Let me explain the lynching vs not lynching thing
Let's assume we suck and always miss, the mafia never fails, and no one else has a kill
Day 1
13 Not-mafia
2 Mafia
2/15 chance to hit
Day 2
11 Not-mafia
2 Mafia
2/13 chance to hit
Day 3
9 Not-mafia
2 Mafia
2/11 chance to hit
Day 4
7 Not-mafia (we actually lost at this point if there are still 2 Illuminati, but I'll pretend they don't exist)
2 Mafia
2/9 chance to hit
Day 5
5 Not-mafia
2 Mafia
2/7 chance to hit
Day 6
3 Not-mafia
2 Mafia
2/5 chance to hit
So if we lynch totally randomly like this, our chances of losing without lynching a single mafia are 13*11*9*7*5*3/(15*13*11*9*7*5) = 1/5 = 20%
But, say we no lynch on day 1. Then it would go like this with the same assumptions
Day 1
13 Not-mafia
2 Mafia
0 chance to hit
Day 2
12 Not-mafia
2 Mafia
1/7 chance to hit
Day 3
10 Not-mafia
2 Mafia
1/6 chance to hit
Day 4
8 Not-mafia (we actually lost at this point if there are still 2 Illuminati, but I'll pretend they don't exist)
2 Mafia
1/5 chance to hit
Day 5
6 Not-mafia
2 Mafia
1/4 chance to hit
Day 6
4 Not-mafia
2 Mafia
1/3 chance to hit
And our chances to miss every time are therefore 6*5*4*3*2/(7*6*5*4*3) = 2/7 = 28.6% ish
Now you can make the argument that more voices means better lynches down the line, but that assumes that people's opinions have a decent chance of being valid. This also means that the mafia has total control over what voices stop being heard, until we start lynching anyways, so they can eliminate the voices that are actually beneficial and providing information. And if everyone is waiting to lynch until we have something perfect, no one is actually going to be speaking anyways. Generally the solid information provided when someone dies is more useful than the flimsy (and possibly outright false, through malicious intent or not) information provided by discussion.
"You rubbed me the wrong way!"
"Yeah, it's Ciffy; that's literally what he does to people"
"Fair enough."
"FD DIDN'T JOKE LYNCH TC!"
"Yeah because I haven't done that in several games?"
"TC isn't in this game."
"GOD DAMMIT FD KILLED TC ALREADY!"
That sounds like a joke, but mafia games are super prone to utter nonsense. It's really just a witch hunt until we have something solid. Like reveals after death. The game is about building something ordered from a disordered system.
...
We're literally violating the Second Law of Thermodynamics like a spin-echo experiment and you should all be ashamed.