I've been thinking about this topic, off and on, at least since September 1997, when I joined the Extropians mailing list, and sent off a "copying related probability question" (which is still in my "sent" folder but apparently no longer archived anywhere that Google can find). Both Eliezer and Nick were also participants in that discussion. What are the chances that we're still trying to figure this out 12 years later?

My current position, for what it's worth, is that anticipation and continuity of experience are both evolutionary adaptations that will turn maladaptive when mind copying/merging becomes possible. Theoretically, evolution could have programmed us to use UDT, in which case this dilemma wouldn't exist now, because anticipation and continuity of experience is not part of UDT.

So why don't we just switch over to UDT, and consider the problem solved (assuming this kind of self-modification is feasible)? The problem with that is that much of our preferences are specified in terms of anticipation of experience, and there is no obvious way how to map those onto UDT preferences. For example, suppose you’re about to be tortured in an hour. Should you make as many copies as you can of yourself (who won’t be tortured) before the hour is up, in order to reduce your anticipation of the torture experience? You have to come up with a way to answer that question before you can switch to UDT.

One approach that I think is promising, which Johnicholas already suggested, is to ask "what would evolution do?" The way I interpret that is, whenever there’s an ambiguity in how to map our preferences onto UDT, or where our preferences are incoherent, pick the UDT preference that maximizes evolutionary success.

But a problem with that, is that what evolution does depends on where you look. For example, suppose you sample Reality using some weird distribution. (Let’s say you heavily favor worlds where lottery numbers always come out to be the digits of pi.) Then you might find a bunch of Bayesians who use that weird distribution as their prior (or the UDT equivalent of that), since they would be the ones having the most evolutionary success in that part of Reality.

The next thought is that perhaps algorithmic complexity and related concepts can help here. Maybe there is a natural way to define a measure over Reality, to say that most of Reality is here, and not there. And then say we want to maximize evolutionary success under this measure.

How to define “evolutionary success” is another issue that needs to be resolved in this approach. I think some notion of “amount of Reality under one’s control/influence” (and not “number of copies/descendants”) would make the most sense.

Whatever the correct answer is, the first step towards it has to be to taboo words like "experience" in sentences like, "But if I make two copies of the same computer program, is there twice as much experience, or only the same experience?"

What making copies is, is creating multiple instances of the same pattern. If you make two copies of a pattern, there are twice as many instances but only one pattern, obviously.

Are there, then, two of 'you'? Depends what you mean by 'you'. Has the weight of experience increased? Depends what you mean by 'experience'. Think in terms of patterns and instances of patterns, and these questions become trivial.

I feel a bit strange having to explain this to Eliezer Yudkowsky, of all people.

To condense my response to a number of comments here:

It seems to me that there's some level on which, even if I say very firmly, "I now resolve to care only about future versions of myself who win the lottery! Only those people are defined as Eliezer Yudkowskys!", and plan only for futures where I win the lottery, then, come the next day, I wake up, look at the losing numbers, and say, "Damnit! What went wrong? I thought personal continuity was strictly subjective, and I could redefine it however I wanted!"

You reply, "But that's just because you're defining 'I' the old way in evaluating the anticipated results of the experiment."

And I reply, "...I still sorta think there's more to it than that."

To look at it another way, consider the Born probabilities. In this case, Nature seems to have very definite opinions about how much of yourself flows where, even though both copies exist. Now suppose you try to redefine your utility function so you only care about copies of yourself that see the quantum coin land heads up. Then you are trying to send all of your measure to the branch where the coin lands up heads, by exercising your right to redefine personal continuity howsoever you please; whereas Nature only wants to send half your measure there. Now flip the coin a hundred times. I think Nature is gonna win this one.

Tired of being poor? Redefine personal continuity so that tomorrow you continue as Bill Gates and Bill Gates continues as you - just better hope Gates doesn't swap again the next day.

It seems to me that experience and anticipation operate at a more primitive level than my utility function. Perhaps I am wrong. But I would like a cleaner demonstration of how I am wrong, than pointing out how convenient it would be if there were no question.

Of course it must be a wrong question - it is unanswerable, therefore, it is a wrong question. That is not the same as there being no question.

Whenever I read about "weight of experience", "quantum goo", "existentness" etc. I can't keep myself of also thinking of "vital spark", "phlogiston", "ether" and other similar stuff... And it somehow spoils the whole fun...

In the history of mankind, hard looking (meta-)physical dilemmas were much more often resolved by means of elimination rather than by introduction of new "essences". The moral of the history of physics so far is that relativity typically trumps absoluteness in the long run.

