Lynching is our power to influence the game. It is something the mafia can not control at this stage.
4 Mafia.
13 Civs.
If we lynch someone, we have a 23% chance of hitting a mafia. If we No-Lynch, the mafia get to start the game, with a 100% chance of killing a civ.
Also, at the very least, it sparks conversation and defences.
However, this game is a bit simpler, so i could be persuaded by No-Lynch, due to the (much smaller) possibility of hitting doc or cop.