"I'll just quietly come round to it"

There's a third option between holding and the climb-down, and it's the one most people take most often. You stop defending the line, you don't say you were wrong, and a few days later you're taking the third exit as though you'd always taken it. Nobody had to lose. It feels like the kind version.

Donald Ferrin and colleagues studied this in 2007, under the name reticence. They compared three responses to being accused of a lapse, apologising, denying, and saying nothing much either way, and found reticence the weakest of the three. When the matter was about competence, saying nothing failed to do what an apology does, which is show you can see the error and mean to do better. When it was about integrity, it failed to do what a denial does. It got the worst of both, in two laboratory studies in two countries. The person who says nothing looks like someone who either hasn't noticed they were wrong or has noticed and won't say.

That's what the slide looks like from the outside. The other person watched you argue for the second exit for ten minutes, and now you're taking the third, and you haven't said a word about it. They notice. They always notice. What they can't tell is whether you've changed your mind or just given up, and whether you know you were wrong or have quietly rewritten it in your head so that you weren't. It's like a wall that's been repainted over a crack. The crack's still there, and everyone who knew it was there can see the paint.

The slide also has a cost you don't see until later, which is that it keeps the second argument alive. Because the line was never withdrawn, it can come back. Six months on, when the route comes up again, your partner says "you were the one who insisted on the second exit," and you say "I never insisted," and you're both right, because the line was neither held nor dropped. It was left.

The climb-down is a sentence. The slide is a silence you'll have to explain later. Of the two, the sentence is the shorter job, and it's the only one that closes the matter, because it's the only one where both of you heard it close.