There's no such thing as an overeager vig

[Thok]

Let A=The number of protown players alive
Let B=The number of proscum players alive
Let C=The average power of a protown player
Let D=The average power of a proscum player

Then AC=Power of the town and BD=Power of the scum. (AC)/(BD) expresses the balance of the game, where a higher number means the town has an advantage and a lower number means scum has the advantage (1 would mean that the game is perfectly balanced).

C and D clearly depend partially on A and B (compare 2 townie and 1 scum to 1 townie and 1 scum). To do this correctly, you'd have C_old, D_old and C_new, D_new (in fact you need C_scumkilled, D_scumkilled, C_townkilled, D_townkilled), and you need to define the dependance of the old variables on the new variables. Your AC/BD above is actually some weird mix of the new version of the variables, and thus need not be equal to AC_old/BD_old.

There are other issues (namely that not all townie deaths are the same) but that's the big issues with your argument.

[Thok]

Ratio of town to scum seem to be wrong thing to use; really it should be some measurement of winning percentage.

There's also an oppurtunity cost issue; making a random vig early on make prevent the vig from making a more informed choice later in the game.

That said, I do agree that there are people who would be better off trying to random vig then to trust there instincts.

[Thok]

Now, let's say the mod decides to make 11 random kills. Suddenly, the odds of the town winning are 75%. Conclusion being that each of those random kills helped the town 1/11 of the 25% gain the town saw.

Sure, but mafia doesn't work that way. A more compelling scenario would be to have the mod start modkilling one person at a time until you either have a guaranteed town win or a guaranteed scum win; in that situation the odds of a mafia win are much higher then you suggest.

[Thok]

I've already explained why this isn't an accurate refutation. You can show me all you want that C and D change with the number of players left alive; I'm with you there. The point I'm making is that it's near-impossible to predict beforehand the change of C and D, so it's rational to make plays assuming the average change (0, unless you'd like to show otherwise).

C and D are not "unpredictable". They are proxies for the relative power of the town/scum, which is clearly directly correlated to the size of town/scum. If town is killed, C will go down and D will go up. If Scum is killed the reverse is true.

You're the one arguing the unconvetional point of view. It's your duty to convince us.

If you want to make this a semialid argument, at the very least throw out C and D, come up with some rough function p(A,B) that determines the probability of town winning give the size of A and B, and use that probability to determine the likelihood of a vig kill being useful. You've basically told us that you think p(A,B)=AC/BD which is just plain wrong from am empirical point of view.