Earlier quoted context omitted.
That's not really an apt analogy; if a hangman refuses to tie a knot, they'll find another hangman. The Supreme Court Justice specifically gets to choose one way or the other.
No, he or she doesn't. Because if they did so arbitrarily then they have likely long since been thrown off the lower benches. A judge doesn't decide: a judge weighs evidence and then states which interpretation of the law they believe is correct. If we had a judicial system arbitrated over by people who could simply say "I want this outcome" and make it so, then the country would and should crumble.
... if?