I just thought of some arguments against this working, that I want to preempt and discuss.
Argument 1: you might look at this and think "well, if I'm a townie and I win 3 points for declaring a conspiracy, and only win 1 point for declaring no conspiracy (and conversely, that you risk losing 3 points by declaring no conspiracy and only risk losing 1 point by declaring a conspiracy) and say "optimal strategy for townies is to just say there's a conspiracy, or at least heavily bias themselves that way".
Argument 2: you might look at this and say "well, if you look at it closely from the perspective of any individual townie, they're actually much more likely to
not
be in a conspiracy. Each location has a 50% chance to have a conspiracy - ergo, we can pretend that each location's status is decided by a coin flip, and the fact that you are a townie in a location makes it more likely that that location has no conspiracy by Bayesian statistics, or by the Pie Observation. Thus, you might say "optimal strategy for townies is just to say there's no conspiracy, or at least heavily bias themselves that way".
So which of these is correct, and which is wrong? Well, both, and both! Both of them are correct, and both of them are wrong. In fact, they cancel each other out. If you are a townie in a given location, you can work out that the probability of there being a conspiracy is 1/4. Ergo, the expected point gain for the town by you saying "conspiracy" is (1/4) * 3 + (3/4) * (-1) = 0, and the expected point gain for the town by you saying "no conspiracy" is (1/4) * -3 + (3/4) * 1 = 0. In other words, since points are what matters, there is actually no mechanical advantage to guessing either way - a smart townie has no reason to bias themself in either direction.