For example, I would not be surprised at all, if it turned out that experienced Born probabilities would not be absolute, but would depend on some reference frame (in a very high dimensional space) just like the experience of time, speed, mass, etc. depends on the relativistic frame of reference.

More near-equivalent reformulations of the problem (in support of the second horn):

• A trillion copies will be created, believing they have won the lottery. All but one will be killed (1/trillion that your current state leads directly to your future state). If you add some uniportant differentiation between the copies - give each one a speratate number - then the situation is clearer: you have one chance in a trillion that the future self will remember your number (so your unique contribution will have 1/trillion chance of happening), while he will be certain to believe he has won the lottery (he gets that belief from everyone.

• A trillion copies are created, each altruistically happy that one among the group has won the lottery. One of them at random is designated the lottery winner. Then everyone else is killed.

• Follow the money: you (and your copies) are not deriving utility from winning the lottery, but from spending the money. If each copy is selfish, there is no dilema: the lottery winnings divided amongst a trillion cancels out the trillion copies. If each copy is altruistic, then the example is the same as above; in which case there is a mass of utility generated from the copies, which vanish when the copies vanish. But this extra mass of utility is akin to the utility generated by: "It's wonderful to be alive. Quick, I copy myself, so now many copies feel it's wonderful to be alive. Then I delete the copies, so the utility goes away".

Just an aside - this is obviously something that Eliezer - someone highly intelligent and thoughful - has thought deeply about, and has had difficulty answering.

Yet most of the answers - including my own - seem to be of the "this is the obvious solution to the dilemma" sort.

Following Nominull and Furcas, I bite the third bullet without qualms for the perfectly ordinary obvious reasons. Once we know how much of what kinds of experiences will occur at different times, there's nothing left to be confused about. Subjective selfishness is still coherent because you're not just an arbitrary observer with no distinguishing characteristics at all; you're a very specific bundle of personality traits, memories, tendencies of thought, and so forth. Subjective selfishness corresponds to only caring about this one highly specific bundle: only caring about whether someone falls off a cliff if this person identifies as such-and-such and has such-and-these specific memories and such-and-those personality traits: however close a correspondence you need to match whatever you define as personal identity.

The popular concepts of altruism and selfishness weren't designed for people who understand materialism. Once you realize this, you can just recast whatever it was you were already trying to do in terms of preferences over histories of the universe. It all adds up to, &c., &c.

It's helpful in these sorts of problems to ask the question "What would evolution do?". It always turns out to be coherent, reality-based actions. Even though evolution, to the extent that it "values" things, values different things than I do, I'd like my actions to be comparably coherent and reality-based.

Regarding the first horn: Regardless of whether simple algorithms move "subjective experience" around like a fluid, if the simple algorithms take some resources, evolution would not perform them.

Regarding the second horn: If there was an organism that routinely split, merged, played lottery, and priced side-bets on whether it had won the lottery, then, given zero information about whether it had won the lottery, it would price the side-bet at the standard lottery odds. Splitting and merging, so long as the procedure did not provide any new information, would not affect its price.

Regarding the third horn: Evolution would certainly not create an organism that hurls itself off cliffs without fear. However, this is not because of it "cares" about any thread of subjective experience. Rather, this is because of the physical continuity. Compare this with evolution's choice in an environment where there are "transporters" that accurately convey entities by molecular disassembly/reassembly. Creatures which had evolved in that environment would certainly step through those transporters without fear.

I can't answer the fourth or fifth horns; I'm not sure I understand them.

I still have trouble biting that bullet for some reason. Maybe I'm naive, I know, but there's a sense in which I just can't seem to let go of the question, "What will I see happen next?" I strive for altruism, but I'm not sure I can believe that subjective selfishness - caring about your own future experiences - is an incoherent utility function; that we are forced to be Buddhists who dare not cheat a neighbor, not because we are kind, but because we anticipate experiencing their consequences just as much as we anticipate experiencing our own. I don't think that, if I were really selfish, I could jump off a cliff knowing smugly that a different person would experience the consequence of hitting the ground.

I don't really understand your reasoning here. It's not a different person that will experience the consequences of hitting the ground, it's Eliezer+5. Sure, Eliezer+5 is not identical to Eliezer, but he's really, really, really similar. If Eliezer is selfish, it makes perfect sense to care about Eliezer+5 too, and no sense at all to care equally about Furcas+5, who is really different from Eliezer.

