Suppose there are only two logically possible deterministic universes A and B, and you know that A has measure 0.9, and B has measure 0.1. Suppose that until time T the history of these two universes are identical. At time T an experiment will be done in both universes. In universe A the outcome of the experiment will be "a", and in universe B the outcome will be "b". If before time T you were given an opportunity to bet $10 that the outcome is "a" at 1:1 odds, so that in universe A you would gain $10, and in universe B you would lose $10, Would you take the bet?
The standard answer is yes, you should take it because A has greater measure. But that assumes you care more about universes that have greater measure than universes that have less measure. But you could say that you don't care about what happens in universe A, only about what happens in universe B, in which case you wouldn't take the bet. So it seems that the measure only affects your decisions if it enters into your utility function somehow, and it's not clear that it must. Even if you knew that only universe A is real, that is, A has measure 1, and B has measure 0, you could still rationally not take the bet. After all, even if universe B doesn't have "real" existence, whatever that means, it still has some sort of platonic existence, and you can still care more about what happens in universe B than what happens in universe A. If people's utilities functions could ignore the "real" measure, then what relevance does it have? Why are we arguing about whether the real measure is the Speed Prior or a more dominant prior? You might argue that most people aproximately behave as if they use the real measure. But by using the word "most" you're already presuming that the real measure is relevant. In the above example (where universe B has measure 0), universe B might be filled with people who ignore the real measure and only care about universe B, and if you yourself only cared about universe B, then you'd act as if you expected most people to ignore the real measure.