Followup to: Quantum Russian Roulette; The Domain of Your Utility Function

The only way to win is cheat
And lay it down before I'm beat
and to another give my seat
for that's the only painless feat.

Suicide is painless
It brings on many changes
and I can take or leave it if I please.

-- M.A.S.H.

Let us pretend, for the moment, that we are rational Expected Utility Maximisers. We make our decisions with the intention of achieving outcomes that we judge to have high utility. Outcomes that satisfy our preferences. Since developments in physics have led us to abandon the notion of a simple single future world our decision making process must now grapple with the notion that some of our decisions will result in more than one future outcome. Not simply the possibility of more than one future outcome but multiple worlds, each of which with different events occurring. In extreme examples we can consider the possibility of staking our very lives on the toss of a quantum die, figuring that we are going to live in one world anyway!

How do preferences apply when making decisions with Many Worlds? The description I’m giving here will be obvious to the extent of being trivial to some, confusing to others and, I expect, considered outright wrong by others. But it is the post that I want to be able to link to whenever the question “Do you believe in quantum immortality?” comes up. Because it is a wrong question!

Utility Applies to Universes, Not (just) Mental States

I am taking for granted here that when we are considering utility and the maximisation thereof we are not limiting ourselves to maximising how satisfied we expect to feel with an outcome in the future. Peter_de_Blanc covered this topic in the post The Domain of Your Utility Function. Consider the following illustration of evaluating expected utility:

Note in particular the highlighted arrow from Extrapolated Future A to Utility of A and not from Extrapolated Mind A to Utility A. Contrary to surprisingly frequent assumptions, the sane construction of expected utility cares not just how we expect our own mind to be. Our utility function applies to our whole extrapolation of the future. We can care about our friends, family and strangers. We can have preferences about the passengers in a rocket that will have flown outside our future light cone. We can have preferences about the state of the universe even in futures where we die.

Quantum Russian Roulette

Given a source of quantum randomness we can consider a game people may play in a hope to exploit the idea of quantum immortality as a way to Get Rich Quick! Quantum Russian Roulette is an obvious example. 16 people pool all their money. They then use a device that uses 4 quantum bits to pick one of the players to live and kills the other 15 painlessly. Winner takes all! Each of the players will wake up in a world where they are the alive, well and rich. One hopes they were at least wise enough not to play the game against their loved ones!

Now, what does the decision of whether to play QRoulette look like?

The idea is that after going to sleep with $300k you will always and only wake up with $600k. Thus it is said by some that if you accept the Many Worlds implications of Quantum Mechanics you should consider it rational to volunteer for Quantum Roulettes whenever they become available. Kind of like future oriented anthropic planning or something.

Friends and Family: The Externalities Cop-Out

When someone dies the damage done is to more than just the deceased. There are all sorts of externalities, most of them negative. The economy is damaged, many people grieve. As such a common rejoinder to a quantum suicide advocate is “The reason that I wouldn’t commit quantum suicide is that all the people who care about me would be distraught”. That is actually a good reason. In fact it should be more than sufficient to prevent just about everyone from getting quantum suicidal all by itself. But it misses the point.

Consider the Least Convenient Possible World. The Quantum Doomsday Lottery. It’s a solo game:

• Build a device that can send our sun supernova. Or even just obliterate earth comprehensively.
• Build another device that can generate quantum bits and use them to buy lottery tickets.
• A third device anaesthetises you, activates the quantum lottery playing machine.
• If you don’t win the lottery the earth is obliterated.
• In a future everett branches in which you wake up and the species exists, and in fact in all such branches, you win the lottery.

Those who have “other people will be sad” as their true rejection of the option of playing quantum roulette can be expected to jump at the opportunity to get rich quick without making loved ones grieve. Most others will instead look a little closer and find a better reason not to kill themselves and destroy the world.

Failure Amplification

In the scenarios above only two options are considered. “Win” and “lose/oblivion/armageddon”. Of course the real world is not so simple. All sorts of other events could occur that aren’t accounted for in the model. For example, the hardware could break, causing your execution to be botched. Instead of waking up only when you win you also wake up when you lose but the machine only manages to make you “mostly dead” then breaks. You survive in huge amounts of pain, crippled and with 40 less IQ points.

Now, you may have extreme confidence in your engineer. You expect the machine to work as specified 99.9999% of the time. In the other 0.0001% of cases minor fluctuations in the power source or a hit by a cosmic ray somewhere triggers a vulnerability and a failed execution occurs. Humans accept that level of risk on a daily basis with such activities as driving a car or breathing (in New York). (In this case we would call it a “Micronotmort”.) Yet you are quantum suicidal and have decided that all Everett branches in which you die don’t count.

So, if you engage in a 1:2,000,000 Quantum Lottery you can consider (approximately) the following outcomes: (1 live:1,999,998 die:2 crippled). Having decided that 1,999,998 of those branches don’t count you are left with a one in three chance of being a cripple. Mind you given the amount of money that would be staked in such a lottery it would probably be pretty good deal financially!

What does this mean?

Don’t try to use Quantum Suicide to brute force cryptoanalysis problems. It just isn’t going to work even if you think the theoretical expected outcome to be worthwhile! You aren’t that good at building stuff.

While this is also also an interesting topic in itself (I believe there are posts about it floating around here someplace) it is also somewhat beside the main point. Is quantum suicide a good idea even when you iron out all the technical difficulties?

Quantum Sour Grapes

People have been gambling for millennia. Most of the people who have lost bets have done so without killing themselves. Much can be learned from this. For example, that killing yourself is worse than not killing yourself. This intuition is one that should follow over to ‘quantum’ gambles rather straightforwardly. Consider this alternative:

Here we see just as many futures in which Blue ends up with the jackpot. And this time Blue manages not to kill himself in branches where he loses. Blue is sad for a while until he makes some more money and gets over it. He isn’t dead. This is obviously just plain better. The only reasons for Blue to kill himself when he loses would be contrived examples such as those involving torture that can only be avoided by payment that can not be arranged any other way.

You get just as much quantum ‘winningness’ if you don’t kill yourself. For this reason I consider games like Quantum Roulette to be poorly named, particularly when “Quantum Immortality” is also mentioned. I much prefer the label “Quantum Sour Grapes”.

Lesson: Don’t make decisions based on anticipated future anthropic reasoning. That’s just asking for trouble.

Not Wrong (But Perhaps Crazy)

I personally consider anyone who wants to play quantum roulette to be crazy. And anyone who wanted to up the stakes to a doomsday quantum variant would be a threat to be thwarted at all costs if they were not too crazy to even take seriously. But I argue that this is a matter of preference and not (just) one of theoretical understanding. We care about possible future states of the states of the universe - of all of the universe. If we happen to prefer futures of our current Everett branch where most sub-branches have us dead but one does not then that we can do that.