As I ate breakfast this morning I was ruminating a bit on game theory and mafia, so allow me to go into a bit of a tangent.
A lot of times when people are lynched and flip town, people will still say that it was the "correct decision" to lynch them, or something along similar lines. I expect that that would be said if NK15 were to be town, and to be fair I have already said that I would say something similar if he were to flip scum – that I think my reasoning was still strong. What do people mean by this? How can something be the "correct decision" if it was incorrect? Are they just unable to accept that they were wrong?
Perhaps, but there
is
at least something deeper there, and it relates to being "probability-oriented" rather than "results-oriented", if you've heard those terms before. I'll illustrate by way of example. Let's say that you're playing a game with a coin weighted so that heads comes up 2/3rds of the time, and tails 1/3rd. If you correctly call the flip, you gain a dollar, and if you're incorrect, you lose one. The correct decision is obviously to always call heads, no? A less obvious example: you're drawing and replacing red and blue cards from a deck where 60% of cards are blue and 40% are red, and similarly to before you have to guess whether you'll draw a red or blue card. Many people will say that the correct strategy is to guess blue 60% of the time and red 40% of the time, but the correct strategy is to always guess blue.
What's my point with all of this? These games have an obvious "correct strategy" – one that maximizes your winrate. Despite that, the coin might still come up tails, and you might still pull a red card. If that happens, does that mean that you made an incorrect decision? Similarly, if you were to guess tails instead and the coin came up tails, did you make the correct decision? This is the core division between being probability oriented and results oriented. A results oriented way of thinking would say that tails was correct if the coin actually came up tails, but being probability oriented tells you that there's no reason to guess anything other than heads. People who say that actions were the correct decision even when they were wrong are being probability oriented, and in some sense they're right to be. Generally being probability oriented is a lot better than being results oriented.
Maybe everyone already knows all of this, and I don't mean to condescend. But I'd like to bring my point back around to mafia now – as I've said, people often say that lynches were correct even when people have flipped town, and in some situations they may be right. But mafia is a lot more complex of a game than those simplified examples I gave – in those, it's obvious what the best strategy is, and so one can be quite confident in saying that even if tails were to come up five times in a row, heads was still the correct decision to make. I don't think the same is true of mafia.
Here we come to basically my thesis of this entire post: I think that, in mafia games, people convince themselves that they're being probability oriented a lot more than they actually are. There's an unbelievable amount of information available in any given game of mafia with which to read people and thus with which to make decisions, and thus to say that something is "the correct decision" is much less clear cut than with a game of weighted coins. Something may be the correct decision under the rule of "generally believe cop claims", but that's not the same thing as
the
"correct decision". Of course, it's no easy task at all to recognize when to go against common rules such as that – in fact, I would say that it's a trait of only the best of the best of town players to be able to recognize when to go against common wisdom, and I don't claim to hold any such consistent ability myself. Even still, I think that most people could do with examining some of the rules that they unknowingly chain themselves to, as well as looking a bit more at some of that unbelievable amount of information available to them – especially after they've been on a lynch that ended up being wrong. At the very least, I think that would be better than immediately jumping to the conclusion that one is always perfectly probability-oriented, because the truth is that's not the case for any of us.
