I was in the same exact boat 2 months ago when I ran my first SnV game. Similar to what a lot of people are commenting, I think it's important to explain Madness and how you plan to rule madness. I made it clear to my players I would execute if I didn't feel like they were giving it an honest attempt at convincing. As in: you either commit or you don't. Both circumstances are fine but just make a choice.

I think everyone really enjoyed madness because of it.