I thought this would be easier if I assume the Fire Mafia will kill Volt, and it turns out it is... slightly.
Assumptions:
Fire Mafia will Kill Volt and then Ice hunt.
Ice Mafia will Fire hunt.
Volt will not use his Doctor power to protect anyone.
Note:
Underlined, italicised text means options that are statistically worse for Town and should therefore theoretically not be taken. I have omitted the details by which I determined which was worse, but it's not too hard to work out if necessary.1 IC, 4 VT, 2 scum
Lynch VT (2/3): 1 IC, 3 VT, 2 scum
- Ice kills VT (3/4): 2 VT, 2 scum
- Lynch VT (1/2): 1 VT, 2 scum
- 1 VT dies, 1 scum dies (1/2): LOSE (total = 2/3*3/4*1/2*1/2 = 1/8)
- 2 scum die (1/4): WIN (total = 2/3*3/4*1/2*1/4 = 1/16)
- Nobody dies (1/4): LOSE* (total = 2/3*3/4*1/2*1/4 = 1/16)
- Lynch scum (1/2): LOSE (total = 2/3*3/4*1/2 = 1/4)
- No-lynch: 2 VT, 2 scum
- 2 VT die (2/9): LOSE (total = 2/3*3/4*2/9 = 1/9)
- 1 VT dies, 1 scum dies (4/9): LOSE (total = 2/3*3/4*4/9 = 2/9)
- 2 scum die (1/9) WIN (total = 2/3*3/4*1/9 = 1/18)
- Nobody dies (2/9): 1 KVT, 1 VT, 2 scum
- Lynch KVT (1/4): 1 VT, 2 scum
- 1 VT dies, 1 scum dies (1/2): LOSE (total = 2/3*3/4*2/9*1/4*1/2 = 1/72)
- 2 scum die (1/4): WIN (total = 2/3*3/4*2/9*1/4*1/4 = 1/144)
- Nobody dies (1/4): LOSE* (total = 2/3*3/4*2/9*1/4*1/4 = 1/144)
- Lynch VT (1/4): WIN** (total = 2/3*3/4*2/9*1/4 = 1/36)
- Lynch scum (1/2): LOSE (total = 2/3*3/4*2/9*1/2 = 1/18)
- No-lynch: 1 KVT, 1 VT, 2 scum
- 1 VT dies, 1 scum dies (1/2): LOSE (total = 2/3*3/4*2/9*1/2 = 1/18)
- 2 scum die (1/4): WIN (total = 2/3*3/4*2/9*1/4 = 1/36)
- Nobody dies (1/4) 2 KVT, 2 scum => no-lynch: WIN** (total = 2/3*3/4*2/9*1/4 = 1/36)
- Ice kills Fire (1/4): 3 VT, 1 scum => no-lynch: 2 VT, 1 scum
- Lynch VT (2/3): LOSE (total = 2/3*1/4*2/3 = 1/9)
- Lynch scum (1/3): WIN (total = 2/3*1/4*1/3 = 1/18)
Lynch scum (1/3): 1 IC, 3 VT, 1 scum => IC dies: 3 VT, 1 scum => no-lynch: 2 VT, 1 scum
- Lynch VT (2/3): LOSE (total = 1/3*2/3 = 2/9)
- Lynch scum (1/3): WIN (total = 1/3*1/3 = 1/9)
No-lynch: 1 IC, 4 VT, 2 scum
- Ice kills VT (4/5): 3 VT, 2 scum
- Lynch VT (3/5): 2 VT, 2 scum
- 2 VT die (2/9): LOSE (total = 4/5*3/5*2/9 = 8/75)
- 1 VT dies, 1 scum dies (4/9): LOSE (total = 4/5*3/5*4/9 = 16/75)
- 2 scum die (1/9) WIN (total = 4/5*3/5*1/9 = 4/75)
- Nobody dies (2/9): 1 KVT, 1 VT, 2 scum
- Lynch KVT (1/4): 1 VT, 2 scum
- 1 VT dies, 1 scum dies (1/2): LOSE (total = 4/5*3/5*2/9*1/4*1/2 = 1/75)
- 2 scum die (1/4): WIN (total = 4/5*3/5*2/9*1/4*1/4 = 1/150)
- Nobody dies (1/4): LOSE* (total = 4/5*3/5*2/9*1/4*1/4 = 1/150)
