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Ah. I guess I'm not sure where to go from here, in that case.
Every level but the last one is supposed to be wrong.
The point is they're supposed to be wrong in a specifically crafted way.
Most of them I start to agree with and then you add a conclusion that I don't think follows from the lead-in.
This is by design. I tried to make the levels mutually exclusive. The way I did this was by having each level add a significant insight to the truth (as I see it) and then say something wrong (as I see it) to constrain any further insight.
I think you've got an unstated and likely incorrect assumption
that "me" in the past, "me" as experiencing something in the moment and "me" in the future are all singular and
necessarily linked. I think they've been singular in my experience, but that's not the only way it could be.
If you insist on mapping to QM, my answers match MWI somewhat. Each branch's past has an amplitude of 1, the future
diverges into all possible states which sum to 1. I'm not actually uncertain that "possible" is sensible concept, though, so
I'll answer these as if we were talking about copies in a classical universe, so they can sum to more than 1 of "me".
My intention is not to ignore QM/MWI or anything, but I did intend to provide levels where someone who doesn't understand (or even know about) QM would find themselves. The language I used was (hopefully) the language someone at that level would use to describe what they think, so all levels that can't be true under QM should sound ignorant of any QM insights. That was my intention. Intuition about QM should automatically push you at least to the first level where it sounds like I stopped describing a classical universe.
Further, this is mostly about our anticipation of subjective experiences. I didn't really mention amplitude, I just alluded to it by mentioning the squares of them we'd use to calculate our anticipation. When I say "me," I mean "some unmangled amplitude of me".
Unfortunately, even if I tried to use precise language, I'd have had trouble, and I wasn't even trying to do that, as this is supposed to be a resource anyone could use to place themselves.
I would address each of your entries, but most of them would probably be rephrasings of what I said above. Each level is supposed to contain something objectionable that pushes you to the next level.
6: Incoherent. Likelihood is about exclusive options, and this framing is not exclusive: both happen in the same universe. I predict that branches of me will experience both.
As far as this goes, I was trying to use the intuitive but inaccurate language from here. If you prefer, pretend I said "squared amplitude". Alternatively, if you have suggestions for better language someone at this level would still intuitively use, I'd be happy to hear it.
7: Good, then a weird "transfer" concept. A perfect duplicate at any point has the same conscous experience, and
diverges when the inputs diverge. It's not transfered, it's just in both places/times.
It's really hard to describe anticipation of subjective experience in these scenarios. If you have a suggestion of language I can use that is still wrong in a way that precludes the insights from successive levels, and also speaks as someone who is wrong in that way would speak about their expectation, I am very open to suggestions.
8: I'm uncertain what level of fidelity is required to be "me". My intuition is that a sufficiently-true simulation is
effectively me, just like a sufficiently-exact copy.
That is the intentional problem with 8, yes.
9: Sure. I don't think it necessarily follows that the ONLY way the superintelligence can "think about what I would do"
is to execute a full-fidelity model, it could very easily use much simpler models (like humans do for each other) for
many questions.
I agree that the only model isn't a perfect model, but I have a strong hypothesis that "perfect model" and "implementation" are synonymous.
Edit: I see your objection with 9 and I (hopefully) fixed it.
I hope, at least, that this back-and-forth has been useful?
Absolutely. Talking to you was refreshing, and it helped me not only flesh out my ladder but also pin down my beliefs. Thank you for taking time to talk about this stuff.
so I don’t think I have much to add past what we’ve already gone over.
I did make an attempt to address your last reply. If you still feel that way after, let me know.
I don’t see that understanding QM would suffice to grant #3 and #4 without having solved the Hard Problem. Without actually having a full reduction of consciousness, there’s just no way to be certain that the reasoning you provide makes sense
This should change when you understand QM. I was trying to black box it.
And how do we do this? What makes a person “feel like the same person”, “from the inside”, through the passage of time? Do those quoted phrases even make sense? What do they mean, exactly? We really don’t know.
