I think the conflict dissolves if you actually try to use your anticipation to do something useful.
Example. Suppose you can either push button A (before 11AM) so that if you're still in the room you get a small happiness reward, or you can push button B so if you're transported to paradise you get a happiness reward. If you value happiness in all your copies equally, you should push button B, which means that you "anticipate" being transported to paradise.
This gets a little weird with the clones and to what extent you should care about them, but there's an analogous situation where I think the anthropic measure solution is clearly more intuitive: death. Suppose the many worlds interpretation is true and you set up a situation so that you die in 99% of worlds. Then should you "anticipate" death, or anticipate surviving? Anticipating death seems like the right thing. A hedonist should not be willing to sacrifice 1 unit of pleasure before quantum suicide in order to gain 10 units on the off chance that they survive.
So I think that one's anticipation of the future should not be a probability distribution over sensory input sequences (which sums to 1), but rather a finite non-negative distribution) (which sums to a non-negative real number).
For some time I've been pondering on a certain scenario, which I'll describe shortly. I hope you may help me find a satisfactory answer or at very least be as perplexed by this probabilistic question as me. Feel free to assign any reasonable a priori probabilities as you like. Here's the problem:
It's cold cold winter. Radiators are hardly working, but it's not why you're sitting so anxiously in your chair. The real reason is that tomorrow is your assigned upload (and damn, it's just one in million chance you're not gonna get it) and you just can't wait to leave your corporality behind. "Oh, I'm so sick of having a body, especially now. I'm freezing!" you think to yourself, "I wish I were already uploaded and could just pop myself off to a tropical island."
And now it strikes you. It's a weird solution, but it feels so appealing. You make a solemn oath (you'd say one in million chance you'd break it), that soon after upload you will simulate this exact moment thousand times simultaneously and when the clock strikes 11 AM, you're gonna be transposed to a Hawaiian beach, with a fancy drink in your hand.
It's 10:59 on a clock. What's the probability that you'd be in a tropical paradise in one minute?
And to make things more paradoxical: What would be said probability, if you wouldn't have made such an oath - just seconds ago?