Time and (objective or subjective) continuity are emergent notions. The more basic notion they emerge from is memory. (Eliezer, you read this idea in Barbour's book, and you seemed to like it when you wrote about that book.)

Considering this: yes, caring about the well-being of "agents that have memories of formerly being me" is incoherent. It is just as incoherent as caring about the well-being of "agents mostly consisting of atoms that currently reside in my body". But in typical cases, both of these lead to the same well known and evolutionarily useful heuristics.

I don't think any of the above implies that "thread of subjective experience" is a ridiculous thing, or that you can turn into being Britney Spears. Continuity being an emergent phenomenon does not mean that it is a nonexistent one.

As for what happens ten seconds after that, you have no way of knowing how many processors you run on, so you shouldn't feel a thing

Here's the problem, as far as I can see. You shouldn't feel a thing, but that would also be true if none of you ever woke up again. "I won't notice being dead" is not an argument that you won't be dead, so lottery winners should anticipate never waking up again, though they won't experience it (we don't anticipate living forever in the factual world, even though no one ever notices being dead).

I'm sure there's some reason this is considered invalid, since quantum suicide is looked on so favorably around here. :)

I suggested that, in some situations, questions like "What is your posterior probability?" might not have answers, unless they are part of decision problems like "What odds should you bet at?" or even "What should you rationally anticipate to get a brain that trusts rational anticipation?". You didn't comment on the suggestion, so I thought about problems you might have seen in it.

In the suggestion, the "correct" subjective probability depends on a utility function and a UDT/TDT agent's starting probabilities, which never change. The most important way the suggestion is incomplete is that it doesn't itself explain something we do naturally: we care about the way our "existentness" has "flowed" to us, and if we learn things about how "existentness" or "experiencedness" works, we change what we care about. So when we experiment on quantum systems, and we get experimental statistics that are more probable under a Born rule with a power of 2 than (hand-waving normalization problems) under a Born rule with a power of 4, we change our preferences, so that we care about what happens in possible future worlds in proportion to their integrated squared amplitude, and not in proportion to the integral of the fourth power. But, if there were people who consistently got experimental statistics that were more probable under a Born rule with a power of 4 (whatever that would mean), we would want them to care about possible future worlds in proportion to the integral of the fourth power of their amplitude.

This can even be done in classical decision theory. Suppose you were creating an agent to be put into a world with Ebborean physics, and you had uncertainty about whether, in the law relating world-thickness ratios (at splitting time) to "existentness" ratios, the power was 2 or 4. It would be easy to put a prior probability of 1/2 on each power, and then have "the agent" update from measurements of the relative thicknesses of the sides of the split worlds it (i.e. its local copy) ended up on. But this doesn't explain why you would want to do that.

What would a UDT/TDT prior belief distribution or utility function have to look like in order to define agents that can "update" in this way, while only thinking in terms of copying and not subjective probability? Suppose you were creating an agent to be put into a world with Ebborean physics, and you had uncertainty about whether, in the relation between world thickness ratios and "existentness" ratios, the power was 2 or 4. And this time, suppose the agent was to be an updateless decision theory agent. I think a UDT agent which uses "probability" can be converted by an expected utility calculation into a behaviorally equivalent UDT agent which uses no probability. Instead of probability, the agent uses only "importances": relative strengths of its (linearly additive) preferences about what happens in the various deterministic worlds the agent "was" copied into at the time of its creation. To make such an agent in Ebborean physics "update" on "evidence" about existentness, you could take the relative importance you assigned to influencing world-sheets, split it into two halves, and distribute each half across world-sheets in a different way. Half of the importance would be distributed in proportion to the cumulative products of the squares of the worlds' thickness ratios at their times of splitting, and half of the importance would be distributed in proportion to the cumulative products of the fourth powers of the worlds' thickness ratios at their times of splitting. Then, in each world-sheet, the copy of the agent in that world-sheet would make some measurements of the relative thicknesses on its side of a split, and it would use use those measurements to decide what kinds of local futures it should prioritize influencing.

But, again, this doesn't explain why you would want to do that. (Maybe you wanted the agents to take a coordinated action at the end of time using the world-sheets they controlled, and you didn't know which kinds of world-sheets would become good general-purpose resources for that action?)

I think there was another way my suggestion is incomplete, which has something to do with the way your definition of altruism doesn't work without a definition of "correct" subjective probability. But I don't remember what your definition of altruism was or why it didn't work without subjective probability.

