Tie Types

[JMMackenzie]

There have been a few papers recently focusing on the types of ties present in sets and rankings, most recently: https://dl.acm.org/doi/10.1145/3731120.3744582

This opens a question on how to handle different types of ties in both sets and rankings. For example, we can have ties that we believe are definitely ties, or ties that are borne out of indecision, and they can both be treated differently.

My view is that to handle this, we should/could:

1. Store the type of tie as a property of the observation and/or reference; and
2. Have the user explicitly tell us which type of tie is under consideration for both (perhaps with a default);
3. Compute and output the appropriate metric based on the user values.

This issue is open so we can discuss this explicitly. In the paper above, the two types of ties are:

• APX: Meaning approximate - ties only occur due to indecision; and
• EQL: Meaning equal - tied elements are really to be considered equivalent.

I think we can essentially build an enum type for these, and then store them as a member of the RBSet and RBRanking types.