The "no lynch" idea bothers me quite a bit. Because as near as I can tell, a vote for "no lynch" is, in effect (if not necessarily by its proponents' design), a vote for the Mafia.
There are 9 of us right now, 2 of whom are Mafia. What happens if we lynch randomly? This:
- Day 1: we lynch someone. 2/9 chance of hitting Mafia. Say we miss.
- Night 1: the Mafia kills someone.
- Day 2: 7 of us left, 2 are Mafia. We lynch someone, with 2/7 success rate. Say we miss again.
- Night 2: the Mafia kills someone.
- Day 3: 5 of us left, 2 are Mafia. We absolutely must lynch a Mafia person this round, or we lose. We have a 2/5 chance of randomly succeeding at that.
Now, what happens if we go "no lynch" this round?
- Day 1: nothing happens.
- Night 1: the Mafia kills someone.
- Day 2: 8 of us left, 2 are Mafia. We lynch someone, with 2/8 success rate. Say we miss.
- Night 2: the Mafia kills someone.
- Day 3: 6 of us left, 2 are Mafia. We lynch someone, with 2/6 success rate. And we need to guess right. Why? Because if we miss...
- Night 3: ...the Mafia kills someone...
- Day 4: ...and there are 4 of us left, 2 Mafia, and the Mafia has won because there is no way to lynch them by majority vote anymore.
The upshot: if we lynch someone today, we get (at minimum) three chances to lynch Mafia before we lose the game. If we DON'T lynch someone today, we get only TWO chances to strike Mafia, and with less odds of success.
Now, math is not my field either, so I am interested to hear bozzball's (and other math-oriented folks') thoughts on this. But from this (admittedly cursory) analysis, it seems to me that a "no lynch" vote this day does nothing but hurt the town.