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First. I think it only creates confusion to put consistent histories in the Everett/many worlds camp, since in one respect they are directly opposite, as I pointed out in my first paper in 1984. Quantum time development in consistent histories is stochastic; in the Everett approach it is deterministic. For a more recent perspective on consistent histories, see my presentation at this workshop.
Second, I would think that your anthropic argument works just as well in a classical world in which entropy is increasing. Quasiclassical frameworks are then useful in telling us that such arguments, whatever their validity, need not change if we believe the world is quantum mechanical, for classical mechanics is a quite adequate approximation to quantum theory in addressing questions of this sort.
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