Can we? It seems like we can, but… is that just an illusion? Somehow? Why does it seemlike consciousness is continuous? Or is that a confused question (as some people indeed seem to claim)?
It doesn't matter, because we can prove they are the same black box, and thus their behavior is the same, even if we don't know how it works (or fully what that behavior even is). As long as we have A === B (which QM says we must), we can say (A->C) -> (B->C) even if we don't know whether A->C or how. To the extent that it A gives off some evidence that convinces us of C, B does exactly the same thing.
Well, and what if it does? We’re back to the “conditioning on reductionism” thing; until we actually have a full reduction, we just can’t blithely toss about assumptions like this!
… actually, we needn’t even go that far. It’s not even certainty of reductionism that you’re suggesting we condition on—it’s certainty of… what? Quantum mechanics applying to everything? But that’s a great deal weaker! I am not nearly as certain of that (in fact, I have no real solid belief about it), so by no means will I condition on a certainty of this claim!
1 and 2 imply this, and you were willing to give me those. QM supports reductionism independent of all the classical and empirical reasons we believe in reductionism. Like I said above, you asked me to black box it, and I'm claiming these are things that are clear when you understand QM. QM is brazen about being the exclusive language our universe uses to describe everything. It's physical nonsense to talk about something that exists and isn't described by QM. That's what existence means.
This part I actually just don’t get the point of. I mean, you’re not wrong, but so what?
It's preparation for the point "we do it all the time and maintain our sense of continuity in every branch" in 5 and 6.
As for #5 and #6, well, there I just don’t understand what you’re saying, so I can’t judge whether it’s relevant.
5 is basically:
When Schrödinger's cat enters a superposition of alive|dead, so does the entire universe, including us. Like the cat, we split into a!us and d!us (us in the world where the cat is alive and us in the world where it is dead). When we observe the cat, and find it out is alive|dead, we are finding out which world we are in, and correlating our brain state with the state of the cat. This is decoherence, and it pushes a!universe and d!universe apart in the mathematical substrate that defines them (so they can't interact anymore).
If we observe the cat is alive, we realize we are a!us. But there is still a d!us. We split, and they are observing a dead cat. a!us and d!us both can think back to the time before the split and say "that's me and I had an unbroken chain of time slices that lead me here - my consciousness was continuous". Both maintain continuity throughout the process.
6 is basically:
The above experience for a person cannot be described differently in QM (which is the language of existence) from the kind of copying that occurs in one branch!universe, except by differences that can't in principle have an effect as per point 2, so they black box as the same thing, and implications about one are implications about the other.
Fair enough. I don't see them as gibberish, so treating them that way is hard. I admit I didn't actually see what you meant.
I made an attempt to treat it as a black box in a different thread reply, but I still had to use the language of QM. I might be able to sum it up into short sentences as well, but I wanted to start with some amount of formality and explanation.
We gain these:
1. Everything obeys QM. To wit, nothing can exist anywhere/when that is not describable in the math of QM in principle.
2. If everything obeys QM, consciousness obeys QM.
3. As long as consciousness is not or does not consist of some fundamental element that does not obey QM, there is nothing anywhere that can differentiate between copies in principle in any way besides how we can differentiate between a person in the past and the same person in the future, having taken a mundane trajectory through spacetime. This includes how it "feels from the inside." If we can claim consciousness is continuous at all, we can claim it is continuous regardless of proximity in spacetime or any other consideration except for a particular change in physical structure across some change in spacetime. There is provably no computable difference, in the structure of our universe, between existing from one second to the next, and blinking out of existence somewhere/when and then into existence somewhere/when else.
4. As long as consciousness is not or does not consist of some fundamental element that does not obey QM, our subjective experience of being in one place at one time is a limitation of our own perceptions. When we exist in multiple places at the same time, each placetime!us perceives a single, unbroken continuity of consciousness in hindsight, but this is an artifact of a failure to perceive or communicate with other placetime!us branches.
