Seeding problem for a 3-way bracket I apologize in advance if this is not the correct place for this question. I'm going to be running a 36-person tournament in a certain activity, with the first two rounds being 3-way competitions (36->12->4).
My question is how to fairly seed these 3-way tournaments. Before the round of 36, I'll have a good idea of player strength, and the seeds will reflect that strength. I can either decide matchups by seed or by a rough estimation of player strength.
My idea was to give the highest strength of schedule to the 36th seed, the 2nd-highest to the 35th seed, etc. Is there any good method out there for figuring out matchups so that this can happen, or is there another method which would be appropriate for seeding such matchups?
 A: Usually, scheduling based on seeding seems to be set up to improve the chance to retain the better players. 
Here's one obvious possibility:
Going by seed, if we want to maximize the chances of keeping the top few seeds, we want the highest seed they face to be low and within that, the average seed they face to be fairly low. 
One approach: Consider that the second-best player in each group is the 'main danger' to the top seeds. We can hold the average of the seedings of the 2nd and 3rd ranked player in each group constant, while keeping the lowest of the second-ranked seeds for the top seed, the second-lowest second-ranked player for the second seed and so on:
 1 24 25
 2 23 26
 3 22 27
 4 21 28
 5 20 29
 6 19 30
 7 18 31
 8 17 32
 9 16 33
10 15 34
11 14 35
12 13 36

This has the advantage that the top second-ranked players also have a reasonable chance to go through (it's not that much worse being 13th seed than 12th), so the difficulty of the draw for the top 2/3 of players seems to increase relatively smoothly. It might be particularly appropriate for the top 2/3 of players if the strengths in the bottom third are more nearly even than in the top groups (though the bottom-ranked players might then argue that the schedule for 36 is easier than for 25).
You could flip the third column top to bottom, but it's not clear to me that it's better. This would make the progression from easy to hard more rapid as you go down the first column of seed (weighting it more strongly to the top few seeds):
 1 24 36
 2 23 35
 3 22 34
 4 21 33
 5 20 32
 6 19 31
 7 18 30
 8 17 29
 9 16 28
10 15 27
11 14 26
12 13 25

This could be more suitable, for example, if the strength in the bottom third goes down more quickly than in the top groups (if the top seeds were more nearly evenly matched than the lowest-ranked 12 players were). If you want to focus on the task for the bottom 12 players, this makes the progression in difficulty more clear for them.
If you have some model for the chances of going through that might give you a better idea of which of those schedules will have the best chances of giving outcomes that are 'desirable'.
