Mafia isn't RP unless you want to make a story about it and explain reasoning, logic, discussions, and arguments in a very story-like fashion as well as "playing the role" of a specific character with things such as names, backstories, adventures, and such case, which in most cases, as we saw in I believe Mafia Season 3, does not work well and generally confuses the player within the Mafia game.
If you want RP, look at Duffie's Minecraft RP, The Afterstory, or the Zombie Apocalypse roleplay for forum sights, or take a gander at RPing in games such as in World of Warcraft, Everquest, Eve Online, and other MMO's as well as a number of RPG's.
This is certainly not "RP" in the traditional sense.
Mafia is a "party-game." It's just a game. You have a goal like any other game, which is to either survive the Mafia, or kill them off. Nothing really more to it.
So this post is just to clear that up.