5. We constantly exist in multiple places, as decoherence is the rule, and factorable subspaces where a particular placetime!us can exist and identify as a "world" are a significant exception. It just so happens that decoherence of a certain kind tends to create locally factorable subspaces that move away from each other in configuration space, so they can't meaningfully interact. For any reasonable definition of "we", "we" are constantly being copied every time there is any detectable (in principle) decoherence anywhere in our "world" (a "universe" that a single placetime!us has access to in principle). By observation, we know that at least every time the "we" we identify as has split, it hasn't interrupted our continuity of consciousness. As there are decoherence events constantly on scales we have trouble imagining in numbers of places we have trouble imagining at once, we can reason that we didn't just get absurdly lucky, and every copy of us looks back on these splits with the same feeling of continuity.
6. The splits we've observed and cannot interact with are in principle no different from a split in a single "world" where we can interact with our copy.
And possibly more. It's a lot and I'm doing the best I can from memory.
My response here would be the same as my responses to the other outstanding threads.
The limit of [the effect your original prior has on your ultimate posterior] as [the number of updates you've done] approaches infinity is zero. In the grand scheme of things, it doesn't matter what prior your start with. As a convenience, if we have literally no information or evidence, we usually use the uniform prior (equally likely as not, in this case), and then our first update is probably to run it through occam's razor.
The rest of your objections, if I understand QM and its implications right, fall upon the previously unintuitive and possibly incoherent things that become intuitively true as you understand QM. As I said elsewhere:
I truly do think we can't move further from this point, in this thread of this argument, without you reading and understanding the sequence :(
I could be mistaken, but it seems to me that the distinction you're trying to make between what I'm saying and what I'd have to say for my answer to be [coherent] dissolves as you understand QM.
I could, of course, be misunderstanding you completely. But there also isn't anything you're linking that I'm unwilling to read :P
The big disconnect here is you are willing to say you'll take my word for it about QM, but then I say "QM allows us to 'reason about the things on the higher parts of the ladder' without 'knowing how consciousness emerges from the physical.'"
I could be wrong, but if I'm wrong, you'd have to dive into QM to show me how. QM provides us a conceptual black swan, I claim, and reasoning about this without it is orders of magnitude less powerful than reasoning with it, in a way that is impossible to conceive of except in hindsight.
I truly do think we can't move further from this point, in this thread of this argument, without you reading and understanding the sequence :(
I could be mistaken, but it seems to me that the distinction you're trying to make between what I'm saying and what I'd have to say for my answer to be responsive dissolves as you understand QM.
I could, of course, be misunderstanding you completely. But there also isn't anything you're linking that I'm unwilling to read :P
This is, fundamentally, no more than a stronger version of your “submerged in a crater of concrete” scenario, so by what right do we claim it to be qualitatively different than “he left work two hours ago”?
I agree. At the core, every belief is bayesian. I don't recognize a fundamental difference, just one of categorization. We carved up reality, hopefully at its joints, but we still did the carving. You seemed to be the one arguing a material difference between "has to" and "is".
As an aside, it's possible you missed my edit. I'll reproduce it here:
I concede that this is all hypothesis, but it is of the same sort as "the Higgs Boson exists, or else we're wrong about a lot of things"... before we found it.
Right. I agree that we don't know how, but I submit that we know that they do, and we believe strongly in reductionism, and we can condition conclusions on reductionism and the belief that they do, without conditioning them on how they do, and I submit further that limiting ourselves in this way is still sufficient to advance up the ladder.
We have a black box - in computer science, an interface - but we don't need to know what's inside if we know everything about its behavior on the outside. We can still use it in an algorithm, and know what to expect will happen.
It doesn't seem like we can know this much in principle (without access to the inside of the black box) until you understand why we know this much, as EY talks about here.
I'd also like to be clear that "inside the black box" (the answer to the hard problem) is not the same as "the subjective feeling inside the mind" (a physical consequence of whatever the black box is doing).
