The multiverse smears me into a messy continuum of me and not-me. In this "least arbitrary" of preference schemes, it is not at all clear what is actually being valued.
If you are saying that the MWI is just a way of visualising probability, then we are back to:
"Making such a decision while not knowing how the probabilty will turn out works just the same classically, with no multiple copies involved. Evidently the decision has nothing to do with "valuing multiple copies" - and is simply the result of the observer's uncertainty."
Observers often place value on future possibilities that they might find themselves witnessing. But that is not about quantum theory, it is about observer uncertainty. You get precisely the same phenomenon in classical universes. To claim that that is valuing your future self in other worlds is thus a really bad way of looking at what is happening. What people are valuing is usually, in part, their own possible future existence. And they value that just the same whether they are in a universe with many worlds physics - or not. The values are nothing to do with whether the laws of physics dictate that copying takes place. If it turns out experimentally that wavefunctions collapse, that will have roughly zero impact on most people's moral systems. They never valued other Everett worlds in the first place - so their loss would mean practically nothing to them.
The "many worlds" do not significantly interfere with each other, once they are remote elements in the superposition. A short while after they have split they are gone for good. There is usually no reason to value things you will never see again. You have no way to influence them at that stage anyway. Actually caring about what happens in other worlds involves counterfactuals - and so is not something evolution can be expected to favour. That is an obvious reason for so few people actually doing it.
Maybe - from the existence of this debate - this is some curious corner of the internet where people really do care about what happens in other worlds - or at least think that they do. If so, IMO, you folk have probably been misled - and are in need of talking down. A moral system that depends on the details of the interpretation of quantum physics? Really? The idea has a high geek factor maybe - but it seems to be lacking in common sense.
Purporting to care about a bunch of things that never happened, that can't influence you and that you can't do anything about makes little sense as morality - but looks a lot like signalling: "see how very much I care?" / "look at all the things I care about". It seems to be an extreme and unbelievable signal, though - so: you are kidding - right?
Since you are writing below my post and I sense detachment from what I've tried to express, I refer you to my http://lesswrong.com/lw/2di/poll_what_value_extra_copies/27ee and http://lesswrong.com/lw/2e0/mwi_copies_and_probability/27f1 comments.
ETA: I retract "detachment". Why you don' play Russian roulette? Because you could get killed. Why a magician plays Russian roulette? Because he knows he won't. Someone who doesn't value Everett branches according to their "reality mass" doesn't win -- no magician would play quantum Russian roule...
Followup to: Poll: What value extra copies?
For those of you who didn't follow Eliezer's Quantum Physics Sequence, let me reiterate that there is something very messed up about the universe we live in. Specifically, the Many Worlds Interpretation (MWI) of quantum mechanics states that our entire classical world gets copied something like 1040±20 times per second1. You are not a line through time, but a branching tree.
If you think carefully about Descartes' "I think therefore I am" type skepticism, and approach your stream of sensory observations from such a skeptical point of view, you should note that if you really were just one branch-line in a person-tree, it would feel exactly the same as if you were a unique person-line through time, because looking backwards, a tree looks like a line, and your memory can only look backwards.
However, the rules of quantum mechanics mean that the integral of the modulus squared of the amplitude density, ∫|Ψ|2, is conserved in the copying process. Therefore, the tree that is you has branches that get thinner (where thickness is ∫|Ψ|2 over the localized density "blob" that represents that branch) as they branch off. In fact they get thinner in such a way that if you gathered them together into a bundle, the bundle would be as thick as the trunk it came from.
Now, since each copying event creates a slightly different classical universe, the copies in each of the sub-branches will each experience random events going differently. This means that over a timescale of decades, they will be totally "different" people, with different jobs, probably different partners and will live in different places though they will (of course) have your DNA, approximate physical appearance, and an identical history up until the time they branched off. For timescales on the order of a day, I suspect that almost all of the copies will be virtually identical to you, even down to going to bed at the same time, having exactly the same schedule that day, thinking almost all of the same thoughts etc.
MWI mixes copies and probability
When a "random" event happens, either the event was pseudorandom (like a large digit of pi) or it was a copy event, meaning that both (or all) outcomes were realized elsewhere in the wavefunction. This means that in many situations, when you say "there is a probability p of event X happening", what this really means is "proportion p of my copy-children will experience X".
LW doesn't care about copies
In Poll: What value extra copies?, I asked what value people placed upon non-interacting extra copies of themselves, asking both about lock-step identical and statistically identical copies. The overwhelming opinion was that neither were of much value. For example, Sly comments:2
"I would place 0 value on a copy that does not interact with me. This might be odd, but a copy of me that is non-interacting is indistinguishable from a copy of someone else that is non-interacting. Why does it matter that it is a copy of me?"
How to get away with attempted murder
Suppose you throw a grenade with a quantum detonator at Sly. The detonator will sample a qbit in an even superposition of states 1 and 0. On a 0 it explodes, instantly vaporizing sly (it's a very powerful grenade). On a 1, it defuses the grenade and dispenses a $100 dollar note. Suppose that you throw it and observe that it doesn't explode:
(A) does Sly charge you with attempted murder, or does he thank you for giving him $100 in exchange for something that had no value to him anyway?
(B) if he thanks you for the free $100, does he ask for another one of those nice free hundred dollar note dispensers? (This is the "quantum suicide" option
(C) if he says "the one you've already given me was great, but no more please", then presumably if you throw another one against his will, he will thank you for the free $100 again. And so on ad infinitum. Sly is temporally inconsistent if this option is chosen.
The punch line is that the physics we run on gives us a very strong reason to care about the welfare of copies of ourselves, which is (according to my survey) a counter-intuitive result.
EDIT: Quite a few people are biting the quantum suicide bullet. I think I'll have to talk about that next. Also, Wei Dai summarizes:
Another way to think about this is that many of us seem to share the follow three intuitions about non-interacting extra copies, out of which we have to give up at least one to retain logical consistency:
I might add a fourth option that many people in the comments seem to be going after: (4) We don't intrinsically value copies in other branches, we just have a subjective anticipation of becoming them.
1: The copying events are not discrete, rather they consist of a continuous deformation of probability amplitude in state space, but the shape of that deformation looks a lot like a continuous approximation to a discrete copying event, and the classical rules of physics approximately govern the time evolution of the "copies" as if they were completely independent. This last statement is the phenomenon of decoherence. The uncertainty in the copying rate is due to my ignorance, and I would welcome a physicist correcting me.
2: There were many others who expressed roughly similar views, and I don't hold it as a "black mark" to pick the option that I am advising against, rather I encourage people to honestly put forward their opinions in a spirit of communal learning.