To summarize, the chain should look like this:
A -> A's scumread -> A's townread (B) -> B's scumread -> B's townread (C) -> C's scumread -> C's townread (D) -> D's scumread -> A
Which is an 8 person chain, with whoever's left out replacing who's exiled.
So... we have a 2/9, or 22% chance, of picking skum to be the person that starts the chain. That would be like the one obvious horrible downside. IDK exactly why I guess, probably they pick their partner... but any which way, giving skum the choice is not good.
Weighing it against random though... I guess it is not horrible based on chance.
Any given doctor, has a 2/6 chance of being a killing doctor. That is 33%.
Any given doctor, has a 2/7 chance at targeting skum tonight. That is 28%.
So... and this is why I suck at math bc I have no clue if this is right or not... but that is a 9% chance if a doctor randomly chose a target, for them to TARGET skum.
Then you would have to factor in that person being doctored and things like that. So, let's just say random chance of a doctor being a killing doctor and randomly selecting a target, and that target is skum, and they actually kill them... is less than 9%.
Whereas, assuming we do not elect Skum to be the picker of course, it is still every doc has a 33% chance of being a doc, and every Doc Target has a 28% chance of being skum... so it is exactly 9% chance (opposed to less than 9% chance) if we follow the chain idea.
And then yeah, IDK what the chances in random are for "random good doctor preventing a town death is" because everything is so potentially open in random... but it is a small thing.
meh, even with the downside... I guess the plan still has it's merits.