Things like lions, and chairs are other examples.
And counted branches.
This is how Wallace defines it (he in turn defines macroscopically indistinguishable in terms of providing the same rewards). It’s his term in the axiomatic system he uses to get decision theory to work. There’s not much to argue about here?
His definition leads to contradiction with informal intuition that motivates consideration of macroscopical indistinguishability in the first place.
We should care about low-measure instances in proportion to the measure, just as in classical decision theory we care about low-probability instances in proportion to the probability.
Why? Wallace’s argument is just “you don’t care about some irrelevant microscopic differences, so let me write this assumption that is superficially related to that preference, and here—it implies the Born rule”. Given MWI, there is nothing wrong physically or rationally in valuing your instances equally whatever their measure is. Their thoughts and experiences don’t depend on measure the same way they don’t depend on thickness or mass of a computer implementing them. You can rationally not care about irrelevant microscopic differences and still care about number of your thin instances.
It doesn’t matter whether you call your multiplier “probability” or “value” if it results in your decision to not care about low-measure branch. The only difference is that probability is supposed to be about knowledge, and Wallace’s argument involving arbitrary assumption, not only physics, means it’s not probability, but value—there is no reason to value knowledge of your low-measure instances less.
It doesn’t? Nothing stops you from making decisions in a world where you are constantly splitting. You can try to maximize splits of good experiences or something. It just wouldn’t be the same decisions you would make without knowledge of splits, but why new physical knowledge shouldn’t change your decisions?