# Meta-Tiebreaker

A meta-tiebreaker takes a fixed list of two or more tiebreakers and breaks a tie of a group of mutually tied players only if each of those tiebreakers creates the same relative order for those players.

The idea is to increase confidence. One tiebreaker applied alone as a particular next placement criterion is often criticized as having too little confidence. When several tiebreakers all give the same order, then that order has greater justification.

# Example 1

Consider a Swiss tournament, which naturally has Wins as the first placement criterion, that uses the meta-tiebreaker of the tiebreakers SOS, SOS-1, SOS-2, DirectComparison. The numbers in the column meta-tiebreaker are the players' final places.

Player Wins SOS SOS-1 SOS-2 DC Meta-Tiebreaker
P1 9 70 63 56 1 1
P2 9 69 62 54 0 2

Because all tiebreakers on which the meta-tiebreaker relies order the players P1 and P2 in the same manner, the meta-tiebreaker confirms this order.

# Example 2

Consider a Swiss tournament that uses the meta-tiebreaker of the tiebreakers SOS, SOS-1, SOS-2, DirectComparison.

Player Wins SOS SOS-1 SOS-2 DC Meta-Tiebreaker
P1 9 70 63 56 1 1
P2 9 70 62 54 0 1

Although SOS-1, SOS-2 and DC might suggest player P1 to be at place 1 and player P2 at place 2, since SOS suggests the players to be equal, the meta-tiebreaker does not break the tie: It lets both players be equal at the tied place 1.

# Example 3

Consider a Swiss tournament that uses the meta-tiebreaker of the tiebreakers SOS, SOS-1, SOS-2, DirectComparison.

Player Wins SOS SOS-1 SOS-2 DC Meta-Tiebreaker
P1 9 70 63 55 1 1
P2 9 69 62 55 0 1

Although SOS, SOS-1, and DC might suggest player P1 to be at place 1 and player P2 at place 2, since SOS-2 suggests the players to be equal, the meta-tiebreaker does not break the tie: It lets both players be equal at the tied place 1.

# Example 4

Consider a Swiss tournament that uses the meta-tiebreaker of these tiebreaking conditions:

• SOS
• DirectComparison
• Conflict: If exactly two players are tied on SOS and DirectComparison violates the SOS order, then each player's Conflict value is 0. Else Conflict is ignored.
Player Wins SOS DC Conflict Meta-Tiebreaker
P1 9 70 0 0 1
P2 9 69 1 0 1

There is a conflict between exactly two players involved: SOS and DirectComparison suggest a different order. Therefore the meta-tiebreaker, noticing this by the tiebreaker "Conflict", does not break the tie.

# Example 5

Consider a Swiss tournament that uses the meta-tiebreaker of these tiebreaking conditions:

• SOS
• DirectComparison
• Conflict: If exactly two players are tied on SOS and DirectComparison violates the SOS order, then each player's Conflict value is 0. Else Conflict is ignored.
Player Wins SOS DC Meta-Tiebreaker
P1 9 70 1 1
P2 9 69 0 2

There is no conflict between exactly two players involved: SOS and DirectComparison suggest the same order. Therefore the meta-tiebreaker breaks the tie: Player P1 gets place 1, player P2 gets place 2.

willemien This doesn't do what it says on the tin. It doesn't break ties. It even reduces the chanche on breaking ties. What to do in a situation like Example 2 what breaks the tie after the Meta-tiebreaker decide that there is no tie to break?

xela: Is meta-tiebreaker a commonly used term? Are there tournaments where it is applied? Can anyone link to tournament rule sets mentioning the term, or to discussion elsewhere? From a naive point of view, the word meta-tiebreaker could admit different interpretations; it's important to be clear on whether the usage described here is standard.

Bass: Funny how the example of SOS + coin toss is missing, since that seems to be what this page is essentially about.

• tapir: In the EGC2009 SOS and DC (if iterated) seems to agree for the first 4 places. A SOS + coin toss would have allowed for a tie here (with 50% probability) - which would have been a real improvement in my opinion.

RobertJasiek: a) I have discovered or rediscovered the concept today. b) If you can find a better name, suggest it. c) Since the concept is new, the term is of course not commonly used yet and the concept has not been applied yet. d) In my opinion, although "meta-" allows different meanings as a word, once the concept is known, the word is used well for it: It applies on a meta-level of calculation. One could also say: second level. e) Does this make "second-level tiebreaker" a better term? Too long. Maybe "secondary tiebreaker" but this could be confused with "of only secondary importance. Therefore I think "meta-tiebreaker" is better than that. f) In Example 2, why break the tie? Meta-tiebreaker is designed to break fewer ties. One can leave it at that. g) Since the meta-tiebreaker breaks fewer ties, it is not the first choice when the aim is to break all ties no matter what. h) Which tiebreakers to include into the list for meta-tiebreaking is up to discussion.