I still think the right way to answer the question, "What is the correct subjective probability?" might be partly to derive "Bayesian updating" as an approximation that can be used by computationally limited agents implementing an updateless or other decision theory, with a utility function defined over mathematical descriptions of worlds containing some number of copies of the agent, when the differences in utility that result from the agent's decisions fulfill certain independence and linearity assumptions. I need to mathematically formalize those assumptions. "Subjective probability" would then be a variable used in that approximation, which would be meaningless or undefined when the assumptions failed.

When you wake up, you will almost certainly have won (a trillionth of the prize). The subsequent destruction of winners (sort of - see below) reduces your probability of being the surviving winner back to one in a billion.

Merging N people into 1 is the destruction of N-1 people - the process may be symmetrical but each of the N can only contribute 1/N of themself to the outcome.

The idea of being (N-1)/N th killed may seem a little odd at first, but less so if you compare it to the case where half of one person's brain is merged with half of a different person's (and the leftovers discarded).

EDIT: Note that when the trillion were told they won, they were actually being lied to - they had won a trillionth part of the prize, one way or another.

Bonus: if you're uncomfortable with merging/deleting copies, you can skip that part! Just use the lottery money to buy some computing equipment and keep your extra copies running in lockstep forever. Is this now an uncontroversial algorithm for winning the lottery, or what?

Oddly, I feel myself willing to bite all three bullets. Maybe I am too willing to bite bullets? There is a meaningful sense in which I can anticipate myself being one of the future people who will remember being me, though perhaps there isn't a meaningful way to talk about which of those many people I will be; I will be all of them.

The problem is that copying and merging is not as harmless as it seems. You are basically doing invasive surgery on the mind, but because it's performed using intuitively "non-invasive" operations, it looks harmless. If, for example, you replaced the procedure with rewriting "subjective probability" by directly modifying the brain, the fact that you'd have different "subjective probability" as a result won't be surprising.

Thus, on one hand, there is an intuition that the described procedure doesn't damage the brain, and on the other the intuition about what subjective probability should look like in an undamaged brain, no matter in what form this outcome is delivered (that is, probability is always the same, you can just learn about it in different ways, and this experiment is one of them). The problem is that the experiment is not an instance of normal experience to which one can generalize the rule that subjective probability works fine, but an instance of arbitrary modification of the brain, from which you can expect anything.

Assuming that the experiment with copying/merging doesn't damage the brain, the resulting subjective probability must be correct, and so we get a perception of modifying the correct subjective probability arbitrarily.

Thought experiments with doing strange things to decision-theoretic agents are only valid if the agents have an idea about what kind of situation they are in, and so can try to find a good way out. Anything less, and it's just phenomenology: throw a rat in magma and see how it burns. Human intuitions about subjective expectation are optimized for agents who don't get copied or merged.

Let's explore this scenario in computational rather than quantum language.

Suppose a computer with infinite working memory, running a virtual world with a billion inhabitants, each of whom has a private computational workspace consisting of an infinite subset of total memory.

The computer is going to run an unusual sort of 'lottery' in which a billion copies of the virtual world are created, and in each one, a different inhabitant gets to be the lottery winner. So already the total population after the lottery is not a billion, it's a billion billion, spread across a billion worlds.

Virtual Yu'el perceives that he could utilize his workspace as described by Eliezer: pause himself, then have a single copy restored from backup if he didn't win the lottery, but have a trillion copies made if he did. So first he wonders whether it's correct to see this as making his victory in the lottery all but certain. Then he notices that if after winning he then does a merge, the certain victory turns back into certain loss, and becomes really worried about the fundamental soundness of his decision procedures and understanding of probability, etc.

Stating the scenario in these concrete terms brings out, for me, aspects that aren't so obvious in the original statement. For example: If everyone else has the same option (the trillionfold copying), Yu'el is no longer favored. Is the trilemma partly due to supposing that only one lottery participant has this radical existential option? Also, it seems important to keep the other worlds where Yu'el loses in sight. By focusing on that one special world, where we go from a billion people, to a trillion people, mostly Yu'els, and then back to a billion, we are not even thinking about the full population elsewhere.

I think a lot of the assumptions going into this thought experiment as originally proposed are simply wrong. But there might be a watered-down version involving copies of decision-making programs on a single big computer, etc, to which I could not object. The question for me is how much of the impression of paradox will remain after the problem has been diluted in this fashion.

....you have to throw away the idea that your joint subjective probabilities are the product of your conditional subjective probabilities....If you win the lottery, the subjective probability of having still won the lottery, ten seconds later, is ~1.

If copying increases your measure, merging decreases it. When you notice yourself winning the lottery, you are almost certainly going to cease to exist after ten seconds.