In my experience the mafia are so happy to be part of the "special" group that they don't mind a non50% (but still decent) chance of winning.'
Also, what is your opinion of the crazier roles, see: jester (If Jester gets lynched, he alone wins).
There's always that buzz factor. If your playgroup can supplement the brutal doc-cop combo with human lie detecting, the mafia should lose a lot more than 50% of the games. Setup balance is dependent on the strength of the players, though. Perhaps your playgroup's mafiosos are cunning enough that the doc-cop-combo is a fun incline to tackle (conventional thinking is generally that experienced playgroups lead to increasingly powerful towns rather than increasingly powerful mafia. In face to face, this is probably reversed, though)
Jester is a rather old topic of discussion. Jester is like KC and Possession, for 4$ each, out of a Black Market deck, when you've never heard of the cards before. It punishes the town for doing what they are supposed to be doing - lynching players not aligned with the town. Lynching players that don't seem interested in finding scum. It is bad design for that reason.
Good power roles reward players for using daytime discussion to find scum or town, like the Doctor. Mediocre power roles at least are neutral about it. Jester is just bad.
Many other "special" roles are accepted though. Serial Killer is a one man mafia and has it's own interesting psychological patterns. Generally the Serial Killer is given a 1 shot "bulletproof vest" to bring him close enough to a 33% chance of his faction's victory so he isn't miserable. Some people are okay with survivors (must live until mafia or town wins to win. It's no longer a zero sum game, punishes scumhunting that tends to lead to the survivor, thus I don't approve) and lynchers (must lynch player X to win, then they leave the game. Similar issues).
Cult is almost as widely unpopular as Jester, if you've heard of that. It's almost impossible to balance well and can punish what's normally good play.
EDIT: Whoa, Rhombus is citing sources as he discusses Monopoly??