Senior research analyst at Open Philanthropy. Doctorate in philosophy at the University of Oxford. Opinions my own.
Joe_Carlsmith
Karma: 3,375
Thanks for making this, Michel :)
Bleh, sorry, looks like this cross-posted twice from LW, but has only one LW copy (and can only be edited via that copy). I’m going to try to keep this version and get rid of the other one.Edit: resolved.
Bleh, sorry, am having some trouble with LW cross-posting here.
(Copying over my response from LessWrong)
Thanks for writing this—I’m very excited about people pushing back on/digging deeper re: counting arguments, simplicity arguments, and the other arguments re: scheming I discuss in the report. Indeed, despite the general emphasis I place on empirical work as the most promising source of evidence re: scheming, I also think that there’s a ton more to do to clarify and maybe debunk the more theoretical arguments people offer re: scheming – and I think playing out the dialectic further in this respect might well lead to comparatively fast progress (for all their centrality to the AI risk discourse, I think arguments re: scheming have received way too little direct attention). And if, indeed, the arguments for scheming are all bogus, this is super good news and would be an important update, at least for me, re: p(doom) overall. So overall I’m glad you’re doing this work and think this is a valuable post.
On other note up front: I don’t think this post “surveys the main arguments that have been put forward for thinking that future AIs will scheme.” In particular: both counting arguments and simplicity arguments (the two types of argument discussed in the post) assume we can ignore the path that SGD takes through model space. But the report also discusses two arguments that don’t make this assumption – namely, the “training-game independent proxy goals story” (I think this one is possibly the most common story, see e.g. Ajeya here, and all the talk about the evolution analogy) and the “nearest max-reward goal argument.” I think that the idea that “a wide variety of goals can lead to scheming” plays some role in these arguments as well, but not such that they are just the counting argument restated, and I think they’re worth treating on their own terms.
On counting arguments and simplicity arguments
Focusing just on counting arguments and simplicity arguments, though: Suppose that I’m looking down at a superintelligent model newly trained on diverse, long-horizon tasks. I know that it has extremely ample situational awareness – e.g., it has highly detailed models of the world, the training process it’s undergoing, the future consequences of various types of power-seeking, etc – and that it’s getting high reward because it’s pursuing some goal (the report conditions on this). Ok, what sort of goal?
We can think of arguments about scheming in two categories here.
(I) The first tries to be fairly uncertain/agnostic about what sorts of goals SGD’s inductive biases favor, and it argues that given this uncertainty, we should be pretty worried about scheming.
I tend to think of my favored version of the counting argument (that is, the hazy counting argument) in these terms.
(II) The second type focuses on a particular story about SGD’s inductive biases and then argues that this bias favors schemers.
I tend to think of simplicity arguments in these terms. E.g., the story is that SGD’s inductive biases favor simplicity, schemers can have simpler goals, so schemers are favored.
Let’s focus first on (I), the more-agnostic-about-SGD’s-inductive-biases type. Here’s a way of pumping the sort of intuition at stake in the hazy counting argument:
A very wide variety of goals can prompt scheming.
By contrast, non-scheming goals need to be much more specific to lead to high reward.
I’m not sure exactly what sorts of goals SGD’s inductive biases favor, but I don’t have strong reason to think they actively favor non-schemer goals.
So, absent further information, and given how many goals-that-get-high-reward are schemer-like, I should be pretty worried that this model is a schemer.
Now, as I mention in the report, I’m happy to grant that this isn’t a super rigorous argument. But how, exactly, is your post supposed to comfort me with respect to it? We can consider two objections, both of which are present in/suggested by your post in various ways.
(A) This sort of reasoning would lead to you giving significant weight to SGD overfitting. But SGD doesn’t overfit, so this sort of reasoning must be going wrong, and in fact you should have low probability on SGD having selected a schemer, even given this ignorance about SGD’s inductive biases.
(B): (3) is false: we know enough about SGD’s inductive biases to know that it actively favors non-scheming goals over scheming goals.
Let’s start with (A). I agree that this sort of reasoning would lead you to giving significant weight to SGD overfitting, absent any further evidence. But it’s not clear to me that giving this sort of weight to overfitting was unreasonable ex ante, or that having learned that SGD-doesn’t-overfit, you should now end up with low p(scheming) even given your ongoing ignorance about SGD’s inductive biases.
