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I think Rufus Drumknott should be given an entry by this point, though I'm not totally sure where to start with him. Once the entry's been made, it'll be easier for tropes to trickle in.
Who is Constable Wee Mad Arthur?
Do you mean constable Buggy Swires? He's the bird-riding watchman, and though he's been described as a "gnome," Pratchett has stated that there "might not be a difference between gnomes, pictsies, and feegles." Furthermore, Wee Mad Arthur only appeared once (to my knowledge, i have yet to read snuff) in Feet of Clay as a free-lance rat-catcher, and was sworn as a watchman only temporarily by a very desperate Fred Colon. I do not believe the position was formalized.
Wee Mad Arthur is, indeed, in Snuff as a constable.
What are we supposed to file Eskarina Smith under now that she's no longer a one-book-wonder and shows up in the latest Tiffany Aching book? To further complicate matters, she isn't really a witch, isn't really a wizard either.
I removed Anti-Hero from Vimes. While he's very much a Knight in Sour Armor, I don't think he fits many of the traits listed under Anti-Hero. Amoral? Hardly. Undesirable or sociopath attributes? Addiction Displacement from alcohol to tobacco. Redeeming qualities? Cares for his family, his men, and his city. Breaks the law to get his way? Not according to the end of Night Watch.
He bends the law. He isn't nice. Carrot is The Cape. The Ideal Hero. Vimes falls short: he is flawed, he hates people, he is an alcoholic. He is an Anti-Hero.
You're looking too far at the extreme end of Anti-Hero. Knight in Sour Armor is a type of Anti-Hero because the antihero is a flawed hero. Opposed to the Ideal Hero.
That's why KISA is a subtrope of Anti-hero.
Should Tiffany Aching be merged with the witches? Granny Weatherwax (and to some degree Nanny Ogg) play a large role in A Hat Full of Sky and Wintersmith. I suppose the main reason not to, besides different target audiences, is that the first witch books were about the power of stories while Tiffany's books are about personal development.
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How well does it match the trope?