Now, I think reductionism is true. But suppose we encounter something we can’t reduce. (Of course your instinct—and mine, in a symmetric circumstance—would be to jump in with a correction: “can’t yetreduce”! I sympathize entirely with this—but in this case, that formulation would beg the question.) We should of course condition on our belief that reductionism is true, and conclude that we’ll be able to find a reduction. But, conversely, we should also condition on the fact that we haven’t found a reduction yet, and reduce our belief in reductionism! (And, as I mentioned in the linked comment thread, this depends on how much effort we’ve spent so far on looking for a reduction, etc.)
What this means is that we can’t simply say “consciouness is completely emergent-from-the-physical”. What we have to say is something like:
“We don’t currently know whether consciousness is completely emergent from the physical. Conditional on reductionism being true, consciousness has to be completely emergent from the physical. On the other hand, if consciousness turns out not to be completely emergent from the physical, then—clearly—reductionism is not true.”
In other words, whether reductionism is true is exactly at issue here! Again: I do think that it is; I would be very, very surprised if it were otherwise. But to assume it is to beg the question.
Okay, this is entirely fair, and I see your point and agree. I counter with the questions: What numerical strength would you give your belief that reductionism is true? Are you willing to extend that number to your belief in things at greater levels of the ladder that condition on it, according to the principles of conditional probability?
If your answers to those questions are "well above 50%" and "yes," why is it so difficult to answer the question:
if you had to hazard a guess in your own words as to what is most likely to be true about identity and consciousness in the case of a procedure that reproduces your physical body (including brain state) exactly - pick the hypothesis you have with the highest prior, even if it's nowhere close to 50% - what would it be
?
To the contrary: the implications of the phrase “has to be”, in claims of the form “[thing] has to be true” is very different from the implications of the word “is” (in the corresponding claims). Any reasonable definition of “has to be” must match the usage, and the usage is fairly clear: you say that something “has to be true” when you don’t have any direct, clear evidence that it’s true, but have only concluded it from general principles.
It seems to me that you're separating (deductive and inductive) reasoning from empirical observation, which I agree is a reasonable separation. But there are different strengths of reasoning. Observe:
A: Is your husband at home right now?
B: He has to be; he left work over two hours ago, and his commute’s only 30 minutes long.
vs.
A: Is your husband at home right now?
B: He has to be; I put him in a straight jacket, in a locked room, submerged the house completely in a crater of concrete, watched it harden without him escaping, and left satisfied, two hours ago.
Neither of these are "is", i.e. direct, contemporaneous, empirical observation. They are both "has to be", i.e. chains of induction. But one assumes the best case at every opportunity, and one at least attempts to eliminate all cases that could result in the negation.
I submit that my "has to be" is of the latter type, but even more airtight.
I concede that this is all hypothesis, but it is of the same sort as "the Higgs Boson exists, or else we're wrong about a lot of things"... before we found it.
In that case, I would say you're between 3 and 4. And I can't say you're wrong about my relative certainty being unwarranted, but obviously I think you're wrong, and it's because I believe that QM leaves only enough wiggle room of uncertainty for the things we don't yet know to never actually affect the physical consequences of such a procedure (even from the inside).
This is why I think QM is necessary to advance up the ladder; it's the reason I advanced up the ladder, and it's the only experimentally true thing we have so far that permits you to advance up the ladder. Trying to go a different route would be dishonest.
Ah, these are much better descriptions now, well done!
Thanks, I sincerely appreciate your help in clarifying :)
We can say that consciousness has to be completely emergent-from-the-physical. But there’s a difference between that and what you said; “consciousness is completely emergent-from-the-physical”
Can you explain why the former doesn't imply the latter? I'm under the impression it does, for any reasonable definition of "has to be", as long as what you're conditioning on (in this case reductionism) is true. I suppose I don't see your objection.
I'm not so sure this fails. I'm inclined to take this to mean you are between 2 and 3 or between 3 and 4, depending on what specifically you object to in 3.