- Lynch VT (1/4): WIN** (total = 4/5*3/5*2/9*1/4 = 2/75)
- Lynch scum (1/2): LOSE (total = 4/5*3/5*2/9*1/2 = 4/75)
- No-lynch: 1 KVT, 1 VT, 2 scum
- 1 VT dies, 1 scum dies (1/2): LOSE (total = 4/5*3/5*2/9*1/2 = 4/75)
- 2 scum die (1/4): WIN (total = 4/5*3/5*2/9*1/4 = 2/75)
- Nobody dies (1/4) 2 KVT, 2 scum => no-lynch: WIN** (total = 4/5*3/5*2/9*1/4 = 2/75)
- Lynch scum (2/5): 3 VT, 1 scum => VT dies: 2 VT, 1 scum
- Lynch VT (2/3): LOSE (total = 4/5*2/5*2/3 = 16/75)
- Lynch scum (1/3): WIN (total = 4/5*2/5*1/3 = 8/75)
- No-lynch: 3 VT, 2 scum
- 2 VT die (3/8): LOSE* (total = 4/5*3/8 =3/10)
- 1 VT dies, 1 scum dies (3/8): 2 VT, 1 scum
- Lynch VT (2/3): LOSE (total = 4/5*3/8*2/3 = 1/5)
- Lynch scum (1/3): WIN (total = 4/5*3/8*1/3 = 1/10)
- 2 scum die (1/16): WIN (total = 4/5*1/16 = 1/20)
- Nobody dies (3/16): 1 KVT, 2 VT, 2 scum
- Lynch KVT (1/5): 2 VT, 2 scum
- 2 VT die (2/9): LOSE (total = 4/5*3/16*1/5*2/9 = 1/150)
- 1 VT dies, 1 scum dies (4/9): LOSE (total = 4/5*3/16*1/5*4/9 = 1/75)
- 2 scum die (1/9) WIN (total = 4/5*3/16*1/5*1/9 = 1/300)
- Nobody dies (2/9): 1 KVT, 1 VT, 2 scum
- Lynch KVT (1/4): 1 VT, 2 scum
- 1 VT dies, 1 scum dies (1/2): LOSE (total = 4/5*3/16*1/5*2/9*1/4*1/2 = 1/1200)
- 2 scum die (1/4): WIN (total = 4/5*3/16*1/5*2/9*1/4*1/4 = 1/2400)
- Nobody dies (1/4): LOSE* (total = 4/5*3/16*1/5*2/9*1/4*1/4 = 1/2400)
- Lynch VT (1/4): WIN** (total = 4/5*3/16*1/5*2/9*1/4 = 1/600)
- Lynch scum (1/2): LOSE (total = 4/5*3/16*1/5*2/9*1/2 = 1/300)
- No-lynch: 1 KVT, 1 VT, 2 scum
- 1 VT dies, 1 scum dies (1/2): LOSE (total = 4/5*3/16*1/5*2/9*1/2 = 1/300)
- 2 scum die (1/4): WIN (total = 4/5*3/16*1/5*2/9*1/4 = 1/600)
- Nobody dies (1/4) 2 KVT, 2 scum => no-lynch: WIN** (total = 4/5*3/16*1/5*2/9*1/4 = 1/600)
- Lynch VT (2/5): 1 KVT, 1 VT, 2 scum
- 1 VT dies, 1 scum dies (1/2): LOSE (total = 4/5*3/16*2/5*1/2 = 3/100)
- 2 scum die (1/4): WIN (total = 4/5*3/16*2/5*1/4 = 3/200)
- Nobody dies (1/4): WIN** (total = 4/5*3/16*2/5*1/4 = 3/200)
- Lynch scum (2/5): 2 VT, 1 scum
- Lynch VT (2/3): LOSE (total = 4/5*3/16*2/5*2/3 = 1/25)
- Lynch scum (1/3): WIN (total = 4/5*3/16*2/5*1/3 = 1/50)
- No-lynch: 1 KVT, 2 VT, 2 scum
- 2 VT die (2/9): LOSE* (total = 4/5*3/16*2/9 = 1/30)
- 1 VT die, 1 scum die (4/9): 2 VT, 1 scum
- Lynch VT (2/3): LOSE (total = 4/5*3/16*4/9*2/3 = 2/45)
- Lynch scum (1/3): WIN (total = 4/5*3/16*4/9*2/3 = 1/45)
- 2 scum die (1/9): WIN (total = 4/5*3/16*1/9 = 1/60)
- Nobody dies (2/9): 2 KVT, 1 VT, 2 scum
- Lynch KVT (2/5): 1 KVT, 1 VT, 2 scum
- 1 VT dies, 1 scum dies (1/2): 2 VT, 1 scum
