As long as these instances are independent of each other—sure. Like with your houses analogy. When we are dealing with simple, central cases there is no diasagreement between probability and weighted probability and so nothing to argue about.
But as soon as we are dealing with more complicated scenario where there is no independence and it’s possible to be inside multiple houses in the same instance
If you can demonstrate how, in the reference class setting, there is a relevant criterion by which several instances should be grouped together, then I think you could have an argument.
If you look at space-time from above, there’s two blue houses for every red house. Sorry I meant there’s two SB(=Sleeping Beauty)-tails instances for every SB-heads instance. The two instances you want to group together (tails-Monday & tails-Tuesday) aren’t actually at the same time (not that I think it matters). If the universe is very large of Many Worlds is true, then there are in fact many instances of Monday-heads, Monday-tails, and Tuesday tails occurring at the same time, and I don’t think you want to group those together.
In any case, from the PoV of SB, all instances look identical to you. So by what criterion should we group some of them together? That’s the thing I think your position requires (just because you accept reference classes are a priori valid and then become invalid in some cases), and I don’t see the criterion.
If you can demonstrate how, in the reference class setting, there is a relevant criterion by which several instances should be grouped together, then I think you could have an argument.
If you look at space-time from above, there’s two blue houses for every red house. Sorry I meant there’s two SB(=Sleeping Beauty)-tails instances for every SB-heads instance. The two instances you want to group together (tails-Monday & tails-Tuesday) aren’t actually at the same time (not that I think it matters). If the universe is very large of Many Worlds is true, then there are in fact many instances of Monday-heads, Monday-tails, and Tuesday tails occurring at the same time, and I don’t think you want to group those together.
In any case, from the PoV of SB, all instances look identical to you. So by what criterion should we group some of them together? That’s the thing I think your position requires (just because you accept reference classes are a priori valid and then become invalid in some cases), and I don’t see the criterion.