You pick your answer in ignorance of who you'll be in the problem. You don't know whether you're the pusher, the pushed, or one of the people tied to the tracks. In this case, the answer is easy: push! There's a 6/7 chance you'll survive so the selfish and utilitarian answers converge.

You mean, the selfish answer becomes the utilitarian one. In general I find arguments which only work when you consciously refuse to take into account some of the information available to you (like whether you are the pusher) quite suspect. It seems anti-Bayesian.