Thus, consider the sort of analogy I discuss in the counting arguments section. Suppose that all we know is that Bob lives in city X, that he went to a restaurant on Saturday, and that town X has a thousand chinese restaurants, a hundred mexican restaurants, and one indian restaurant. What should our probability be that he went to a chinese restaurant?
In this case, my intuitive answer here is: “hefty.”[1] In particular, absent further knowledge about Bob’s food preferences, and given the large number of chinese restaurants in the city, “he went to a chinese restaurant” seems like a pretty salient hypothesis. And it seems quite strange to be confident that he went to a non-chinese restaurant instead.
Ok but now suppose you learn that last week, Bob also engaged in some non-restaurant leisure activity. For such leisure activities, the city offers: a thousand movie theaters, a hundred golf courses, and one escape room. So it would’ve been possible to make a similar argument for putting hefty credence on Bob having gone to a movie. But lo, it turns out that actually, Bob went golfing instead, because he likes golf more than movies or escape rooms.
How should you update about the restaurant Bob went to? Well… it’s not clear to me you should update much. Applied to both leisure and to restaurants, the hazy counting argument is trying to be fairly agnostic about Bob’s preferences, while giving some weight to some type of “count.” Trying to be uncertain and agnostic does indeed often mean putting hefty probabilities on things that end up false. But: do you have a better proposed alternative, such that you shouldn’t put hefty probability on “Bob went to a chinese restaurant”, here, because e.g. you learned that hazy counting arguments don’t work when applied to Bob? If so, what is it? And doesn’t it seem like it’s giving the wrong answer?
Or put another way: suppose you didn’t yet know whether SGD overfits or not, but you knew e.g. about the various theoretical problems with unrestricted uses of the indifference principle. What should your probability have been, ex ante, on SGD overfitting? I’m pretty happy to say “hefty,” here. E.g., it’s not clear to me that the problem, re: hefty-probability-on-overfitting, was some a priori problem with hazy-counting-argument-style reasoning. For example: given your philosophical knowledge about the indifference principle, but without empirical knowledge about ML, should you have been super surprised if it turned out that SGD did overfit? I don’t think so.
Now, you could be making a different, more B-ish sort of argument here: namely, that the fact that SGD doesn’t overfit actively gives us evidence that SGD’s inductive biases also disfavor schemers. This would be akin to having seen Bob, in a different city, actively seek out mexican restaurants despite there being many more chinese restaurants available, such that you now have active evidence that he prefers mexican and is willing to work for it. This wouldn’t be a case of having learned that bob’s preferences are such that hazy counting arguments “don’t work on bob” in general. But it would be evidence that Bob prefers non-chinese.
I’m pretty interested in arguments of this form. But I think that pretty quickly, they move into the territory of type (II) arguments above: that is, they start to say something like “we learn, from SGD not overfitting, that it prefers models of type X. Non-scheming models are of type X, schemers are not, so we now know that SGD won’t prefer schemers.”
But what is X? I’m not sure your answer (though: maybe it will come in a later post). You could say something like “SGD prefers models that are ‘natural’” – but then, are schemers natural in that sense? Or, you could say “SGD prefers models that behave similarly on the training and test distributions” – but in what sense is a schemer violating this standard? On both distributions, a schemer seeks after their schemer-like goal. I’m not saying you can’t make an argument for a good X, here – but I haven’t yet heard it. And I’d want to hear its predictions about non-scheming forms of goal-misgeneralization as well.
Indeed, my understanding is that a quite salient candidate for “X” here is “simplicity” – e.g., that SGD’s not overfitting is explained by its bias towards simpler functions. And this puts us in the territory of the “simplicity argument” above. I.e., we’re now being less agnostic about SGD’s preferences, and instead positing some more particular bias. But there’s still the question of whether this bias favors schemers or not, and the worry is that it does.
This brings me to your take on simplicity arguments. I agree with you that simplicity arguments are often quite ambiguous about the notion of simplicity at stake (see e.g. my discussion here). And I think they’re weak for other reasons too (in particular, the extra cognitive faff scheming involves seems to me more important than its enabling simpler goals).
