[etyszpnp] Consecutive round robin

A series of smaller round robin tournaments, possibly applicable to chess Candidates.

A swiss system tournament to select the top 16.

A single round robin among those 16, selecting the top 8, 15 games per player.

A double round robin among the 8, selecting the top 4, 14 games per player.

A quadruple round robin among the top 4, selecting the top 2, 12 games per player.

A match between the top 2.

Another possibility has sizes 17, 9, 5 with a constant 16 games per tournament.  It has an odd person out every round.

Numbers for other possibilities given below.

I don't know about how much fraud and collusion will happen right along the bubble for each tournament.  Probably a lot.

Lessen the incentive for such fraud by having only the top (n-1) guaranteed to advance into the next tournament of size n, while the last entrant is selected among everyone else probabilistically weighted by tournament performance.  No one is ever eliminated until the end, and throwing any game lowers your probability of advancing.

Play a single elimination blitz among the players not automatically advancing to determine the last entrant.  When two players with round robin point difference of D meet in a blitz mini match, their scores are initially 4*D to 0, and the first to 4*D+1 points wins the match.  The multiplier 4 and offset +1 may be adjusted.

If there are multiple players tied on the bubble (after applying any tie break procedures), first a mini tournament among them to select the certain qualifiers, then the losers get relegated to the single elimination tournament.  Can these be combined?  Single elimination is not good for selecting multiple winners. Actually, I think the simplest solution of drawing lots to see who advances and who is relegated to the single elimination is the best.

To prevent players who have clinched advancing from throwing their games, round robin point totals carry over to the next round.

Number of games per player depending on round-robin tournament size and rounds in each mini-match:

16 player single (1) round robin 15 games
15 1 14
14 1 13
13 1 12

9 2 16
8 2 14
7 2 12

5 4 16
4 4 12

5 6 24
4 6 18
3 6 12