But I'm curious, if you had to hazard a guess in your own words as to what is most likely to be true about identity and consciousness in the case of a procedure that reproduces your physical body (including brain state) exactly - pick the hypothesis you have with the highest prior, even if it's nowhere close to 50% - what would it be, completely independent of what I've said in this ladder?
That's fair; I wasn't sure how to phrase the idea in 8 to exclude 9, so the language isn't perfect, and I agree, now that I've seen it, that your proposed 10 is conceptually a step above my 9. Let me know if it is okay for me to add your 10 to my list.
Out of curiosity, do you consider the 10 you wrote "intuitively true", or just the logical next step in a hypothetical ladder?
Edit: I did my best to fix 8.
You just did, right? That’s the description, right there. (But it’s not identical with #4 as written! … was it meant to be?)
Fair, I did my best to fix 3 and 4.
And I disagree about the first part of what I quoted; I see no reason to assent to that. Why do you think this?
Can you be more specific about what exactly I said that you're referring to? Forgive me but I actually am not sure which part you mean.
I was able to follow the QM sequence just enough to… well, not to grasp this point, precisely, but to grasp thatEliezer was claiming this. But I don’t see how it entails or implies ot even suggests that a solution to the Hard Problem is unnecessary here?
EY's assertion, and I tend to see his point, is that there can't possibly be anything about [you] that isn't true of [a perfect copy of you] that would distinguish - to the universe itself or anything in it - between the instances, other than their positions in spacetime.
And, since we change positions in spacetime all the time without claiming we've lost our identities or consciousnesses, that method of distinction is not sufficient to threaten any consideration of identity or consciousness. Further, because consciousness is completely emergent-from-the-physical, if there's nothing physically different about two instances besides spacetime displacements (which do not threaten consciousness), there's no way in principle that consciousness doesn't behave this way.
And since these aren't things we think, as long as we don't find anything in the future that contradict them, but rather are things that are most assuredly true, unless the universe is lying to us, it ought not matter what we don't yet know, because this positive fact about identity (or lack thereof) is sufficient to make this conclusion.
That said, I think that if your approach relies on your interlocutor having a solid understanding of quantum mechanics, then… I’m afraid it’s even more flawed than I thought at first… :(
:(
----
I wanted to say an additional couple of things that may take this in a different direction. To go back to your top level comment:
That is, if you ask me whether I believe the mid-to-high-numbered statements, I won’t say “yes” or “no”; I’ll say “I don’t know, and I don’t know if they even make sense enough to be right or wrong, and really the whole subject is deeply confusing to me”. You can’t convince me to accept (say) rung #7, because I don’t currently reject it; rather, I don’t know whether it even makes sense as a position, or whether there is (as seems to me to be likely) something that we’re missing about the whole matter
I want to clarify that I consider this position (indeed, any position that isn't "yes, I believe it could be no other way") a rejection of that intuition. To be an intuition, it should be intuitively true.
Also:
it’s hard to know what intuition to have
My goal with this ladder, specifically, is not to change anyone's mind, but rather to provide enough resolution to where everyone can point to some level and say either:
1. That is true, or
2. That could be true
and then point to the level below it and say either:
1. That is clearly not true, or
2. That is not the whole picture.
If you don't have an adjacent pair of levels like that, I do in fact need to fix my ladder. Namely, I need to include a level that corresponds to your intuition. I suppose I'm looking for the highest level someone thinks is clearly wrong.
That said, with all due respect, I don't think that implies that levels higher than that point should make intuitive sense to you. The fact that they don't was legitimately my intention.
Fair enough. Would you say that if the discussion reaches this part of the ladder, a digression must then be made to ensure that both parties well and truly understand QM?
I'm not sure it "must" be made, but that's exactly the route I would go at this point.
suppose one lacks the mathematical aptitude / physics background / whatever to grasp QM; is further progress impossible? In that case, what ought one’s view of this topic be?
I guess I haven't considered this. When I find myself in this position, I try to gain the requisite skills. EY's QM sequence on this very site isn't too hard to follow.
