Equation for dealing with potential trolls.

let P be the probability that he is a troll (1 for certainly a troll, 0 for definitely not a troll).

let A be the benefit of being nice to him if he is not a troll and let B be the benefit of being nasty to him if he is a troll.

Now calculate Action = P*A - (1-P)*B.

If Action is positive treat him nicely and if it's negative just ignore him or kick him out.

For example, says everyone hates him and he has friends then the benefit of being nice is high because he might cheer up, but the benefit of being nasty is low because you'll just be playing into his game so if you don't know if it's a troll or not (P = 0.5) the best action is just treat him nice for now.

Another example, if a guy is acting ridiculously "concerned" about a minor topic you probably wont change his mind by being nice and explaining the truth, but you will get more benefit (people reading the discussion wont get tricked by him) by just saying he's doing a typical troll, in that case even if you aren't realy sure if he's a troll or not the calculation will tell you to treat him like one.

Post if you get any more mathematical formula useful for dealing with trolls.