[Mechanic] Partially Mafia-led public investigations

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[Mechanic] Partially Mafia-led public investigations

Post Post #0 (ISO) » Fri Jul 20, 2018 4:32 am

Post by Umlaut »

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.
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Post Post #1 (ISO) » Fri Jul 20, 2018 4:45 am

Post by Umlaut »

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.
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Post Post #2 (ISO) » Fri Jul 20, 2018 9:37 am

Post by BBmolla »

Can’t mafia just generate both statements to make things simpler? One true, one false?
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Post Post #3 (ISO) » Fri Jul 20, 2018 10:49 am

Post by Irrelephant11 »

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
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Post Post #4 (ISO) » Fri Jul 20, 2018 12:21 pm

Post by Umlaut »

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.)
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Post Post #5 (ISO) » Fri Jul 20, 2018 1:32 pm

Post by Umlaut »

Actually it might work in a nightless. By giving these results scum are directly manipulating the lynches anyway.
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Post Post #6 (ISO) » Sat Jul 21, 2018 7:46 am

Post by Umlaut »

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?
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Post Post #7 (ISO) » Mon Jul 23, 2018 10:04 am

Post by mith »

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.
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Post Post #8 (ISO) » Mon Jul 23, 2018 11:21 am

Post by Umlaut »

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."
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Post Post #9 (ISO) » Mon Aug 06, 2018 3:51 am

Post by Gamma Emerald »

This setup looks interesting, I'd try it
what's a good playerlist size to test this mechanic?
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Post Post #10 (ISO) » Sun Dec 13, 2020 10:24 am

Post by Umlaut »

Necro-bump! I'd like to try fleshing this out again.

What about the following version?
  • 2 Mafia, 6 Town. (I can raise or lower these numbers depending on what seems fair.)
  • The Mafia has no nightkill (so town gets at least 3 miselims and possibly 4).
  • Plurality elimination.
  • Each night, the Mafia must choose two living players (or else two will be chosen for them at random). There is no restriction on repeating themselves.
  • The mod chooses randomly (by rolling 1d2) which player to report truthfully about, then chooses randomly again (by rolling another 1d2) whether to report the other player as innocent or guilty.
  • If there are somehow no legal pairs left for the Mafia to choose, there will be no more investigations.
  • To avoid town trying to read into things that shouldn't be informational, the mod should explicitly publish the two results in signup order (e.g. "Player 2 is innocent
    or
    Player 5 is innocent," rather than the other way around).
I think this might work better than some of my other versions. It does have a random element, which I understand many people dislike on principle, but it's a fairly contained random element that can be reasoned about. As mith pointed out, if the Mafia have precise control of results they would never want to report someone as guilty, which sort of degenerates the setup, and this fixes that. It's also just cleaner and simpler to give what control exists to the informed minority, and randomize the rest, rather than trying to have town vote on it or something.

If there are two confirmed innocents, nothing stops the Mafia from just choosing those two players for all future investigations, and this seems like a feature rather than a bug since having two confirmed innocents means the Mafia have almost lost anyway. If there is only one confirmed innocent, the Mafia probably
don't
want to include them in future investigations since there's a 25% chance it reveals the other subject's alignment outright. If there are none, town can stop the Mafia from repeating themselves indefinitely by eliminating one of the two, and potentially confirm the other's alignment in the process.

If Mafia include themselves in the investigation, there is a 25% chance of a double-guilty result which is a worst case scenario for them. This gives some WIFOM potential around their choices, since 25% to me seems just high enough to be scary but not high enough to completely overwhelm the fear of being PoE'd if they
don't
include themselves.
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Post Post #11 (ISO) » Sun Dec 13, 2020 1:12 pm

Post by Isis »

This is definitely not a 2:6 setup concept, 2:6 is 50% EV and this is tons of value added to the town. I think it's more like a 3:6 or a 3:7, leaning 3:6.

You probably want the dice for random cop check to be a guilty with the probability of (scum divided by total players). That kind of probability means the investigation result isn't revealing the likelihood of its legitimacy based on its results (if there is one innocent and one guilty result, it's more likely the innocent result is the truthful result. With scum/players, the investigations would be equally likely to be legitimate).

This has a knockon effect of making it easier for scum to include themselves in investigations which wasn't my intent but is probably a positive?
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Post Post #12 (ISO) » Sun Dec 13, 2020 2:43 pm

Post by Umlaut »

3:6 sounds fine to me (I have basically no experience thinking about nightless setup balance so I'll take your word on that). The only reason I might prefer 3:7 is so there's one more chance for the mechanics to actually 'do something'; it seems like in games where town only gets two mislynches it's often the case that scum win before anything really happens mechanic-wise.