Sorry, I guess I was not clear… I take this answer to be just pushing the problem back one irrelevant step, since my question applies to this scenario also!
Well, that’s the thing; I don’t know (after reading this) whether you’re spouting utter nonsense! That’s precisely the problem I was trying to point to: I, for example, couldn’t tell you where on the ladder I am, for the reasons I outlined in the grandparent.
I suppose that's entirely fair. I'm not sure how to improve the ladder to this end, though.
https://en.wikipedia.org/wiki/Hard_problem_of_consciousness
I am familiar with this after all. I believe solving this may be necessary to implement or even possibly successfully copy a mind, but not to reason about the consequences of such assuming we've figured it out. In any case, as a reductionist, I believe very strongly that the solution arises from the structure of physical things only, and thus is only as hard a problem as GAI.
Further, EY goes into pretty great depth about how our current understanding of QM gives us an affirmative belief that there's no identity difference between one copy or another in principle, particularly here and here but also in many posts in the QM sequence. This further suggests the solution to the HPoC isn't necessary to reason about our identities.
I can speak for myself only, but—I’m not past #4, for exactly the reasons I outlined. (I think #4 is incoherent, for—apparently—the reason you intended it to be incoherent; but the steps above that are problematic, as I said.)
I admit I have no idea what the subjective experience of dying could be, especially in your sleep, but it seems like whatever lack of experience or end or whatever that you'd have when you die normally would occur here if you believed this?
But I'm inclined to believe manyworlds implies subjective quantum immortality to an extent, as well, so 4 is possibly even more meaningless. I'm just not sure how to fix it, or if I should even try, because I know people who wouldn't fork-and-die teleport because they thing the person waking up isn't them; they're dead.
How do I describe that position on this ladder?
I have expanded on 1 in an edit. Let me know if it makes sense.
This needs more elaboration, if you want to use it in the way you do. I know what you mean here (at least, I think I do), but it may not be obvious to many interlocutors—“the same thing” in what way, exactly? (Especially since this is step #1.)
I see your point. Admittedly, I built this while talking to someone who was past 1, and I consider the position a gross misunderstanding of current technology. I'll consider how to describe the proposition better, though.
Or is it your intention to show that this view is incoherent, for exactly this reason
Precisely. I expect any lesswronger to be past 4. Perhaps I am building a strawman?
How does this step on the ladder work for people who are not learned in quantum mechanics? (Which is to say—I have no idea what #6 means.)
I suppose it's enough to intuitively consider it "vaguely less likely" that you'll wake up as one copy or the other based on "some unknown criteria that possibly includes likelihood of future survival", but I submit that either:
1. one doesn't understand fully why he is at this step if he isn't familiar with QM, or
2. I don't understand QM or the subject at hand as well as I think I do.
I confess to being confused about how the concept of “probability” is being used here (and in similar comments I’ve seen). Can you elaborate?
That... might be a pretty long discussion. Essentially, whatever you, before you undergo a copying procedure, anticipate happening to you (subjectively experiencing ending up in the grown body vs. ending up in the body that walked in, each with some respective probability), you have the same anticipation about staying on Earth vs. instantaneously mind-warping to where-ever the hell a human brain could possibly have formed that not only implements you, but has exactly your memories of growing up on earth up to that moment.
As for your entire approach… I think it’s an interesting and worthy attempt, but flawed, for this reason: that around #4 or #5 (I’m not sure, due to the unclearness mentioned above), it’s hard to know what intuition to have—whether to reject or accept the higher rungs of the ladder
One thing that perhaps isn't obvious, is that this ladder isn't meant to convince anyone of anything upon reading it, other than perhaps that I might have a consistent position and not be spouting utter nonsense. Once someone and I have agreed about where they are, then we can get to work on the task of advancing up the ladder. One level at a time.
do you have a solution to the Hard Problem?
Could you elaborate? I may know what you're talking about, but not by name.
To think he could have had twice as many readers.
