Alright, so uh are we into round 2 now? I believe we are moving there, and that will make me next president.
Eh... can you back that up somehow? I mean, going by last round's election process, Tables seem very liberal, so I'm intrigued to hear your points about how he is fascist.
So uh not to dig my own grave but bear in mind I was voting no because I knew it'd make me president 3rd, which is a powerful position to be in regardless of my loyalty. I don't think my votes last round really indicate much about my loyalty. There is the point that fascists did vote the mission up, to some degree at least, so maybe that's a minor point shifting probabilities towards me being liberal, but it's probably minor.
That said, I want to know why I'm suspected as well.
Helps know what I need to hide betterAnyway, I've just checked the numbers for last round. Basically re-checking EgorK's calculations. I believe that the chances are as follows:
FFF is 1/4
FFL is 1/2
FLL is 1/4
LLL is impossible as F was chosen.
Assuming Hitler is playing liberal (i.e. for now 'liberal' means 'liberal or Hitler'), which I think is almost certainly going to be the case on card 1, the chance of anyone being normal fascist is 1/3 (3/9) and the chance of being liberal is 2/3. For two given people it becomes a 1/12 chance (3/9*2/8 = 1/3*1/4).
Also assuming liberal doesn't lie
There are four cases which give the result we've seen:
1) Arch draws FFF and is liberal, ghost is any alignment (1/4*2/3 = 1/6 = 6/36)
2) Arch draws FFF and is fascist, ghost is any alignment (1/4*1/3 = 1/12 = 3/36)
3) Arch draws FFL and is fascist, ghost is any alignment (1/2*1/3 = 1/6 = 6/36)
4) Arch draws FLL and is fascist, ghost is fascist (1/4*1/12 = 1/36)
These probabilities don't add up to 100% because the remaining probabilities are those of an L being played instead. In total that means the probability of getting an F played here was 16/36, so given an F was played what we actually get as our odds are:
1) Arch draws FFF and is liberal, ghost is any alignment - 6/16
2) Arch draws FFF and is fascist, ghost is any alignment - 3/16
3) Arch draws FFL and is fascist, ghost is any alignment - 6/16
4) Arch draws FLL and is fascist, ghost is fascist - 1/16
Or to put that another way, purely based on the fact this mission failed and the information revealed afterwards there's a 3/8 or a 37.5% chance that Arch is liberal, and a 62.5% or 5/8 chance that he's fascist. And of that 3/8 chance he's loyal there's a 1/6 chance he's Hitler meaning it's actually more like 5/16 or a 31.25% chance he's loyal and a 68.75% chance he's some kind of fascist.
TL;DR: Mathematically speaking you should suspect Arch, but there's still a very good chance he's loyal based on the numbers, so suspect but don't write him off.