As a decision theoretic agent being told you are not the decider is equivalent to dying.

Or more precisely it is equivalent to falling into a crack in spacetime without Amelia Pond having a crush on you. ;)

It is an anthropic problem.

Depends of what you mean by "Anthropic problem". The first google result for that term right now is this post, so the term doesn't seem to have a widely-agreed upon meaning, though there is some interesting discussion on Wikipedia.

Maybe we could distinguish

• "Anthropic reasoning", where your reasoning needs to take into account not only the facts you observed (i.e. standard bayesian reasoning) but also the fact that you are there to take the decision period.

• "Anthropic scenarios" (ugh), where the existence of agents comes into account (ike the sleeping beauty problem, our universe, etc.)

Anthropic scenarios feature outlandish situations (teleporters, the sleeping beauty) or are somewhat hard to reproduce (the existence of our universe). So making scenarios that aren't outlandish anthropic scenarios but still require anthropic reasoning is nice for intuition (especially in an area like this where everybody's intuition starts breaking down), even if it doesn't change anything from a pure decision theory point of view.

I'm not very happy with this decomposition; seems to me "is this an anthropic problem?" can be answered by "Well it does require anthropic reasoning but doesn't require outlandish scenarios like most similar problems", but there may be a better way of putting it.