First scenario: there is no such gnome. The number of gnomes is also determined by the coin flip, so every gnome will see a human. Then if we apply the reasoning from http://lesswrong.com/r/discussion/lw/l58/anthropic_decision_theory_for_selfish_agents/bhj7 , this will result with a gnome with a selfish human agreeing to x<$1/2.

If the gnomes are created after the coin flip only, they are in exactly the same situation like the humans and we cannot learn anything by considering them that we cannot learn from considering the humans alone.

Instead, let's now make the gnome in the head world hate the other human, if they don't have one themselves. The result of this is that they will agree to any x<$1, as they are (initially) indifferent to what happens in the heads world (potential gains, if they are the gnome with a human, as cancelled out by the potential loss, if they are the gnome without the human).

What this shows is that "Conditional on me existing, the gnome's utility function coincides with mine" is not a sufficient condition for "I should follow the advice that the gnome would have precommited to give".

What I propose is instead: "If conditional on me existing the gnome's utility function coincides with mine, and conditional on me not existing the gnome's utility function is a constant, then I should follow the advice that the gnome would have precommited to."

ETA: Speaking of indexicality-dependent utility functions here. For lexicality-independent utility functions, such as total or average utilitarianism, the principle simplifies to: "If the gnome's utility function coincides with mine, then I should follow the advice that the gnome would have precommited to."