Support for partial/incomplete orderings without enforcing ties

[ZhuRuncong]

I’m working on a game system where rounds return incomplete orderings — some teams are known to be better than others, but the relative ordering between certain pairs is intentionally undefined.

This is not a case of all teams tying, nor of a full ranking. Rather, it resembles a partial order like:

Team A, Team B > Team B, Team C
where the relation between A and B is not defined, i.e., they are not tied, but also not comparable in this game instance.

Is there a way to currently model this?

[glandfried]

I do not understand this notation:

Team A, Team B > Team B, Team C

Can you explain how to interpret it?

[ZhuRuncong]

Sorry mistake in my original post, I had meant
Team A, Team B > Team C, Team D
i.e. A and B beat C and D

However, A and B are neither in a team, nor tied, we only know the outcome of this match in the fact that both A and B have beaten team B and C

[glandfried]

I saw two options.

1. If the outcomes comes from independent games, just do

A > C
A > D
B > C
B > D

2. If the outcome comes from just one game,

(A+B) > (C+D) treating both sides as teams.

3. Others options are, treating one side as a team

A > (C+D)
or
(A+B) > C

I do not know much about the context so I don't know which is the best option

[ZhuRuncong]

The context is there is a 4 team, 1v1v1v1 game (i.e. they do not work together), where the outcome is that 2 teams "win" and the other 2 "lose". What would you recommend as the best option?
Also, to clarify my understanding, what is the difference between independent games and non-independent games? What is the difference between [(A > B > C)] and [(A > B), (A > C), (B > C)] (where skill doesn't change i.e. in the same time period)?

[glandfried]

Version V2.0.0 is coming soon.