Conversations with believers (and others who disagree with us)

I've had a few conversations with people who disagree with me.  Believers, anti-vaxers, etc.  I've even had arguments with other atheists on things like last week's topic.  Often, it's easy to allow these conversations to become nothing but shouting contests, but does that really help?

I'm beginning to think about tactics.  I still think there is a place for loud, adversarial arguments, but does every disagreement need to escalate to this?  I think we might make more headway with a different strategy.

So let's talk strategy.  When do we chose diplomacy over diatribe?  

The awesome is strong in all who listen.