Ah, but stupidfighter, if tomorrow we end up with 2 1 1, which if SK and mafia know who the other is will happen (which we do), then town has no incentive to kill either side, right?
If you kill mafia, then SK kills you during the night, if you kill SK, mafia kills you during the night. Therefore, townie optimal strategy given 2 1 1 is to vote for a NoLynch, as far as I can tell. Town can't win 2 1 1 unless an evil side dies in the night. So town has to wait until SK kills mafia (mafia can't kill SK).
Now, SK. If I kill the mafia, the next day, my head is on the chopping block, town wins. No thanks. If I kill one of you I just force the stalemate.
As for Mafia, I think your analysis is sound, since he can't kill someone without causing stalemate.
Long story short, mafia won't kill in the night because it would cause a draw, SK won't kill during the night because it either causes draw or loss, and town won't shoot in the day because they don't have the numbers to win.