It’s not at all clear in what sense one can be correct about “hoping for a particular outcome”.
It’s simply a question of: which of these possibilities, if you observed them, would maximize your expected final utility. There is a ‘fact of the matter’ about this, regardless of whether the spectator’s judgements make any difference.
If you take an updateless look at the situation, observations never influence utility. You can consider relevant “observational events” that contain the worlds that you expect being able to influence in the future given what you’ve observed, and then different observational events would have different utility. But possible reasons to actually compare these numbers are nonobvious (e.g. you might be able to control your observations, but then it’s not necessarily a good way to parse the consequences of that control decision), so you could just as well treat them as unrelated. Also, these are heuristic rules for simplifying the updateless calculation (by moving a constant term outside maximization operator), and given that you are stipulated to be unable to influence anything, I wonder if these should just all be empty, giving you trivially zero utility, both for all observations and a priori.
If you take an updateless look at the situation, observations never influence utility. You can consider relevant “observational events” that contain the worlds that you expect being able to influence in the future given what you’ve observed, and then different observational events would have different utility. But possible reasons to actually compare these numbers are nonobvious (e.g. you might be able to control your observations, but then it’s not necessarily a good way to parse the consequences of that control decision), so you could just as well treat them as unrelated. Also, these are heuristic rules for simplifying the updateless calculation (by moving a constant term outside maximization operator), and given that you are stipulated to be unable to influence anything, I wonder if these should just all be empty, giving you trivially zero utility, both for all observations and a priori.