RobertJasiek: Reflecting it, I think several years ago some (mostly German) players suggested not to apply SOS when DC conflicts. Presumably this is where subconsciously I got the idea from. Whether the generalization had also been suggested informally before I can't recall.

Herman: I do not know whether meta is the right prefix for this, perhaps "combined" is better. The concept of combining tiebreakers is not new of course. The very common "first SOS, then SOSOS" tie breaker is a combined tie breaker which cascades (apply further tie breakers only if the earlier tie breakers have not broken the tie). Similarly, Jeff Boscole's research into tie breakers had the idea of summing tie breakers (he found that SOS+SODOS was good, IIRC). Other ways of combining are possible. One would be the one you describe above, which might be dubbed "consensus", and which I've not seen before. Another, similar, combination might be where the majority or plurality of tie breakers decides (with the option of a casting vote if the tie breakers are tied. :-)

RobertJasiek: Jeff's studies were, IIRC, made to optimize tiebreakers globally for all players in the tournament down to the weakest.

xela: On reflection I do think that the name "meta-tiebreaker" is liable to cause confusion. It implies that this page describes the only possible second-level tiebreaker. As Herman points out, there are other choices for second-level tiebreaking. Therefore, in my opinion, "meta-tiebreaker" should be a generic term that can refer to any second-level tiebreaker, and we need a specific name for the particular meta-tiebreaker described on this page. Unfortunately I'm not feeling inspired right now, so I don't have a good suggestion for a new name. Maybe Herman's idea of "consensus (meta-)tiebreaker"?

Eventually we can expect to see discussion regarding which of various meta-tiebreakers is "superior". I hope that such discussion will remain focussed, polite and constructive!

RobertJasiek: What about AND-tiebreaker? This is a very formalistic name though. Consensus-tiebreaker opens ambiguity, too. Democracy is about changing majorities, not about permanent, uniform agreement.

Herman: How about a generic page on "combining tiebreakers", with subpages named "by cascading", "by consensus", "by majority", "by summing". So this current page would become Combining Tiebreakers / by Consensus? (or perhaps "by Agreement").

RobertJasiek: SOS-SOSOS is a combining tiebreaker. This is something else than meta-tiebreakers. We can alter the contents of the meta-tiebreaker page to be the general page and then list the subtypes. Usually consensus and agreement are social actions, so I am not happy with these names. But apart from AND I cannot find some better so far.

Herman: The current page is also a combining tiebreaker, not a meta tiebreaker. Using the term "meta" correctly would mean, IMO, that a meta tiebreaker is a tiebreaker that decides between tiebreakers. If, for example, you run a tournament and specify: "Ties will be broken by DC if exactly two players are tied, otherwise by SOS", then "Number of Tied Players" is the meta tiebreaker that decides between the tie breakers SOS and DC.

We could describe the usual implementation of SOS-SOSOS as:

A ends above B if SOS(A) > SOS(B) OR ( SOS(A) == SOS(B) AND SOSOS(A) > SOSOS(B) )
B ends above A if SOS(A) < SOS(B) OR  ( SOS(A) == SOS(B) AND SOSOS(A) < SOSOS(B) )
A ties with B otherwise

We could similarly describe your proposed meta tiebreaker (of e.g. SOS+DC) as:

A ends above B if SOS(A) > SOS(B) AND DC(A) > DC(B)
B ends above A if SOS(A) < SOS(B) AND DC(A) < DC(B)
A ties with B otherwise

Very similar, once you write it out as a simple logical construct, so I think the term "combing tie breakers" applies to both quite well.

I think that Consensus is more of a procedural term, used in voting, while agreement is more of a social action. It would be very normal, for example, to write: "We all agreed to eat at restaurant A". But not to write "We achieved consensus to eat at restaurant A". On the other hand it would be more normal to write "The court reached it's verdict by consensus" than to say "The court reached its verdict by all agreeing with each other". Another term here might be Unanimity, which is even more formal that consensus (ie: "The court reach a unanimous verdict")

RobertJasiek: The major difference is: SOS-SOSOS can be expressed as SOS is applied with greater priority than SOSOS versus SOS and DC are applied with equal priority.

unkx80: From where I come from, once I see the "meta-" prefix combined with the "tiebreaker" measure, I knew straightaway that we are going to combine two or more tiebreakers. How these are combined is another question and not conveyed by the "meta-" prefix alone.

I don't think "AND-tiebreaker" is going to be a good name. What happens if the first tiebreaker ranks player A before player B, and the second tiebreaker ranks player B before player A? (Here, I am not interested to discuss the merits of different tiebreakers, but just assume that an ordered list of different tiebreakers is given as input.) Taking inspiration from the Apache Commons Collections API, I would suggest a name along the lines of "chained tiebreaker", if a more precise name is desired.

Meta-Tiebreaker last edited by Unkx80 on March 19, 2010 - 13:39