The encoding scheme you're talking about is Huffman Coding, and the ambiguity you're trying to avoid explicitly occurs when one symbol is the prefix of another. The mechanism to build an optimal prefix(-free) code is called the Huffman Tree, and it uses a greedy algorithm that builds a full binary tree from the bottom up based on the frequencies of the symbols. Leaves are symbols, and the code for a symbol is the sequence of left or right branches you must traverse the reach that symbol.
To get more specific, you add all the symbols to a heap based on their frequency of appearance, lowest-at-the-front. You extract two symbols, foo and bar. These become children of a common parent node, the pseudosymbol baz. baz.freq = foo.freq + bar.freq. Add baz to the heap. Loop until the heap contains one node at the end of this process. That node is the root of the Huffman Tree.
Sorry, but I'm not in the habit of taking one for the quantum superteam.
If you're not willing to "take one for the team" of superyous, I'm not sure you understand the implications of "every implementation of you is you."
And I don't think that it really helps to solve the problem;
It does solve the problem, though, because it's a consistent way to formalize the decision so that on average for things like this you are winning.
it just means that you don't necessarily care so much about winning any more. Not exactly the point.
I think you're missing the point here. Winning in this case is doing the thing that on average nets you the most success for problems of this class, one single instance of it notwithstanding.
Plus we are explicitly told that the coin is deterministic and comes down tails in the majority of worlds.
And this explains why you're missing the point. We are told no such thing. We are told it's a fair coin and that can only mean that if you divide up worlds by their probability density, you win in half of them. This is defined.
What seems to be confusing you is that you're told "in this particular problem, for the sake of argument, assume you're in one of the worlds where you lose." It states nothing about those worlds being over represented.
So here's why I prefer 1A and 2B after doing the math, and what that math is.
1A = 24000
1B = 26206 (rounded)
2A = 8160
2B = 8910
Now, if you take (iB-iA)/iA, which represents the percent increase in the expected value of iB over iA, you get the same number, as you stated.
(iB-iA)/iA = .0919 (rounded)
This number's reciprocal represents the number of times greater the expected value of iA is than the marginal expected value of iB
iA/(iB-iA) = 10.88 (not rounded)
Now, take this number and divide it by the quantity p(iA wins)-p(iB wins). This represents how much you have to value the first $24000 you receive over the next $3000 to pick iA over iB. Keep in mind that 24/3 = 8, so if $1 = 1 utilon in all cases, you should pick iA only when this quotient is less than 8.
1A/(1B-1A)/[p(1A wins)-p(1B wins)] = 369.92
2A/(2B-2A)/[p(2A wins)-p(2B wins)] = 1088
I have liabilities in excess of my assets of around $15000. That first $15000 is very important to me in a very quantized, thresholdy way, but it is not absolute. I can make the money some other way, but not needing to - having it available to me right now because of this game - represents more utility than a linear mapping of dollars to utility suggests, by a large factor.
The next threshold like this in my life that I can think of is "enough money to buy a house in Los Angeles without taking out a mortgage," of which $3000 is a negligible portion.
I'd say that the utility I assign the first $24000 because of this lies between 370 and 1080 times the utility I assign the next $3000. This is why I take 1A and 2B given that this entire thing is performed only once. Once my debts are paid, all bets (on 1A) are off.
If we're dealing with utilons rather than dollars, or I have repeated opportunity to play (which is necessary for you to "money pump" me) iB is the obvious choice in both cases.
It seems to me the answer becomes more obvious when you stop imagining the counterfactual you who would have won the $10000, and start imagining the 50% of superpositions of you who are currently winning the $10000 in their respective worlds.
Every implementation of you is you, and half of them are winning $10000 as the other half lose $100. Take one for the team.
If you count the amount of "wanting to switch" you expect to have because the cable guy hasn't arrived yet, it should equal exactly the amount of "wishing you hadn't been wrong" you expect to have if you pick the second half because the cable guy arrived before your window started.
I'm not sure how to say this so it's more easily parseable, but this equality is exactly what conservation of expected evidence describes.