- Lynch VT (2/3): LOSE (total = 4/5*3/16*2/9*2/5*1/2*2/3 = 1/225)
- Lynch scum (1/3): WIN (total = 4/5*3/16*2/9*2/5*1/2*1/3 = 1/450)
- 2 scum die (1/4): WIN (total = 4/5*3/16*2/9*2/5*1/4 = 1/300)
- Nobody dies (1/4): WIN** (total = 4/5*3/16*2/9*1/4 = 1/300)
- Lynch VT (1/5): WIN** (total = 4/5*3/16*2/9*1/5 = 1/150)
- Lynch scum (2/5): 2 VT, 1 scum
- Lynch VT (2/3): LOSE (total = 4/5*3/16*2/9*2/5*2/3 = 2/225)
- Lynch scum (1/3): WIN (total = 4/5*3/16*2/9*2/5*1/3 = 1/225)
- No-lynch: 2 KVT, 1 VT, 2 scum
- 1 VT dies, 1 scum dies (1/2): 3 VT, 1 scum => no-lynch: 2 VT, 1 scum
- Lynch VT (2/3): LOSE (total = 4/5*3/16*2/9*1/2*2/3 = 1/90)
- Lynch scum (1/3): WIN (total = 4/5*3/16*2/9*1/2*1/3 = 1/180)
- 2 scum die (1/4): WIN (total = 4/5*3/16*2/9*1/4 = 1/120)
- Nobody dies (1/4): WIN** (total = 4/5*3/16*2/9*1/4 = 1/120)
- Ice kills Fire (1/5): 4 VT, 1 scum
- Lynch VT (4/5): 3 VT, 1 scum => VT dies: 2 VT, 1 scum
- Lynch VT (2/3): LOSE (total = 1/5*4/5*2/3 = 8/75)
- Lynch scum (1/3): WIN (total = 1/5*4/5*1/3 = 4/75)
- Lynch scum (1/5): WIN (total = 1/5*1/5 = 1/25)
So if we lynch:
Pr(WIN) = 1/18+1/36+1/36+1/18+1/9 = (2+1+1+2+4)/36 = 10/36 = 5/18 ~ 27.8%
Pr(LOSE) = 1/9+2/9+1/18+1/9+2/9 = (2+4+1+2+4)/18 = 13/18 ~ 72.2%
If we no-lynch:
Pr(WIN) = 1/10+1/20+1/45+1/60+1/180+1/120+1/120+4/75+1/25 = (180+90+40+30+10+15+15+96+72)/1800 = 137/450 ~ 30.4%
Pr(LOSE) = 3/10+1/5+1/30+2/45+1/90+8/75 = (135+90+15+20+5+48)/450 = 313/450 ~ 69.6%
*I am considering cases with 2 scum and 1 Town a loss for Town. Perhaps the Townie could convince one of the scum to no-lynch, but I wouldn't bet on it.
**If we assume that both scum are scumhunting, then in situations where it is Night and they both know exactly who the other is, then in theory that results in a win for Town. Obviously one may decide to kingmake and give the other the win, but if they play optimally they kill each other and hope the other decided to kingmake.
Now obviously we can't be sure that the Fire Mafia will kill Volt, but if he doesn't that just makes the no-lynch even better.
So statistically no-lynching (and continuing to no-lynch when appropriate) is better than lynching (and then no-lynching when appropriate) by around 2.6%. Of course if we compared no-lynching when appropriate to always lynching, it would be a significantly bigger difference. Of course if we trust our collective reads more than the individual reads and desire to scumhunt of the two remaining scum by at least 2.6%, then maybe we should lynch Today anyway. But I'm not sure that we do.
So as boring as it is, I think our best option is to
Vote: no lynch