But beyond “what is simplicity anyway,” you also offer some other considerations, other than SGD-not-overfitting, meant to suggest that we have active evidence that SGD’s inductive biases disfavor schemers. I’m not going to dig deep on those considerations here, and I’m looking forward to your future post on the topic. For now, my main reaction is: “we have active evidence that SGD’s inductive biases disfavor schemers” seems like a much more interesting claim/avenue of inquiry than trying to nail down the a priori philosophical merits of counting arguments/indifference principles, and if you believe we have that sort of evidence, I think it’s probably most productive to just focus on fleshing it out and examining it directly. That is, whatever their a priori merits, counting arguments are attempting to proceed from a position of lots of uncertainty and agnosticism, which only makes sense if you’ve got no other good evidence to go on. But if we do have such evidence (e.g., if (3) above is false), then I think it can quickly overcome whatever “prior” counting arguments set (e.g., if you learn that Bob has a special passion for mexican food and hates chinese, you can update far towards him heading to a mexican restaurant). In general, I’m very excited for people to take our best current understanding of SGD’s inductive biases (it’s not my area of expertise), and apply it to p(scheming), and am interested to hear your own views in this respect. But if we have active evidence that SGD’s inductive biases point away from schemers, I think that whether counting arguments are good absent such evidence matters way less, and I, for one, am happy to pay them less attention.
(One other comment re: your take on simplicity arguments: it seems intuitively pretty non-simple to me to fit the training data on the training distribution, and then cut to some very different function on the test data, e.g. the identity function or the constant function. So not sure your parody argument that simplicity also predicts overfitting works. And insofar as simplicity is supposed to be the property had by non-overfitting functions, it seems somewhat strange if positing a simplicity bias predicts over-fitting after all.)
A few other comments
Re: goal realism, it seems like the main argument in the post is something like:
Michael Huemer says that it’s sometimes OK to use the principle of indifference if you’re applying it to explanatorily fundamental variables.
But goals won’t be explanatorily fundamental. So the principle of indifference is still bad here.
I haven’t yet heard much reason to buy Huemer’s view, so not sure how much I care about debating whether we should expect goals to satisfy his criteria of fundamentality. But I’ll flag I do feel like there’s a pretty robust way in which explicitly-represented goals appropriately enter into our explanations of human behavior – e.g., I have buying a flight to New York because I want to go to New York, I have a representation of that goal and how my flight-buying achieves it, etc. And it feels to me like your goal reductionism is at risk of not capturing this. (To be clear: I do think that how we understand goal-directedness matters for scheming—more here—and that if models are only goal-directed in a pretty deflationary sense, this makes scheming a way weirder hypothesis. But I think that if models are as goal-directed as strategic and agentic humans reasoning about how to achieve explicitly represented goals, their goal-directedness has met a fairly non-deflationary standard.)
I’ll also flag some broader unclarity about the post’s underlying epistemic stance. You rightly note that the strict principle of indifference has many philosophical problems. But it doesn’t feel to me like you’ve given a compelling alternative account of how to reason “on priors” in the sorts of cases where we’re sufficiently uncertain that there’s a temptation to spread one’s credence over many possibilities in the broad manner that principles-of-indifference-ish reasoning attempts to do.
Thus, for example, how does your epistemology think about a case like “There are 1000 people in this town, one of them is the murderer, what’s the probability that it’s Mortimer P. Snodgrass?” Or: “there are a thousand white rooms, you wake up in one of them, what’s the probability that it’s room number 734?” These aren’t cases like dice, where there’s a random process designed to function in principle-of-indifference-ish ways. But it’s pretty tempting to spread your credence out across the people/rooms (even if in not-fully-uniform ways), in a manner that feels closely akin to the sort of thing that principle-of-indifference-ish reasoning is trying to do. (We can say “just use all the evidence available to you”—but why should this result in such principle-of-indifference-ish results?)
Your critique of counting argument would be more compelling to me if you had a fleshed out account of cases like these—e.g., one which captures the full range of cases where we’re pulled towards something principle-of-indifference-ish, such that you can then take that account and explain why it shouldn’t point us towards hefty probabilities on schemers, a la the hazy counting argument, even given very-little-evidence about SGD’s inductive biases.
More to say on all this, and I haven’t covered various ways in which I’m sympathetic to/moved by points in the vicinity of the one’s you’re making here. But for now: thanks again for writing, looking forward to future installments.
(Oops, sorry, something got messed up with the LessWrong cross-posting here, such that the old version of this post, including comments and upvotes, disappeared. Working on trying to fix.)
(Also copied from LW. And partly re-hashing my response from twitter.)