I like that change on the random result--I momentarily considered something like that, and really the only thing stopping me was that 50-50 is easily stated whereas I'm not sure how to word "chosen uniformly among the roles of the living slots" so everyone will understand. Maybe if one described an explicit procedure (something like "choose randomly from among the living players and report
that
player's role") that would be clear enough.
Last edited by Umlaut on Fri Jun 18, 2021 2:28 pm, edited 2 times in total.
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Post Post #13 (ISO) » Sun Dec 13, 2020 2:59 pm

Post by Isis »

I find the formula easier, the report someone else's role thing makes me want to inject dependency that doesn't exist though it's elegant. Maybe both?
"Let us say that you are right and there are two worlds. How much, then, is this 'other world' worth to you? What do you have there that you do not have here? Money? Power? Something worth causing the prince so much pain for?'"
"Well, I..."
"What? Nothing? You would make the prince suffer over... nothing?"
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Post Post #14 (ISO) » Sun Dec 13, 2020 5:33 pm

Post by Umlaut »

There is one thing missing: I need a snappy name for the setup.
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Post Post #15 (ISO) » Tue Dec 15, 2020 1:46 am

Post by JacksonVirgo »

So the two statements are guaranteed to have one a lie and one a truth? You say that both halves can be true so why not allow scum to have full control over it so it removes any RNG in the setup which is inherently swingy. Scum has to reveal one piece of information that's the truth and the other can be either the truth or a complete fabrication.

The rules to avoid breaking the setup could be the following:
  • You cannot select the same player twice.
  • You cannot repeat a previously selected pair.
  • You cannot select a player that you know for a certain is going to die.
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Post Post #16 (ISO) » Tue Dec 15, 2020 7:32 am

Post by Jake The Wolfie »

In post 14, Umlaut wrote:There is one thing missing: I need a snappy name for the setup.
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Post Post #17 (ISO) » Tue Dec 15, 2020 9:49 am

Post by Ircher »

In post 14, Umlaut wrote:There is one thing missing: I need a snappy name for the setup.
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Post Post #18 (ISO) » Tue Dec 15, 2020 10:13 am

Post by Umlaut »

In post 15, JacksonVirgo wrote:So the two statements are guaranteed to have one a lie and one a truth? You say that both halves can be true so why not allow scum to have full control over it so it removes any RNG in the setup which is inherently swingy. Scum has to reveal one piece of information that's the truth and the other can be either the truth or a complete fabrication.

The rules to avoid breaking the setup could be the following:
  • You cannot select the same player twice.
  • You cannot repeat a previously selected pair.
  • You cannot select a player that you know for a certain is going to die.
It has to be that both halves might be true, or else flipping one of the two players would always tell you the alignment of the other.

If you give scum full control over it, then as was pointed out there is never any incentive for them to list someone as guilty (town just yeets that player, and either they've yeeted scum or they've confirmed the other player's alignment). In order to make the results interesting you need some way for guilty results to appear that doesn't require anyone to do something strictly suboptimal.
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Post Post #19 (ISO) » Tue Dec 15, 2020 4:27 pm

Post by Gamma Emerald »

In post 17, Ircher wrote:
In post 14, Umlaut wrote:There is one thing missing: I need a snappy name for the setup.
To Tell the Truth
This honestly is a good setup name, partly because it's also the name of a game show
also, this is kinda like the public investigation mechanic from mbos 10
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Post Post #20 (ISO) » Tue Dec 15, 2020 6:18 pm

Post by JacksonVirgo »

In post 18, Umlaut wrote:
In post 15, JacksonVirgo wrote:So the two statements are guaranteed to have one a lie and one a truth? You say that both halves can be true so why not allow scum to have full control over it so it removes any RNG in the setup which is inherently swingy. Scum has to reveal one piece of information that's the truth and the other can be either the truth or a complete fabrication.

The rules to avoid breaking the setup could be the following:
  • You cannot select the same player twice.
  • You cannot repeat a previously selected pair.
  • You cannot select a player that you know for a certain is going to die.
It has to be that both halves might be true, or else flipping one of the two players would always tell you the alignment of the other.

If you give scum full control over it, then as was pointed out there is never any incentive for them to list someone as guilty (town just yeets that player, and either they've yeeted scum or they've confirmed the other player's alignment). In order to make the results interesting you need some way for guilty results to appear that doesn't require anyone to do something strictly suboptimal.
Then perhaps give incentives for that, since RNG as a mechanic I will always fight against.
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Post Post #21 (ISO) » Tue Dec 15, 2020 7:08 pm

Post by Isis »

I think RNG is appropriate here, setup might not be for you
"Let us say that you are right and there are two worlds. How much, then, is this 'other world' worth to you? What do you have there that you do not have here? Money? Power? Something worth causing the prince so much pain for?'"
"Well, I..."
"What? Nothing? You would make the prince suffer over... nothing?"
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Post Post #22 (ISO) » Tue Dec 15, 2020 7:18 pm

Post by JacksonVirgo »

:c
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Post Post #23 (ISO) » Fri Dec 25, 2020 3:37 pm

Post by JacksonVirgo »

Back to this. If three RNG runs come up saying [X] is Mafia, [Y] is whatever in a row. That's all three mafia (assuming 3 mafia) caught instantly. That's literally 3 1 for 1's that Town can afford, and if they can't they can keep doing it until the very end and then gauge approriately.
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Post Post #24 (ISO) » Mon Jun 21, 2021 4:12 pm

Post by Umlaut »

Wiki page: To Tell the Truth

If you made a suggestion in this thread that was used, feel free to credit yourself on the wiki (I'm thinking of Isis in particular who suggested setup size and probabilities, and Ircher for the name)
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