebreaker" that determines who wins, or otherwise award one of the players the win even though you don't really want to.

2. If it's most important that there be a player for the next round, but you really don't want it to be one of the players that was disqualified in the current round, then you need to decide on some sort of "tiebreaker" to determine somebody who moves forward in that slot despite not being one of the original players. For example, it may be that the highest-scoring non-disqualified loser of that round ends up with a "wild card" of sorts and ends up paired in the next round, despite having lost their "own" match. This of course doesn't really help if your double-loss happens in the final round, and could lead to some weird cases especially if double-losses are common and you run out of "wild cards". (Plus, it's probably just going to be confusing for everybody.)

3. If it's most important that there be no winner, then you need to just accept that nobody moves on for that round, and the next round opponent gets a bye. (And it will be really unsatisfying for everybody if it happens in the final round, to end a tournament with no winner and two "finalists".) For what it's worth (just because this is the game which I'm most familiar with the tournaments of, or at least I used to be), for competitive tournaments in the Magic: the Gathering card game, if an event is single-elimination, and both players lose due to a match-loss penalty resulting in a double-loss, this is the way it's handled and the next round opponent gets a bye. I'm not aware of this ever having happened in practice, as both match-loss penalties and single-elimination tournaments are rather rare.

Really, for any tournament with matches more complicated than results that are clearly "win" or "loss", you want to look for alternatives to elimination bracket formats. Elimination-format tournaments don't deal well with anything beyond winning and losing, such as ties, double-losses, ranking based on score, or players withdrawing. If you want a format where people can earn (for example) 0 for loss, 1 for tie, or 2 for win, where each player could get any of those values, you want something like Swiss or Round Robin.

And if I could expand for a bit beyond what you're directly asking, it sounds like your actual problem is trying to find the right method of including "penalties" in your matches. This has been handled in many different ways by different games, and it's probably worth looking at a few. For your particular issue, perhaps you want to allow for double-hits to count as a point (or half a point?) for both players, but not allow it to count for a player for which it would then award a win (or within n points of winning). Or perhaps a double-hit gives some kind of "strike" separate from the score, which is used for tiebreaking, seeding, invites to future events, or just plain public shaming but doesn't directly impact the result of that particular match.