My understanding is that regardless of the interpretation you put behind the quantum measurements you have to calculate as if there are multiple worlds
You have to do this in any probabilistic calculation, especially when you have chains of dependent probabilities. The mere fact that, e.g., the behavior of a ball bouncing around on a roulette wheel can be understood in terms of branching possible worlds, is not usually interpreted as implying that those possible worlds actually exist, or that they interact with this one.
The peculiarity of quantum probability is that you can get cancellation of probability amplitudes (the complex numbers at the step just before probabilities are computed). Thus in the double slit experiment, if you try to analyze what happens in a way analogous to Galton's Quincunx, you end up saying that particles don't arrive in the dark areas, because the possible paths 'cancel' at the amplitude level. This certainly makes no sense for probabilities, which are always nonnegative and so their sum is monotonically increasing - adding a possible path to an outcome can never decrease the overall probability of that outcome occurring. Except in quantum mechanics; but that just means that we are using the wrong concepts to understand it, not that there is such a thing as a negative probability.
However, it is not as if we know that the only way to get quantum probabilities is by supposing the existence and interaction of parallel worlds in the multiverse, and in fact all the attempts to make that idea work in detail end up in a conceptual shambles (see: measure problem, relativity problem, preferred basis problem). We don't need a multiverse explanation; we just need a single-world explanation that gives rise to the same probability distributions that are presently obtained from wavefunctions. The Nobel laureate Gerard 't Hooft has some ideas in this direction which deserve to be much better known; they are at least as important as anything in the "famous" interpretations associated with Bohm, Everett, and Cramer.
Thanks for the additional info and explanation. I have some books about QM on my desk that I really ought to study in depth...
I should mention though that what you state about needing only a single-world is in direct contradiction to what EY asserts: "Whatever the correct theory is, it has to be a many-worlds theory as opposed to a single-world theory or else it has a special relativity violating, non-local, time-asymmetric, non-linear and non-measurepreserving collapse process which magically causes blobs of configuration space to instantly vanish [....
Suppose you believe in the Copenhagen interpretation of quantum mechanics. Schroedinger puts his cat in a box, with a device that has a 50% chance of releasing a deathly poisonous gas. He will then open the box, and observe a live or dead cat, collapsing that waveform.
But Schroedinger's cat is lazy, and spends most of its time sleeping. Schroedinger is a pessimist, or else an optimist who hates cats; and so he mistakes a sleeping cat for a dead cat with probability P(M) > 0, but never mistakes a dead cat for a living cat.
So if the cat is dead with probability P(D) >= .5, Schroedinger observes a dead cat with probability P(D) + P(M)(1-P(D)).
If observing a dead cat causes the waveform to collapse such that the cat is dead, then P(D) = P(D) + P(M)(1-P(D)). This is possible only if P(D) = 1.
If you don't say that only conscious agents can collapse waveforms, then you have to agree that something in the box collapses the waveform as seen from inside the box, while it's still uncollapsed to Schroedinger. And Schroedinger's opening the box collapses that waveform for him; but it is still uncollapsed for someone outside the room. This seems like it might be equivalent to many worlds - all possibilities already exist; you just haven't chosen which one you're going to access until you open the box.
But if you do say that only conscious agents can collapse waveforms, then it's something about their mental processes that does the collapsing. This could mean their beliefs matter. And then, the cat is always dead.
ADDED: People. Read the entire post before responding. I am not claiming that the cat is always dead. I am not claiming that consciousness collapses waveforms. I am claiming that there are only 2 known alternatives:
If you can't produce another alternative, and you don't believe in many-worlds, you owe me an upvote.
Finally, this post is supposed to be fun! You are crushing all whimsy and playfulness on LessWrong when you pile downvotes like bricks on anything playful because it does not provide a complete and satisfactory resolution.