Wei Dai wrote:
Now suppose that two people, Alice and Bob, somehow agree that a measure M
is the objectively correct measure, but Bob insists on using measure M' in
making decisions. He says "So what if universe A has a bigger measure than
universe B according to M? I just care more about what happens in universe
B than universe A, so I'll use M' which assigns a bigger measure to
universe B." What can Alice say to Bob to convince him that he is
not being rational? I don't see what the answer could be.

But measures aren't just about making decisions about what to *do*, the main argument for a single objective measure is that such a measure could make predictions about what we *see*, like why we see regular laws of physics and never see any "white rabbits". Although Bob can decide that only universes where gravity is repulsive matter to him in terms of his decision-making (so that he'd be happy to bet his life's savings that a dropped ball would fall up), he'll have to agree with Alice on what is actually observed to happen when a particular ball is dropped. Without an objective measure, I don't think there's any way to explain why we consistently see outcomes that obey the known laws of physics (like why we always see dropped balls fall towards the earth).

Jesse Mazer

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