It's safe to say that most people make their decisions based on emotions and use logic - even incorrect logic - to back up their choices.
So clearly, an appeal to logic usually doesn't work.
But before you go try and change someone elses mind, I encourage you to listen actively. I'm not suggesting that they're right, but I am suggesting that they probably feel like you're not really listening to them.
I'm too sleepy right now to give a breakdown of what active listening is all about, but you can find some good stuff
here. Try some of those techniques to hear the others out. Once they've had their say, they may be more willing to entertain other points of view.