If "you" is not just one Everett branch, but a set of sufficiently similar Everett branches, that makes the coinflip even more similar to quantum measurement, in the sense that when "you" flip the coin, the different branches flip it slightly differently, so you get heads in some of them, and tail in others.
Some keywords you may find useful: logical uncertainty, probability is in the mind.
If I push the classical uncertainty into the past by, say, shaking a box with the coin inside and sticking it in a storage locker and waiting a year (or seeding a PRNG a year ago and consulting that) then even though the initial event might have branched nicely, right now that cluster of sufficiently-similar Everett branches are facing the same situation in the original question, right? Assuming enough chaotic time has passed that the various branches from the original random event aren't using that randomness for the same reason.
I understand from things like this that it doesn't take a lot of (classical) uncertainty or a lot of time for a system to become unpredictable at scale, but for me that pushes the question down to annoying concrete follow-ups like:
I think the quantum uncertainty can propagate to large scale relatively fast, like on the scale of minutes. If we take an identical copy of you (in an identical copy of the room, isolated from the rest of the universe), and five minutes later you flip a coin, the result will be random, as the quantum uncertainty has propagated through your neurons and muscle fibers.
(Not sure about this. I am not an expert, I just vaguely remember reading this somewhere.)
Usually we do not notice this, because for non-living things, such as rocks, a few atoms moved here or there does not matter on the large scale; on the other hand, living things have feedback and homeostatis, keeping them in some reasonable range. However, things like "flipping a coin" are designed to be sensitive to noise. The same is true for pinball.
Question 5 is really the most important one here.
It seems likely that however you map the concept of 'you' into physical terms, it pretty much has to be based on classical properties rather than quantum coherent ones. So in fact quantum theory and MWI is almost irrelevant here, except as a reason why 'you' may be somewhat more plural than you think. Even in a classical multiverse, 'you' could be plural so MWI isn't actually necessary here. Quantum theory just makes it far more likely that such plurality does exist even when we don't more directly detect it.
No matter how finely you define 'you' in terms of pre-flip observations and thought processes, it is very likely that roughly equal parts of 'you' post-flip see heads and tails. This would not hold if for some reason a large fraction of 'you' flips the coin in a way that is highly correlated with those pre-flip observations and thought processes e.g. knowingly starting with the coin heads-up and just dropping it a short distance.
I'm not convinced that the specifics of "why" someone might consider themselves a plural smeared across a multiverse are irrelevant. MWI and the dynamics of evolving amplitude are a straightforward implication of the foundational math of a highly predictive theory, whereas the different flavors of classical multiverse are a bit harder to justify as "likely to be real", and also harder to be confident about any implications.
If I do the electron-spin thing I can be fairly confident of the future existence of a thing-which-claims-to-be-me experiencing both outcomes as well as my relative likelihood of "becoming" each one, but if I'm in a classical multiverse doing a coin flip then perhaps my future experiences are contingent on whether the Boltzmann-brain-emulator running on the grand Kolmogorov-brute-forcing hypercomputer is biased against tails (that's not to say I can make use of any of that to make a better prediction about the coin, but it does mean upon seeing heads that I can conclude approximately nothing about any "me"s running around that saw tails).
Fully agreed, I wasn't trying to say that there are just as good justifications for a classical multiverse as a quantum multiverse. Just that it's the "multiverse" part that's more relevant than the "quantum" part. If you accept multiverses at all, most types include the possibility that there may be indistinguishable pre-flip versions of 'you' that experience different post-flip outcomes.
MWI and the dynamics of evolving amplitude are a straightforward implication of the foundational math of a highly predictive theory,
No they are not straightforward, MWI is controversial and subject to ongoing research.
What do you think about quantum immortality/suicide? Seems like it has a direct bearing on what you are asking.
For me the only "obvious" takeaway from this re. quantum immortality is that you should be more willing to play quantum Russian roulette than classical Russian roulette. Beyond that, the topic seems like something where you could get insights by just Sitting Down and Doing The Math, but I'm not good enough at math to do the math.
The thing you are calling quantum indeterminacy is actually MWI.
You can't solve the decision theoretic problem without knowing whether the "you" in other branches is "really" you, which QM doesn't tell you.
Let's say I've got an electron, either spin-up or spin-down. Let's make it easy and say its state is just |↑⟩+|↓⟩. I do an observation and then my Everett branch gets split in two: there's a version of me with exactly half the measure/amplitude/reality-fluid of my pre-observation branch which observes the electron as spin-up, and another version which observes the electron as spin-down. Standard stuff.
Compare and contrast with me flipping a coin. I'm uncertain whether it will land heads-up or tails-up, and I'm fairly sure the system is chaotic enough and symmetric enough and I know little enough about it that betting anything other than 0.50/0.50 would be a bad idea. Yet, post-flip, there's only one version of me: if I see the coin heads-up I'm pretty confident there's no version of me out there with meaningful measure who sees it tails-up.
The quantum indeterminacy situation seems lower-variance to me, because post-observation you have a built-in "hedge": your other branches. If I make a bet on the observation, gaining $1 on spin-up/heads and losing $1 on spin-down/tails, and I value my balance linearly in dollars and linearly in (relative) measure across branches, then:
The difference is clearer to me if you crank up the stakes. Let's take the old classic of "flip a coin/observe an electron, if it's heads/|↑⟩ you get an additional copy of Earth and if it's tails/|↓⟩ you lose your one existing copy". Leaving aside the details of how valuable an additional copy of Earth is, it certainly feels to me like there's a difference between:
My questions are: