I think it's most likely the mafia doesn't have a way to affect a 1-time daypower directly, or at least effectively. The best thing they can do is, and me explaining this would defeat the purpose of Chair asking the question, is to bluff their way, and ask to be investigated. Of course, if there is anyone amongst the mafia who would appear good anyway, this person would be safe. Chair just wants to see the reactions to his question, decide who's reactions he deems genuine, and then for maximum effect he should go for a random person amongst the people who's reactions he doesn't deem genuine or who didn't react at all or defensively.