I’m seeing your main argument here as a version of what I call, in section 4.4, a “speed argument against schemers”—e.g., basically, that SGD will punish the extra reasoning that schemers need to perform.
(I’m generally happy to talk about this reasoning as a complexity penalty, and/or about the params it requires, and/or about circuit-depth—what matters is the overall “preference” that SGD ends up with. And thinking of this consideration as a different kind of counting argument *against* schemers seems like it might well be a productive frame. I do also think that questions about whether models will be bottlenecked on serial computation, and/or whether “shallower” computations will be selected for, are pretty relevant here, and the report includes a rough calculation in this respect in section 4.4.2 (see also summary here).)
Indeed, I think that maybe the strongest single argument against scheming is a combination of
“Because of the extra reasoning schemers perform, SGD would prefer non-schemers over schemers in a comparison re: final properties of the models” and
“The type of path-dependence/slack at stake in training is such that SGD will get the model that it prefers overall.”
My sense is that I’m less confident than you in both (1) and (2), but I think they’re both plausible (the report, in particular, argues in favor of (1)), and that the combination is a key source of hope. I’m excited to see further work fleshing out the case for both (including e.g. the sorts of arguments for (2) that I took you and Nora to be gesturing at on twitter—the report doesn’t spend a ton of time on assessing how much path-dependence to expect, and of what kind).
Re: your discussion of the “ghost of instrumental reasoning,” “deducing lots of world knowledge ‘in-context,’ and “the perspective that NNs will ‘accidentally’ acquire such capabilities internally as a convergent result of their inductive biases”—especially given that you only skimmed the report’s section headings and a small amount of the content, I have some sense, here, that you’re responding to other arguments you’ve seen about deceptive alignment, rather than to specific claims made in the report (I don’t, for example, make any claims about world knowledge being derived “in-context,” or about models “accidentally” acquiring flexible instrumental reasoning). Is your basic thought something like: sure, the models will develop flexible instrumental reasoning that could in principle be used in service of arbitrary goals, but they will only in fact use it in service of the specified goal, because that’s the thing training pressures them to do? If so, my feeling is something like: ok, but a lot of the question here is whether using the instrumental reasoning in service of some other goal (one that backchains into getting-reward) will be suitably compatible with/incentivized by training pressures as well. And I don’t see e.g. the reversal curse as strong evidence on this front.
Re: “mechanistically ungrounded intuitions about ‘goals’ and ‘tryingness’”—as I discuss in section 0.1, the report is explicitly setting aside disputes about whether the relevant models will be well-understood as goal-directed (my own take on that is in section 2.2.1 of my report on power-seeking AI here). The question in this report is whether, conditional on goal-directedness, we should expect scheming. That said, I do think that what I call the “messyness” of the relevant goal-directedness might be relevant to our overall assessment of the arguments for scheming in various ways, and that scheming might require an unusually high standard of goal-directedness in some sense. I discuss this in section 2.2.3, on “‘Clean’ vs. ‘messy’ goal-directedness,” and in various other places in the report.
Re: “long term goals are sufficiently hard to form deliberately that I don’t think they’ll form accidentally”—the report explicitly discusses cases where we intentionally train models to have long-term goals (both via long episodes, and via short episodes aimed at inducing long-horizon optimization). I think scheming is more likely in those cases. See section 2.2.4, “What if you intentionally train the model to have long-term goals?” That said, I’d be interested to see arguments that credit assignment difficulties actively count against the development of beyond-episode goals (whether in models trained on short episodes or long episodes) for models that are otherwise goal-directed. And I do think that, if we could be confident that models trained on short episodes won’t learn beyond-episode goals accidentally (even irrespective of mundane adversarial training—e.g., that models rewarded for getting gold coins on the episode would not learn a goal that generalizes to caring about gold coins in general, even prior to efforts to punish it for sacrificing gold-coins-on-the-episode for gold-coins-later), that would be a significant source of comfort (I discuss some possible experimental directions in this respect in section 6.2).
Thanks for this thoughtful comment, Ben. And also, for putting the “The Gold Lily” and “Mother and Child” on my radar—they hadn’t been before. I agree that “Mother and Child” evokes a sort some kind of sort of intergenerational project in the way you describe—“it is your turn to address it.” It seems related to the thing I was trying to talk about at the end of the post—e.g., Gluck asking for some kind of directness and intensity of engagement with life.
