Hi!
I have been thinking about the topic of collusion, and how to prevent it.
First of all, there are at least three types of collusion:
1. One fencer throws a bout in a situation where his loss will hurt him little, but the other fencer stands to gain a lot in that competition.
2. One fencer throws a bout in a situation where he expects to have that favor done to him in a later competition.
3. One fencer throws a bout in a situation where he gains favors outside the competition, monetary or otherwise.
The two latter types are decidedly more difficult to prevent than the first, so I will only deal with the first type from now on.
There are two major ways of preventing an undesirable behavior:
1. Outlawing it, relying on outer monitoring for compliance.
2. Making it counterproductive in the eyes of the possible sinner, effectively putting the monitoring inside him.
If both are possible, the latter is usually better, since the monitoring is always vigilant, and other people are relieved of the duties of monitoring and punishing.
As it is, fencing relies on the 1st way (always) and also often uses competition formats that use way #2 – straight DE.
Straight DE has the advantages of being easy to understand, all bouts mean something, prevents collusion #1, and the winner being decided at the very end. Its drawbacks – only one bout for half of the competitors, single bad bout being very decisive, and good seeding necessary for fairness – are so important so that straight DE is fairly rare in fencing.
Below are some ideas on how to construct competition formats, which are as effective in preventing collusion as straight DE, but lack some of its drawbacks.
Apart from straight DE, other sports have tried two main formats to prevent collusion:
1. Single competitor limitation – many sports have formats where only one competitor, or team, may enter a given competition.
2. Sumo solution – several team members allowed in a given competition, but bouts between teammates are expressly forbidden. In a sumo competition, 40 competitors compete in a restricted round-robin format, each competitor having one bout each against the 15 other closest to him in rank. The intra-team bout prohibition gives a huge help to teams with several highly ranked competitors. It is called the Futogoyama factor, after a team that recently held spots #1, #3, #5, and two more in the #10-20 span. Their #1 met a much easier line of opponents than the overall #2, who did not have any teammates at all among the top 40. In the rare case that two competitors from the same team have the same number of wins after 15 bouts and both are candidates for total win, the there is a kettei-sen (playoff) and the intra-team prohibition rule is waived. Imagine a fencing competition where the top 40 from the whole world compete, and the Europeans did not have to bout against each other.
It is obvious that neither of these solutions would be acceptable in fencing. Here come my ideas on collusion-resistant competition formats.
Reverse DE
A usual DE tableau is written up, with the difference that the losers are demoted to the next round until an ultimate loser is found. All other fencers start over again until the second worst fencer is found, and so on until a winner is left standing. In order to speed things up and also prevent collusion, bouts between fencers who have fought before are not redone, the first result is used again.
Pro: Not at all rankings-sensitive, all bouts important, bouts become increasingly more important for the total result with time.
Contra: Long waiting times in the beginning, difficult to use load balancing where several events are competed more or less concurrently
Reverse DE -> straight DE
A few rounds of reverse DE are run. The results are then used to seed the survivors in a straight DE table, and rank those who fall out in the same round.
Pro: much faster than above, quite rankings-insensitive, crescendo being built
Contra: as above, but less
Quick-sort algorithm -> straight DE
Fencers are paired against each other in the same way as a quick-sort algorithm is used in a computer program to sort variables. It is possible to prove that this is the fastest possible way to sort so that all get exactly the right final result, provided that there are no upsets. The best fencers are then promoted to a straight DE.
Pro: Each fencer knows beforehand how many ranking bouts he will fence, total time for competition reasonably easy to estimate, thrown bouts are either useless for throwee or devastating for thrower, load balancing relatively easy
Contra: A single bad bout can be very important, fencers must run about the pistes a great deal, competition organizers must announce bout schedule only one bout in advance, high workload on bout committee and results runners
Modified poules -> straight DE
The same as the usual poules->DE format. The change is in how the poule results are calculated: each fencer fencers against every other in his poule, but in the final calculation he may not include the result of his best bout. In this way, a thrown bout would hurt the thrower a lot, while helping the throwee very little. Both fencers would lose incentive for collusion.
Pro: Little change from present
Contra: If you win a once-in-a-lifetime bout against someone ranked much higher than you, would you like to get that result tossed out in seeding?
Anyway, these are my musings. Anyone who has suggestions from further refinements on formats, or other comments?
Have a nice time!
Peter Gustafsson
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