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Currently, Broken Ace and The Ace are merely related tropes. If there was a Super-Trope and Sub-Trope relationship, then you'd only be expected to list the more precise trope because the subtrope is always an example of the supertrope. Squidward from Spongebob should only list Jerk with a Heart of Gold because it is a Sub-Trope of Jerkass.
You can find the statement on Super-Trope; the trope relationship is defined by the idea that every subtrope also counts as an example of the supertrope (although subtropes are often created by playing with the supertrope). Link to TRS threads in project mode here.
There was a similar post about this fairly recently:
https://tvtropes.org/pmwiki/query.php?parent_id=71502&type=att
Both Sister Tropes should be listed. Only the Sub-Trope should be listed and the Super-Trope removed.
Exception: If there are several examples of Super-Trope, and only one of them is a Sub-Trope, both can be listed in this way:
- Example 1 - also a Sub-Trope, preferably with shorter description
- Example 2 - not a Sub-Trope
- Example 3 - not a Sub-Trope
Sub-Trope: Example 1, preferably with longer description
If you have doubt regarding trope relationships (Super-Trope and Sub-Trope or Sister Tropes), you can ask in this thread
.

Here's something that's been confusing me for a while. Okay, so I don't know what's the best way to properly ask this, but I'll give it a shot: Is it true that Broken Ace should be used instead of The Ace, rather than in addition to? I'd ask the same thing about Jerk with a Heart of Gold instead of Jerkass, Genius Ditz instead of The Ditz, etc.
I'm pretty sure I've seen this question asked before, but I can't remember what the answer was. Does it really depend on the character? For example, the character page for Squidward from SpongeBob uses both the Jerkass and Jerk with a Heart of Gold tropes, which really confuses me because how kindhearted he is depends on the writer (he is by default a cynical, pessimistic, narcissistic grouch but has shown himself able to warm up to others and the title character on numerous occasions, but only if the plot demands it).
This is overall confusing and I can't seem to find a rule about this in administrivia pages whatsoever. :/