Thanks! Re: one in five million and .01% -- thanks, edited. And thanks for pointing to the Augenblick piece—does look relevant (though my specific interest in that footnote was in constraints applicable to a model where you can only consider some subset of your evidence at any given time).
I’m sorry to hear about this, Nathan. As I say in the post, I do think that the question how to do gut-stuff right from a practical perspective is distinct from the epistemic angle that the post focuses on, and I think it’s important to attend to both.
Noting that the passage you quote in your appendix from my report isn’t my definition of the type of AI I’m focused on. I’m focused on AI systems with the following properties:
Advanced capability: they outperform the best humans on some set of tasks which when performed at advanced levels grant significant power in today’s world (tasks like scientific research, business/military/political strategy, engineering, and persuasion/manipulation).
Agentic planning: they make and execute plans, in pursuit of objectives, on the basis of models of the world.
Strategic awareness: the models they use in making plans represent with reasonable accuracy the causal upshot of gaining and maintaining power over humans and the real-world environment.
See section 2.1 in the report for more in-depth description.
Hi Jake,
Thanks for this comment. I discuss this sort of case in footnote 33 here—I think it’s a good place to push back on the argument. Quoting what I say there:
there is, perhaps, some temptation to say “even if I should be indifferent to these people burned alive, I’m not! Screw indifference-ism world! Sounds like a shitty objective normative order anyway – let’s rebel against it.” That is, it feels like indifference-ism worlds have told me what the normative facts are, but they haven’t told me about my loyalty to the normative facts, and the shittyness of these normative facts puts that loyalty even more in question.
And perhaps, as well, there’s some temptation to think that “Well, indifference-ism world is morally required to be indifferent to my overall decision-procedure as well – so I’ll use a decision-procedure that isn’t indifferent to what happens in indifference-ism world. Indifference-ism world isn’t allowed to care!”
These responses might seem dicey, though. If they (or others) don’t end up working, ultimately I think that biting the bullet and taking this sort of deal is in fact less bad than doing so in the nihilism-focused version or the original. So it’s an option if necessary – and one I’d substantially prefer to biting the bullet in all of them.
That is, I’m interested in some combination of:
Not taking the deal because you’re uncertain of your loyalty to the normative facts (e.g., something about internalism/externalism etc)
Not taking the deal because indifference-ism world is indifferent to your decision procedure (or to your actions more generally), so whatever, let’s save my family in those worlds.
Biting the bullet and taking the deal if it comes to that, but not taking it in the other cases discussed in the post.
Adding a few more thoughts, I think part of what I’m interested in here is the question of what you would be “trying” to do (from some kind of “I endorse this” perspective, even if the endorsement doesn’t have any external backing from the normative facts) conditional on a given world. If, in indifference-ism world, you wouldn’t be trying, in this sense, to protect your family, such that your representative from indifference-ism world would indeed be like “yeah, go ahead, burn my family alive,” then taking the deal looks more OK to me. But if, conditional on indifference-ism, you would be trying to protect your family anyway (maybe because: the normative facts are indifferent, so might as well), such that your representative from indifference-ism world would be like “I’m against this deal,” then taking the deal looks worse to me. And the second thing seems more like where I’d expect to end up.
I found this helpful, thanks for writing.
A few questions about this:
Does this view imply that it is actually not possible to have a world where e.g. a machine creates one immortal happy person per day, forever, who then form an ever-growing line?
How does this view interpret cosmological hypotheses on which the universe is infinite? Is the claim that actually, on those hypotheses, the universe is finite after all?
It seems like lots of the (countable) worlds and cases discussed in the post can simply be reframed as never-ending processes, no? And then similar (identical?) questions will arise? Thus, for example, w5 is equivalent to a machine that creates a1 at −1, then a3 at −1, then a5 at −1, etc. w6 is equivalent to a machine that creates a1 at −1, then a2 at −1, a3 at −1, etc. What would this view say about which of these machines we should create, given the opportunity? How should we compare these to a w8 machine that creates b1 at −1, b2 at −1, b3 at −1, b4 at −1, etc?
Re: the Jaynes quote: I’m not sure I’ve understood the full picture here, but in general, to me it doesn’t feel like the central issues here have to do with dependencies on “how the limit is approached,” such that requiring that each scenario pin down an “order” solves the problems. For example, I think that a lot of what seems strange about Neutrality-violations in these cases is that even if we pin down an order for each case, the fact that you can re-arrange one into the other makes it seem like they ought to be ethically equivalent. Maybe we deny that, and maybe we do so for reasons related to what you’re talking about—but it seems like the same bullet.
