They clearly exist but they don’t exist for the purpose of this system. It defines what we think it means to be better over a series of games in a way that encourages certain things and discourages others.
We don’t think someone who says more true things on average is “better” at mafia than someone who says less so the system doesn’t reflect it. Same holds for a lot of your other examples.
An analogous example that might surprise you - at the top level the players who win more/are higher rated at chess (with the exception of carlsen) actually have a lower computer accuracy move to move than people sometimes significantly lower rated.
Likewise in the market the one who is right more often doesn’t necessarily make more money.
Anyway my point is you have to make a choice for what you define as the final arbiter of what is to be measured and we think of the social component as a means to the end and not the metric to be measured. If you want to make a game that directly rewards people for saying true things you can go make that game, this isn’t it.
Funnily enough no. The first metric people try for most binary result games is winning and losing. And if there’s reason to need more granularity (sample size!) you look at the next most concrete thing. The social component is looked as more of “ah this item A has some correlation with result X” but it doesn’t into itself give the reward.
One last example that might help: Consider salesmen. Their important metric is making more sales. Their job is often based on social competence. We have some sense that x, y, and z social abilities are good things for a salemen to have and do. Someone does all those things but get less sales than someone who doesn’t. The latter is the better salesman. The first gets no bonus points for being better at x, y, and z.
We won’t be taking your approach of looking at qualitative things. Please stop discussing it here.
The social part helps you know who to vote/kill/etc and to convince others to act in certain ways, but it doesn’t mean much on its own.
If I had 100% accuracy and pretended I was a cop with red checks on all the mafia, telling the truth doesn’t really matter, the things I said are just a means to convince people to vote in a certain way and get me the win.
You can even run games entirely without really talking at all (see: Shut Up and Vote games).