With the chain idea, no matter how the order is determined, we are practically guaranteeing at least 2 deaths and seriously risking 3. It's 3 if the weak doctor is unlucky or if the nk doesn't hit one of the other victims, and they are more likely not to hit someone already dying than they are to double up a death. 4 if everything goes wrong. 1 death if the weak doctor is lucky and the nk hits the CPR doctor's target.
That's probably the cost of doing business, but how does this help us catch scum? If a vig hits scum, then yeah. But otherwise, we won't know anything very helpful.
Here is my pairs idea. I don't know if it is better, but we might want to think about it.
2 ways to die: nk, quack // 2 protectors: Real, jk. // 2 Switch hitters: CPR, weak. // 4 neutral: naive, nurse, 2 scum. If nurse decided to claim, they would be removed from plan.
Players A - I. A, C, E, G and I are targeted. Assuming all town deaths for this exercise.
A and B Target C. C Dies, flips town.
C and D target E. E lives
E and F Target G. F Dies, flips town
G and H Target I. I Dies, flips town
I Targets A. A lives
We can infer a few things.
1. {A, B, G, H} contains at most one protector. If there is a protector, they were jk'd or nk hit their target as well.
2. None of them are the jk.
3. {A, B, G, H} contains the CPR doctor (If CPR was used when needed, then there would only be 2 deaths). They were paired with a neutral person (naive, nurse or scum).
4. F died without being targeted. They are weak or the nk target. G might be scum.
5. I is not the quack. A, B, D and H were not the nk target.
That's all I've got now. Maybe I'll think of more later.