[Mechanic] Partially Mafia-led public investigations

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Umlaut
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Post Post #0  (ISO)  » Fri Jul 20, 2018 10:32 am

This isn't a full setup proposal, just something that could be worked into an open setup.

Each morning, the town gets a message of the following sort:
Umlaut is innocent or mith is guilty.

This disjunction is guaranteed to be true. It's possible that both halves are true. The order of the guaranteed-true half and the other half are randomized.

The guaranteed-truthful half is generated in a manner that is town-friendly or at least not town-averse. I'm working on ideas for how it might work, but one option would be to have everyone submit an investigation at night and choose either randomly from the submissions or by plurality. Having a single Cop doesn't work because he would know which result was true.

The other half is generated by the Mafia who can name any player as either alignment.

Town doesn't want to agree in public about who to investigate, because then the Mafia would just submit a false result for that same person and the result would be worthless. Mafia doesn't want to name the same player over and over, because Town will catch on and just assume that's the falsified result for each investigation.

I don't see any immediate issues to make this unworkable but I'd still like to run it by you all for a sanity check before I spend a lot of time trying to turn it into a full setup.
“Umlaut is a riddle, wrapped in a mystery, inside an enigma, coated in something sticky.” – boring

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Umlaut
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Post Post #1  (ISO)  » Fri Jul 20, 2018 10:45 am

Mafia definitely doesn't want a double guilty because then town can just assume one of those two is actually guilty and lynch the scummier. But calling everyone innocent is not a strictly optimal strategy either because it means guilty results are always true. I haven't ruled out the possibility that they should just lie every time.
“Umlaut is a riddle, wrapped in a mystery, inside an enigma, coated in something sticky.” – boring

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BBmolla
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Post Post #2  (ISO)  » Fri Jul 20, 2018 3:37 pm

Can’t mafia just generate both statements to make things simpler? One true, one false?

Irrelephant11
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Post Post #3  (ISO)  » Fri Jul 20, 2018 4:49 pm

I like this. I think an important aspect is that one is true, and the other *might* be true. Guaranteeing that one is true and the other is fase is too much info.

But yeah, giving scum total control makes more sense. You could flavor it in a 7:2 like they’re those two cliche gatekeepers, one of which tells the truth and the other doesn’t always, or whatever

Umlaut
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Post Post #4  (ISO)  » Fri Jul 20, 2018 6:21 pm

If scum have free rein they just say "the guy we're shooting is innocent, and Randomly Selected Player is Random Alignment" over and over.

In post 3, Irrelephant11 wrote:I like this. I think an important aspect is that one is true, and the other *might* be true. Guaranteeing that one is true and the other is fase is too much info.

You made me realize here that there is a downside for Mafia of always lying (assuming Town figures out they're doing that). It means after seeing one person in an investigation pair flip the town knows the alignment of the other 100%, even if that first result was true. (Otherwise they would only know if it was false.)
“Umlaut is a riddle, wrapped in a mystery, inside an enigma, coated in something sticky.” – boring

Playing: Micro 820
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Umlaut
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Post Post #5  (ISO)  » Fri Jul 20, 2018 7:32 pm

Actually it might work in a nightless. By giving these results scum are directly manipulating the lynches anyway.
“Umlaut is a riddle, wrapped in a mystery, inside an enigma, coated in something sticky.” – boring

Playing: Micro 820
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Umlaut
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Post Post #6  (ISO)  » Sat Jul 21, 2018 1:46 pm

If I let the Mafia run the whole investigation, what restriction on "repeating themselves" would be sufficient to prevent obvious strategies like just saying the same thing or nearly the same thing every time, but not so strong that they can run out of legal targets?
“Umlaut is a riddle, wrapped in a mystery, inside an enigma, coated in something sticky.” – boring

Playing: Micro 820
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mith
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Post Post #7  (ISO)  » Mon Jul 23, 2018 4:04 pm

Nightless would probably be too tough on scum if you don't let them repeat themselves.

If you do, most of the interest would be in the first investigative result, and giving either target as Mafia is strictly bad - town should always lynch that player, and either they got scum or they have a confirmed innocent (which is quite good*). Given two innocent results, I'm sure we could find the Nash equilibrium between both/one true on the Mafia side and lynch result/other on the Town side, but I don't know how interesting it would be vs. a regular Nightless game.

*For example, if we limited to only a D1 investigation statement and Mafia gave one innocent and one scum, lynching the scum result in 4:8, say, either reduces to 3:8 (EV = 5/11) or 4:6:1 (EV = 3/7), vs. the 1/3 for 4:8 Nightless.

Umlaut
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Post Post #8  (ISO)  » Mon Jul 23, 2018 5:21 pm

Hmm. Yeah, you'd calculate the town EV for parameters (M,T,p) where p is the probability that one of the named targets is mafia, and then minimize in p to get the equilibrium.

I think I'm better off going back to the non-nightless, Mafia-don't-pick-all-the-targets version if I want to mess with this. That version also allows the possibility that Mafia try to predict the target and give a false result on same, to produce a genuinely worthless combination like "Umlaut is guilty or Umlaut is innocent."
“Umlaut is a riddle, wrapped in a mystery, inside an enigma, coated in something sticky.” – boring

Playing: Micro 820
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Gamma Emerald
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Post Post #9  (ISO)  » Mon Aug 06, 2018 9:51 am

This setup looks interesting, I'd try it
what's a good playerlist size to test this mechanic?
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