You HAVE to build a case. Random play lets the Mafia win. Yes, we're all Dominion players, and cunning, sly players. We're also human, and are prone to imperfect play. But a point-and-lynch system is doomed to fail. You will NEVER gain relevant information that way.
Not to harp on, but how are our discussions going to lead to anything that isn't random?
While the end resulting vote is never likely to be 100% accurate (I would hazard a guess that in MOST games of Mafia, a Townie is hit first, if for no other reason than volume.), information mining, and reading into every reaction can be HUGELY beneficial.
My focus in Poli-Sci was Constitutional Law. I mention this because the Constitution is a written document hundreds of years old in which there are STILL many questions unanswered. And interpretations abound about every little detail. But are we more informed of the views of the Authors at the time for their having written it? Of course.
Try this: (Note: Don't try this) Walk up to a random person, and say quite loudly "You need to return the money to the bank that you stole". See what their reaction is. Sure, in person is different than in forum. But accuse someone in any medium, and they will have an unnatural urge to defend themselves. It's human nature. What can be gained from that reaction is ultimately up to you, and those around you.
Now, I advocated "playing nice", and I still feel that way. My first accusation was against Voltgloss, primarily since he came out of the gate playing the exact opposite. Since then, he's become more focused, and most of the time, I feel has presented valid points. My second real case was against Morgrim, although I withheld my vote until more responses from him and others came in. As they've arrived, I've felt more and more confident. Could I be wrong? Sure. I actually think I'll be wrong 33% of the time (See earlier posts). But being right 66% of the time seems pretty good right now. My third accusation came at you Bozzball, because of the issues discussed here. Your willingness and almost wanting of the vote to be random.
Now, the more you post, the more I get the feeling that your cover* of being a Mathematician may be truer than I gave credit for. You appear and act like one. For every value of X, there can be only 1 Y, else the equation is undefined. Is it raining, or has it cleared up? Yes. You take everything at face value, and rather literally. So you may not see value or reason in trying to extract information.
But as pointed out by Jotheonah, that's the game man. If you follow a mathematical formula here, you'll lose. Point-and-Lynch, or lynch in order of signups, or whatever, just won't work. It's find and use whatever info you can, or...