Thanks! Fixed.
Thanks for doing this! I’ve found it useful, and I expect that it will increase my engagement with EA Forum/LW content going forward.
“that just indicates that EDT-type reasoning is built into the plausibility of SIA”
If by this you mean “SIA is only plausible if you accept EDT,” then I disagree. I think many of the arguments for SIA—for example, “you should 1⁄4 on each of tails-mon, tails-tues, heads-mon, and heads-tues in Sleeping Beauty with two wakings each, and then update to being a thirder if you learn you’re not in heads-tues,” “telekinesis doesn’t work,” “you should be one-half on not-yet-flipped fair coins,” “reference classes aren’t a thing,” etc—don’t depend on EDT, or even on EDT-ish intuitions.
you talk about contorting one’s epistemology in order to bet a particular way, but what’s the alternative? If I’m an EDT agent who wants to bet at odds of a third, what is the principled reasoning that leads me to have credence of a half?
The alternative is to just bet the way you want to anyway, in the same way that the (most attractive, imo) alternative to two-boxing in transparent newcomb is not “believe that the boxes are opaque” but “one-box even though you know they’re transparent.” You don’t need to have a credence of a half to bet how you want to—especially if you’re updateless. And note that EDT-ish SSA-ers have the fifthing problem too, in cases like the “wake up twice regardless, then learn that you’re not heads-tuesday” version I just mentioned (where SSA ends up at 1/3rd on heads, too).
You argue that questions like “could I have been a chimpanzee” seem ridiculous. But these are closely analogous to the types of questions that one needs to ask when making decisions according to FDT (e.g. “are the decisions of chimpanzees correlated with my own?”) So, if we need to grapple with these questions somehow in order to make decisions, grappling with them via our choice of a reference class doesn’t seem like the worst way to do so.
I think that “how much are my decisions correlated with those of the chimps?” is a much more meaningful and tractable question, with a much more determinate answer, than “are the chimps in my reference class?” Asking questions about correlations between things is the bread and butter of Bayesianism. Asking questions anthropic reference classes isn’t—or, doesn’t need to be.
I’m reminded of Yudkowsky’s writing about why he isn’t prepared to get rid of the concept of “anticipated subjective experience”, despite the difficulties it poses from a quantum-mechanical perspective.
Thanks for the link. I haven’t read this piece, but fwiw, to me it feels like “there is a truth about the way that the world is/about what world I’m living in, I’m trying to figure out what that truth is” is something we shouldn’t give up lightly. I haven’t engaged much with the QM stuff here, and I can imagine it moving me, but “how are you going to avoid fifth-ing?” doesn’t seem like a strong enough push on its own.
It’s a good question, and one I considered going into in more detail on in the post (I’ll add a link to this comment). I think it’s helpful to have in mind two types of people: “people who see the exact same evidence you do” (e.g., they look down on the same patterns of wrinkles on your hands, the same exact fading on the jeans they’re wearing, etc) and “people who might, for all you know about a given objective world, see the exact same evidence you do” (an example here would be “the person in room 2”). By “people in your epistemic situation,” I mean the former. The latter I think of as actually a disguised set of objective worlds, which posit different locations (and numbers) of the former-type people. But SIA, importantly, likes them both (though on my gloss, liking the former is more fundamental).
Here are some cases to illustrate. Suppose that God creates either one person in room 1 (if heads) or two people (if tails) in rooms 1 and 2. And suppose that there are two types of people: “Alices” and “Bobs.” Let’s say that any given Alice sees the exact same evidence as the other Alices (the same wrinkles, faded jeans, etc), and that the same holds for Bobs, and that if you’re an Alice or a Bob, you know it. Now consider three cases:
For each person God creates, he flips a second coin. If it’s heads, he creates an Alice. If tails, a Bob.
God flips a second coin. If it’s heads, he makes the person in room 1 Alice; if tails, Bob. But if the first coin was tails and he needs to create a second person, he makes that person different from the first. Thus, if tails-heads, it’s an Alice in room 1, and a Bob in room 2. But if it’s tails-tails, then it’s a Bob in room 1, and an Alice in room 2. (I talk about this case in part 4, XV.)
God creates all Alices no matter what.
