Some EC proposals use modified Swiss. Therefore it is worth looking more into it. Proposals 1 and 3 use a constant 8 (or a similar value) rounds modified Swiss for their core stage, Proposal 2 uses a dynamic 9+ rounds. Both have to be studied separately to some extent. So far I have looked at the 9+ rounds variant:

Suppose we start with 32 players, drop out all players with 0 wins after 2 rounds and all players with 1 win after 3 rounds. Then from round 4 on, there are exactly 16 remaining players in the tournament. (One might further reduce this a tiny bit, but such would be fine tuning only.)

What can happen? The easy case is one top player is running away the field and the tournament will be over after exactly 9 rounds. In the other case, there will be 2 to a few players with the most wins after 9 rounds. Now one has two principle opinions of how to proceed:

1) Use forced pairings for the top wins players to contain an implicit KO within the Swiss. The side effect is that some KO pairs will repeat earlier pairs. Not all KO players will have such games or the same number of such repeated pair games.

2) Use automatic pairings also for the top wins players. The side effects will be: a) Part of these top wins players have played more games against other top wins players and now get easier opponents (could have two wins less) while the other part of these top wins players plays against each other (new pairs but now tough games). b) One or two more extra rounds than in (1) might be necessary.

Is (1) the more agreeable option? Also the constant 8 rounds variant of modified Swiss will use but start to contruct the contained KO earlier. Actually the 9+ rounds variant could also start a bit earlier than after round 9 with constructing the contained KO to hopefully avoid cases like exactly 5 players with the top number of wins after round 9.

Thus the tournament system design problem is: How in general to embed well a contained KO in a (modified) Swiss by using good and fair forced pairings so that the tournament ends with a single top wins player after the given constant number or a dynamic number (beyond a minimim) of rounds? What exactly can be called "good" and "fair" for this purpose?

SOS is not really a helpful measure here because (modified) Swiss (with fold pairing) tends to create top wins players with rather varying SOS values after ca. 8 to 10 rounds. Swiss for sure is not round-robin...

If we use automatic pairing, we can simply trust the program to create as fair pairings as possible. If we use forced pairings during late rounds though, then the burden on pairing well becomes great.

Surely there must be solutions but are they known? Or would the TDs have to learn by doing?

If you use automatic pairing, I assume non repeated pairings. We can get ther following result at the top (> means beats):
A > B > C > A.

No matter how many games you add with new rounds and opponents there is no guarantee that one of the three players loses.

For the late rounds of a modified Swiss, it is not necessary to let the top players play an extra, implicit round-robin. So I am not sure what you are aiming at.

In a constant rounds modified Swiss, automatic pairing might create the problem you suggest though.

I meant that option 2) should be ruled out and option 1) used in case of tied top after the fixed part.

I see.

For EC Proposals 1 or 3 (in their basic form), this would not be applicable though because they refer to a constant number of (e.g., 8) rounds modified Swiss.

Unlike you seem to indicate, it is not always necessary, I think, to start (1) only after the fixed part. If it can be foreseen that just after a fixed part (possibly) more than one player will have the most wins, then one can already start planning the rest of the tournament with the aid of forced pairings a bit earlier: like one, two, or (if one extremely cute) three rounds before that last round of the fixed part. Thereby the number of rounds afterwards could be decreased and the pairings could be made yet fairer (I hope) in some sense of fairness yet to be defined.

Small correction:

At the start of round 4 you have 4 players with 3 wins and 12 players with 2 wins.

What are you going to do with this winscore difference?

If you just ignore it then at the start of round 8 there is one player with 4 wins in round 4 /5/6 and 7

Suppose this player loses in round 8 (the dreaded scenario) then after round 8 there will be 3 players with 4 wins

To let the play against eachother you need 3 rounds a total the of 11 rounds


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