Oh, and just for clarification, mafia shoots before vigilante.
That means, if the mafia pick the vig and the vig picks someone, only the vig dies. If they both visit the same person, the vig and that person dies. The only way the vig kills the mafia is to visit them without them visiting him.
This makes it harder for mafia to claim cop; you can now lynch between cops, and if the one you lynch is the REAL cop, the vig can shoot the fake. Just a thought.