Let’s write people’s names with “A” or “B,” in order of room number. And let’s say you wake up as an Alice.
In case one, “coin 1 heads” (I’ll write the coin-1 results in parentheses) corresponds to two objective worlds — A, and B — each with 1⁄4 prior probability. Coin 1 tails corresponds to four objective worlds — AA, AB, BA, and BB — each with 1/8th prior probability. So as Alice, you start by crossing off B and BB, because there are no Alices. So you’re left with 1⁄4 on A, and 1/8th on each of AA, AB, and BA, so an overall odds-ratio of 2:1:1:1. But now, as SIA, you scale the prior in proportion to the number of Alices there are, so AA gets double weight. Now you’re 2:2:1:1. Thus, you end up with 1/3rd on A, 1⁄3 on AA (with 1/6th on each of the corresponding centered worlds), and 1/6th on each of AB and BA. And you’re a “thirder” overall.
Now let’s look at case two. Here, the prior is 1⁄4 on A, 1⁄4 on B, 1⁄4 on AB, and 1⁄4 on BA. So SIA doesn’t actually do any scaling of the prior: there’s a maximum of one A in each world. Rather, it crosses off B, and ends up with 1/3rd on anything else, and stays a “thirder” overall.
Case three is just Sleeping Beauty: SIA scales in proportion to the number of Alices, and ends up a thirder overall.
So in each of these cases, SIA gives the same result, even though the distribution of Alices is in some sense pretty different. And notice, we can redescribe case 1 and 2 in terms of SIA liking “people who, for all you know about a given objective world, might be an Alice” instead of in terms of SIA liking Alices. E.g., in both cases, there are twice as many such people on tails. But importantly, their probability of being an Alice isn’t correlated with coin 1 heads vs. coin 1 tails.
Anthropics cases are sometimes ambiguous about whether they’re talking about cases of type 1 or of type 3. God’s coin toss is closer to case 1: e.g., you wake up as a person in a room, but we didn’t specify that God was literally making exact copies of you in the other rooms—your reasoning, though, treats his probability of giving any particular objective-world person your exact evidence is constant across people. Sleeping Beauty is often treated as more like case 3, but it’s compatible with being more of a case 1 type (e.g., if the experimenters also flip another coin on each waking, and leave it for Beauty to see, this doesn’t make a difference; and in general, the Beauties could have different subjective experiences on each waking, as long as —as far as Beauty knows — these variations in experience are independent of the coin toss outcome). I’m not super careful about these distinctions in the post, partly because actually splitting out all of the possible objective worlds in type-1 cases isn’t really do-able (there’s no well-defined distribution that God is “choosing from” when he creates each person in God’s coin toss—but his choice is treated, from your perspective, as independent from the coin toss outcome); and as noted, SIA’s verdicts end up the same.
Cool, this gives me a clearer picture of where you’re coming from. I had meant the central question of the post to be whether it ever makes sense to do the EDT-ish try-to-control-the-past thing, even in pretty unrealistic cases—partly because I think answering “yes” to this is weird and disorienting in itself, even if it doesn’t end up making much of a practical difference day-to-day; and partly because a central objection to EDT is that the past, being already fixed, is never controllable in any practically-relevant sense, even in e.g. Newcomb’s cases. It sounds like your main claim is that in our actual everyday circumstances, with respect to things like the WWI case, EDTish and CDT recommendations don’t come apart—a topic I don’t spend much time on or have especially strong views about.
“you’re going to lean on the difference between ‘cause’ and ‘control’”—indeed, and I had meant the “no causal interaction with” part of opening sentence to indicate this. It does seem like various readers object to/were confused by the use of the term “control” here, and I think there’s room for more emphasis early on as to what specifically I have in mind; but at a high-level, I’m inclined to keep the term “control,” rather than trying to rephrase things solely in terms of e.g. correlations, because I think it makes sense to think of yourself as, for practical purposes, “controlling” what your copy writes on his whiteboard, what Omega puts in the boxes, etc; that more broadly, EDT-ish decision-making is in fact weird in the way that trying to control the past is weird, and that this makes it all the more striking and worth highlighting that EDT-ish decision-making seems, sometimes, like the right way to go.
Not sure exactly what words people have used, but something like this idea is pretty common in the non-CDT literature, and I think e.g. MIRI explicitly talks about “controlling” things like your algorithm.
Very glad to hear it, Lizka :) -- and thanks for letting me know.