Situation 1 is better for person X than situation 2 (that is, it gives X higher utility) if and only if person X prefers that situation.
I think you need “prefers that situation for themselves”. Otherwise, imagine person X who is a utilitarian—they’ll always prefer a better world, but most ways of making the world better don’t “benefit X”.
Then, unfortunately, we run into the problem that we’re unable to define what it means to prefer something “for yourself”, because we can no longer use (even idealised) choices between different options.
I think you need “prefers that situation for themselves”. Otherwise, imagine person X who is a utilitarian—they’ll always prefer a better world, but most ways of making the world better don’t “benefit X”.
Then, unfortunately, we run into the problem that we’re unable to define what it means to prefer something “for yourself”, because we can no longer use (even idealised) choices between different options.
Good point, thanks! Edited.