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Mafia Theory: The Gettier Problem

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4/9/2016 10:27:39 PM
Posted: 2 years ago
So, as some of you already know I recently started playing mafia (live only so far), and in the few times I've played I've noticed some interesting epistemological themes playing out that I want to discuss.

This may or may not become a series of threads of Mafia-theory. I don't intend for these to be lessons on playing mafia better, because God knows I'm not nearly experienced enough to justify teaching anyone how to play better (except for Rosalie, who sucks). These are just my observations.

Okay, onto the content.

For those of you who don't know, the Gettier problem is an issue calling into question the validity of using the "justified true belief" standard in epistemology for justifying knowledge-claims. That is to say, it is typically (or at least it was typically) accepted that for a thought to count as knowledge, it must be believed, it must be true, and it must have reasonable justification.

Gettier cases are where all three conditions are met, but you still cannot be said to have knowledge. For example, let's say you see a clock. The clock says it's 3 o'clock. As it happens it actually is 3 o'clock. From this you conclude it is, in fact, 3 o'clock. This would be justified true belief, as clocks are a reasonable means of telling time.

The problem is, unbeknownst to you, the clock is broken and always says "3 o'clock." Given this, your justification is wrong, and therefore your knowledge claim is effectively no more valid than a claim only comprised of true belief, which isn't considered rigorous for defining true knowledge-claims as it doesn't rule out the possibility that your knowledge-claim is only true by coincidence.

The Gettier problem is the result of a disconnect between your justification for a belief, and the truth-value of the belief itself. In this case, the disconnect is the result of not ruling out the possibility that an underlying assumption (the clock might not be working). In this case, the specific conclusion is true (it is 3 o'clock), but the general conclusion is wrong (this clock is reliably telling me the time).

I've seen quite a few Gettier problems arise in live mafia so far, and we're going to look at one instantiation of this here. In a game I was in a few days ago, we managed a successful DP1 mafia lynch. By the next day phase, somebody (can't remember whom) scum-read TUF, who was then strongly defended by YYW. From this, suspicion drifted onto YYW, who was in turn strongly defended by TUF. Neither one could give good reason why the other shouldn't be suspected (for a good reason we didn't know at the time), which naturally made us (or at least me) suspicious of the both of them.

TUF had claimed miller and YYW had claimed vanilla townie. Neither of these roles would give them special knowledge to justify their certainty that the other was town, which naturally suggests the possibility they are both scum-buddies, but for this to be true would mean there were 3 mafia, rather than the usual 2. This lead me to the conclusion that there was 3 mafia in this game. This claim was justified by reading the behaviour of TUF and YYW, I believed this claim to be true, and as it happened, it actually was true. There were, in fact, 3 mafia in this game.

Here's the problem, neither TUF nor YYW were mafia. As it turns out, TUF actually was lying about his role, but rather than lying to cover up being mafia, he lied about being a cop in order to avoid being night-killed. The soundness of his new claim was apparent by YYW being night-killed and turning vanilla town, as he claimed. Since my theory of TUF being scum relied upon his seemingly overzealous defence of YYW (whom he had previously investigated to determine innocent, btw), and YYW's seemingly overzealous defence of TUF, for one of them to have had justified certainty of the other's innocence neutralized my justification for the other being mafia, and therefore the possibility of either being mafia.

In other words, I knew YYW wasn't mafia because he flipped vanilla and I no longer had a reason to suspect TUF because my only reason for suspecting him in the first place hinged upon the assumption that YYW was mafia (which itself was hinged upon the idea the TUF was mafia, as evidenced by the combination of his insistence we don't lynch YYW despite refusing to give a compelling reason why we shouldn't).

What happened from here is worth analyzing, because like I said, there actually was 3 mafia, but having my justification proven wrong meant I no longer had justification to believe there was 3 mafia and so the belief was dropped, because I could no longer claim it as knowledge. In this case, the problem was actually the opposite of the clock example above. Rather than having the general conclusion (there are two more mafia) proven wrong, it was the specific conclusion (TUF and YYW are mafia) that was proven wrong.

So the question is, did I have knowledge of the two additional mafiosos? I certainly had justified true belief, but was it a mistake to drop the belief just because my justification was proven false? After all, just because my justification for P was wrong doesn't prove ~P, it just makes the truth-value of P indeterminant. But since the game relies upon committing to an assumption (presumably based on probability of the assumption being correct) and proceeding accordingly until your hypothesis is verified or falsified, one belief had to be taken over the other.

Since there actually was 3 mafia, dropping the belief that there was 3 meant we played the rest of the game under the assumption that we only needed to find 1 more, which meant we had no prepared plan for finishing the game after we had lynched the second mafia and we ended up losing the game. It's possible had we continued to operate under the assumption there was 2 more mafia, we could have successfully rooted out who it was, but that's just not the way it worked out.

So what lesson(s) did I learn here? I learned that Mafia games are potentially subject to the Gettier problem, and that this greatly complicates the nature of the game, because if justified true belief isn't enough to reliably constitute knowledge in the game, the "justified true belief" method doesn't function as a standard for determining what constitutes a knowledge claim in Mafia, but rather it functions merely a formula for determining the probability of a certain knowledge claim being accurate.

I think it would be interesting to postulate how a mod could intentionally work Gettier problems into a specific game type and the implications for balancing that would have.
I'm just a cro magnon masquerading as one of you.