Let's play around with the quantum measure some more. Specifically, let's posit a theory T that claims that the quantum measure of our universe is increasing - say by 50% each day. Why could this be happening? Well, here's a quasi-justification for it: imagine there are lots and lots of of universes, most of them in chaotic random states, jumping around to other chaotic random states, in accordance with the usual laws of quantum mechanics. Occasionally, one of them will partially tunnel, by chance, into the same state our universe is in - and then will evolve forwards in time exactly as our universe is. Over time, we'll accumulate an ever-growing measure.
That theory sounds pretty unlikely, no matter what feeble attempts are made to justify it. But T is observationally indistinguishable from our own universe, and has a non-zero probability of being true. It's the reverse of the (more likely) theory presented here, in which the quantum measure was being constantly diminished. And it's very bad news for theories that treat the quantum measure (squared) as akin to a probability, without ever renormalising. It implies that one must continually sacrifice for the long-term: any pleasure today is wasted, as that pleasure will be weighted so much more tomorrow, next week, next year, next century... A slight fleeting smile on the face of the last human is worth more than all the ecstasy of the previous trillions.
One solution to the "quantum measure is continually diminishing" problem was to note that as the measure of the universe diminished, it would eventually get so low that that any alternative, non-measure diminishing theory, not matter how initially unlikely, would predominate. But that solution is not available here - indeed, that argument runs in reverse, and makes the situation worse. No matter how initially unlikely the "quantum measure is continually increasing" theory is, eventually, the measure will become so high that it completely dominates all other theories.