The Case for Quantum Morality

A thought experiment in support of the many-worlds philosophy
Electrical Engineering and Computer Science
I should start by saying that everything that I'm about to write may or may not be completely bogus. Still, I haven't convinced myself that it's not bogus, so I guess I'll share it anyway.
I want to make the claim that our understanding of physics should influence our ethical decisions. To ease you into my rather ridiculous proposal, let me introduce this subject with an even more ridiculous story.
Imagine that you're trapped in a room with a maniacal killer. In his hands he clutches two six-sided dice, and he offers you the following deal: If he rolls the dice and they're both sixes, he'll let you go. Otherwise... well, I think you get the idea.
Okay, lousy deal or not, you don't have much choice, so, stoically and unperturbed you nod and await your rather bizarre fate. You hear the dice clatter across the table, and you force yourself to look down. Two sixes gleam beneath your eyes.
"No fair," bellows the madman. "Let's try again!"
Before you have a chance to lecture him on contractual obligations, the dice are once more in his hands, and he tosses them across the table. Sixes again.
"Impossible!" he exclaims.
Actually, one out of one thousand two-hundred and ninety-six is far from a statistical impossibility, but you're grateful for your life, and so you decide that pointing out his logical fallacy isn't the best way to maintain your current state of being not dead.
"Again!" says the madman... You're starting to notice a pattern in his train of thought. He rolls the dice a thousand more times. Each time the dice come up sixes.  
"Outrageous!" the madman foams at the mouth. By now, you can't help but agree with him. The chance that you've survived is more unlikely than the chance that cosmic rays from outer space have caused your computer to crash while you were reading this sentence.
Sweating and out of breath, the madman jumps out of his chair and hurls the dice across the room. He leaves, slamming the door behind him. You're alive. You look down at the dice as they lie there on the floor:  a one and a three.
If you think that story is a bit farfetched, then you're probably right. Before you allow reality to set in, I want to try to convince you that with a small modification, the story above is not as completely unreasonable as it may seem. That is, let us suppose that instead of rolling run-of-the-mill six-sided dice, our beloved madman chooses to roll some strange "quantum" dice.  
To understand what happens when you roll quantum dice, we should first understand what I mean when by "normal" dice. Well, when you roll normal dice, you can always predict which sides they will land on provided that you know all of the initial conditions of the roll (such as the velocity of the dice when leaving your hand, their rotational momentum, and so on).
With quantum dice, you really have no idea. Like really, really fundamental-property-of-quantum-mechanics have no idea. Indeed, the apparatus required to roll quantum dice is quite complex, and at any rate, wouldn't look anything like the common dice we know and love. Nevertheless, we can still think of rolling a single quantum die as an experiment that yields the numbers 1 through 6 with equal probability.  
So you're probably asking yourself how this minor distinction could possibly be that important. What's so different about rolling quantum dice? This is actually something that people have been debating for years.
Let's consider different interpretations of what happens when you roll a single quantum die. On one side, you have people who say that the world just transitions to one of these random states and that's it. On the other side, you have people who believe that the world splits into six almost-identical worlds corresponding to the six outcomes of the die. Your consciousness just happens to be one of those six almost-identical consciousnesses.
Believe it or not, this "many-worlds" interpretation of quantum mechanics is perhaps the most dominant view held by scientists. (I would be remiss not to offer a third view which is snarkily dubbed the "shut up and calculate" interpretation. It says that since we can't devise any experiment that could distinguish the two interpretations above, we should just "shut up" and marvel at the incredible accuracy with which the formalism of quantum mechanics allows us to measure things.)
Okay, let's go back now to the madman and his obsession with ending your life via quantum dice. Supposing that the many-worlds interpretation of quantum mechanics is true, how should you feel when you see the two sixes? Relieved? Hey, you just survived a one and thirty-six chance of dying. Not bad. But wait, if the many-worlds interpretation of quantum mechanics is true, then there are thirty-five almost-identical worlds to your own in which you're now dead. Ahhhhhhhh!
Think of what happens when he rolls again, and then again, and again. The number of worlds in which the madman triumphs are growing in number. You're dead in almost all of them. Not exactly the bedtime story you want to be telling your kid at night.
Suppose that you've been incredibly lucky (for indeed, if the many-worlds interpretation of quantum mechanics is true, one of your quantum doppelgangers must have survived all of the dice rolls). How do you punish the madman? Attempted murder? Or do we count all the people he actually murdered in the other worlds
Punishing him like this may seem harsh or even ridiculous since we don't know that the many-worlds interpretation is correct. Nevertheless, a lot of smart people think that the many-worlds interpretation is correct. Should even the possibility that the many-worlds interpretation is true force harsher punishments for the madman? Are the people studying the fundamental way the universe works providing more ethical insight than an armchair philosopher ever could?
You might have the following objection to the above thought experiment. Namely, if the probability you find yourself in one of these weird worlds for which all of the dice show sixes is so small, then why waste your ethical mindspace on such a statistically impossible event. Surely, the world you find yourself in won't be the one in which this issue arises.
In light of that, let's imagine that instead of killing you when any dice shows anything besides a six, that the madman kills you only if he rolls the dice a thousand times and they all come up sixes. Assuming the many-worlds interpretation of quantum mechanics, this quasi-madman has killed you in one of the worlds, but left you unscathed in all the others. Should you really punish him for running this experiment?
There's a greater chance that you will kill a pedestrian when you get in your car in the morning than that you'll find yourself in a world in which the madman has killed you. We certainly don't punish people for attempting to drive to work. Therefore, should the madman's punishment be proportional to the number of worlds in which he actually killed you?
I imagine that the answers to some of these questions are tied to our answers to some other thorny issues. For instance, should we care about the suffering of animals? Animals are separated from humans by some sort of biological barrier, while the humans in other worlds are separated from humans in our world by some sort of causal barrier.
Thankfully, madmen rolling quantum dice probably aren't so big of an issue (at least for now). To find out if we should be taking quantum ethics seriously, we probably require some more science to decide if these sorts of weird quantum effects actually manifest themselves in our daily lives.