I follow a rule that is kind of dumb. If I make the last play to end a game (win or lose), then I start the rematch. If someone else makes the last play, I wait for them to initiate. There is nothing inherently logical about it, really, yet it makes sense in my head.
That's what I do, but I've found a few people that will restart it either way (so we end up playing two games, which I don't mind if my list isn't full) and others that won't restart in any case, but will play if you start one.
I've started checking my list to see if they've started a game with me already before doing a rematch.
I would like Words With Friends to check for me, and say, "You already have a match in progress. Would you like to switch to that one, or start a second one?" when I attempt a rematch with someone who has already started one. Then I could always choose rematch, and it will give me an opportunity to switch to the existing game if the other person has already rematched me.
Yeah, I think about this stuff way too much...