"I want it back!"
"It's my turn!"
Delphine and Cordelia had both decided that the orange sled was the only sled worth using. We were out with their friend Ursa (and Ursa's two sleds, the green one and the blue one). There had been a horrible misunderstanding when Cordelia lent Ursa the orange sled for JUST ONE TURN, but then Ursa gave it to Delphine instead of back to Cordelia. Delphine refused to relinquish it, but Cordelia insisted she must have it back.
When I stepped in they were in the screaming-tug-of-war stage of the fight — I separated them and took custody of the sled, and then we talked. We talked about Cordelia's preferred resolution ("I want the sled!") and Delphine's preferred resolution ("I want the sled!"), we talked about how much Cordelia was willing to compromise ("She can't use it!") and how much Delphine was willing to compromise ("She can't use it!") We talked about the possibility of taking turns ("No!") and using the other sleds ("I want the orange one!") We talked and talked but neither girl would compromise and I had run out of ideas.
Then Blake made an excellent point. Both girls were under the impression that the orange sled was the best, but how could they be so sure? We should definitely do some experiments to figure out which sled was the best, just in case it turns out they were fighting about the wrong sled! They must pit sled against sled in a rigorous and methodical series of distance trials. First the orange sled with Delphine versus the blue sled with Cordelia, then the blue sled with Delphine versus the orange sled with Cordelia, next the green sled...
By the third round of these trials the girls had forgotten they were fighting, and by the fifth they had forgotten what they were doing altogether and they were just having fun.
The moral of the story is, sometimes you can't reason with them (because no-one wants to be reasonable) but you can usually distract them — the more byzantine the distraction, the better. Daddies are especially good for that.