Wine in front of me
A perennial tis.so discussion topic is anti-inductivity, situations where observing a pattern makes it less likely to occur in the future. Blueberry-picking is inductive: when you’re looking for blueberries and you find some, you’ll update your views on “is this a good place to look blueberries?” to be more positive. But when you go home and see that same location has gone viral on SuperAwesomeBlueberryLocations.biz.site, you don’t think “That’s a second piece of evidence this is a good place for blueberries! I’ll update even more positively!” No, you think “Shit, it’s now common knowledge there are blueberries here; I bet it’ll be picked clean by the next time I visit.”
Social deduction games like Mafia/Werewolf are one of the purest examples of an anti-inductive game. Any time you figure out a tell to distinguish a mafioso from a truth-telling townsperson and use it to get the mafioso killed, it creates future opportunities for the bad guys to trick you knowing that you view the world through that lens. An ostensible signal that’s been completely captured by these anti-inductive dynamics is called “WIFOM”, short for “Wine in front of me” after the classic scene from the Princess Bride:
“All right: where is the poison? The battle of wits has begun. It ends when you decide and we both drink, and find out who is right and who is dead.”
“But it’s so simple. All I have to do is divine from what I know of you. Are you the sort of man who would put the poison into his own goblet, or his enemy’s?”
WIFOM arises when you have a clearly imbalanced choice presented by an agent who can easily choose between multiple options and each side understands that the other side is heavily scrutinizing their choice. People usually drink from the cup in front of them, so that’s the obvious choice for a poisoner to pick. But since you’re aware that people usually drink from cups in front of them, obviously you’d want to avoid the obvious choice. But the poisoner also knows you’d want to avoid the obvious conclusion that people drink from the cup in front of them, and could have put the poison in your glass for that reason…etc.
Now let’s extend this example to Mafia. Westley is the one presenting Vizzini with the hidden information game, so he’s going to be our mafioso against townsperson Vizzini, who has no hidden information. Suppose Vizzini presented a compelling case on Westley and he’s slated for execution. Westley knows that the whole town is about to learn he’s a member of the mafia when he flips.1 Right before the hammer falls, he comments: “Fair play. You got me, Vizzini.” Read literally, this statement gives the non-Vizzini townspeople extremely important information: Vizzini was not one of Westley’s buddies bussing2 him for cred, but an actual townsperson. But of course, Westley knows that people will interpret it this way, and if Vizzini is actually his buddy, that false clear will give him a free pass to win the game. So maybe some townspeople think: Vizzini must be Westley’s buddy for him to make a comment like that! Let’s kill him next! But Westley also knows you’d want to avoid that obvious conclusion that those wry comments are about townspeople, and so could have said it about a townsperson to get them killed next…etc.
This is classic WIFOM, and like the titular example, it regresses without end. As such, when a mafioso make a seeming-slip in a situation where their death is assured, experienced players will usually say “that’s just WIFOM” and ignore it. Yes, technically speaking Vizzini is or isn’t Westley’s buddy, but trying to develop a good general heuristic of which to believe given “You got me, Vizzini” will see that heuristic instantly gamed. But wait — isn’t the whole enterprise of playing Mafia all a bunch of WIFOM, then? Won’t anything that gets used to catch Mafia players be instantly subject to this unproductive infinite regress? If WIFOM is the stuff that experienced players ignore in an anti-inductive game, then what don’t they ignore?
One tell I have a lot of faith in is something I call “caught for the wrong reasons”. Let’s suppose Westley’s alive and not under particularly much suspicion. He makes a comment like “Nice going, killer”, and Vizzini remarks: “Killer! You must be subconsciously thinking about the murder you committed last night, you dastardly mafioso!” Westley actually says killer all the time and it has no bearing on alignment, but no matter how much he tries to point this out, Vizzini keeps doubling down. Westley calls him an an idiot, but the other townspeople start taking Vizzini’s side, and soon Westley is ranting about how stupid EVERYONE is—
—Completely forgetting to pretend that he thinks some of his accusers could be mafia arguing in bad faith. Westley was so annoyed that Vizzini’s stupid theory would be “confirmed” by his flip that he vented completely honest frustration without mixing in fake suspicion. Good townspeople will wordlessly coordinate on “believing” stupid theories if they see glimmers of this dynamic to try to get a telling reaction. Let’s say they pull it off, and Westley’s about to be executed. Right before the hammer falls, he makes a wry little comment: “Genius work, Vizzini. You really know the magic words only bad guys say.”
Superficially this may look like it’s governed by the same WIFOM dynamics as last time: it’s confirming Vizzini as a townsperson, but Westley knows it looks like that, and so on. But I would treat this as strong (though not definitive) evidence that Vizzini is a townsperson. Why? Because we’re specifically in a “caught for the wrong reasons” situation, and the whole reason we pegged Westley as a mafioso is that he’s letting earnest frustration dictate his posting. If Westley was a more experienced player who knew about these dynamics, I’d be less inclined to take his last words as evidence towards Vizzini’s alignment. But also, if Westley had parceled out “caught for the wrong reasons” as a concept to the point where he could be anti-inductive in that specific frame, he wouldn’t be in this situation in the first place.
WIFOM dynamics require the person offering the choice to be able to replicate the other person’s internal monologue, which means they need a similar vocabulary, which means they need a similar ontology. This point is often missed by people studying game theory, since the formal rules of the game are assumed to be the ontology the players share. The rules are certainly part of the player’s ontologies, and we can see that a nominally anti-inductive game can collapse if one player doesn’t understand the rules, or if they convince the other player they don’t. But while games have ontologies “built in” owing to the verbs of interaction, experienced players will extend their ontologies beyond that to conceptualize higher-level patterns. This ontological asymmetry is what stops anti-inductive games from collapsing into unusable WIFOM. Two players may be looking at the same formal game state and the same stream of public information, but if only Vizzini resolves it into the state of “caught for the wrong reasons”, Westley can’t recreate Vizzini’s internal monologue in order to subvert it. Vizzini has representational privilege over Westley.
When you hear about the back-and-forth of “information” in an anti-inductive game, always remember: agents don’t act on information, they act on perceived states generated by motivated ways of seeing they develop over time. That development is oftentimes what we mean by “experience”, an advantage difficult to gain but also difficult to fool with WIFOM once gained.
As a fun aside, some Mafia games are actually no-reveal, where you aren’t told the alignment of the players you kill and have to decide if you’re in a “world of 1 [remaining Mafioso]”, or 2, etc. That adds an extra dimension to the dynamic we’re describing, but I’m going to keep the example simple by assuming it’s immediate flip, full reveal.↩︎
As in “thrown under a bus”, the term of art when mafia kill off one of their own to look more credibly townie.↩︎