I was recently rereading the paper On Being a Random Sample, written by a former professor of mine. The paper is extremely good at explaining clearly why the self-indication assumption is the right view of anthropics. Here, I’m going to present three more arguments for the SIA. The first is inspired by the paper, the other two are not.
What is the self-indication assumption? It’s a view according to which your existence is rendered more probable according to theories on which there are more people who you might be. So consider:
Clone coin toss: There are five empty rooms. A coin is tossed. If it comes up heads, someone is created in the first room. If it comes up tails, someone is created in all five rooms. Upon being created, what should your credence be that the coin came up heads?
SIA answers: 1/6. If the coin came up tails, then five copies of you got created, rather than just one. In contrast, if it came up heads, only one copy got created. So SIA reasons: if five copies of me get created, it’s 5x likelier that whichever copy I am would get created. Tails is therefore 5x likelier than heads.
Note that SIA is the only view that thinks this. Its two primary rivals *conflict *with this judgment. The reason affirming the 1/6 answer in clone coin toss entails SIA is that the only difference between the worlds where the coin comes up heads and where it comes up tails are that in the tails worlds, more people get created. So unless you think your existence is likelier if more people get created, you will think heads and tails are equally likely.
So why think this judgment is right (aside from all the reasons I’ve given at other times)?
An SIAer will think that their existence, in the above scenario, is 5x likelier given tails than heads. They reason: “odds are good that I only exist because the coin came up tails.” In contrast, a non-SIAer will treat their existence as being *guaranteed *on either outcome. Non-SIAers don’t think their existence favors the hypothesis that the coin came up tails.
But the SIAer is simply right about this. There are some people who will only exist if the coin came up tails. While the heads coin flip, we might imagine, creates the same clone as the first clone created by the tails coin flip, the tails coin flip creates four other people who wouldn’t have existed unless the coin came up tails. If I’m the first person, then I would have existed either way—my existence isn’t any likelier given heads than tails. In contrast, if I’m one of the other four people, then I would only have existed if the coin came up tails.
Here’s another way to put the core thought: a person following non-SIA views thinks that they would have existed whichever way the coin came up, so their existence gives no evidence either way. If the coin came up tails, then all five people should think they would have existed either way. But that is just straightforwardly false. If the coin had come up heads, only one of them would have existed. If the heads coin flip only leads to the creation of one person, it simply *cannot *be true that all five people would have existed either way. So it sure seems like non-SIA views depend crucially on assuming something false.
Here’s another way to make the scenario even clearer. Consider:
Clone coin toss crosstemporal: One person is created in the year 2020. Then, in the year 2040, a fair coin is tossed. If it comes up tails, four more clones are created in the year 5483. All the clones have exactly the same experiences—none of them know the year they were created in. Upon being created, how likely should you think it is that the coin flipped in 2040 comes up heads?
For the reason described before, SIA is alone in thinking that tails is five times likelier than heads—giving heads a probability of just 1/6. But here’s a very straightforward explanation of why you should think this: if you’re the first person, then you’d have existed either way, so you have no evidence. Thus, the probability you’re the first person and the coin will come up heads = the probability that you’re the first person and the coin will come up tails.
However, the probability that you’re the first person and the coin will come up tails = the probability that you’re the second person and the coin has come up tails = the probability that you’re the third person and the coin has come up tails = the probability that you’re the fourth person and the coin has come up tails = the probability that you’re the fifth person and the coin has come up tails. Thus, all six events are equally probable. Tails is, in total, 5x likelier than heads.
What the non-SIAer must think about this case just isn’t right. They must think that they’d have existed either way, so their existence doesn’t favor either hypothesis. But that’s simply *false *as long as they’re not the first person. Only the first person would have existed either way. If everyone follows a view other than SIA, then all five people will, if the coin comes up tails, think that they’d have existed if the coin came up heads. But only one person would have existed if it came up heads.
Now, here’s one response that a non-SIAer could give. They might *deny *that you’d have existed either way. However, they might think that *if *you’d existed, it would have been unlikely that you’d have been whichever person you are. If five clones get created, the odds I’d be whichever one I am are only 20%. So maybe this cancels out the fact that there are five times more clones.
But the SIAer agrees with this inference (in a way). After being created, I should think that odds are only 1/5, given tails, that I’m any particular clone (say, clone 3). However, if I’m any of the clones other than the first one—the one who would have existed whether or not the coin came up tails—then my existence simply confirms tails. So without knowing which one I am, I split my credence in my being any clone five ways.
Similarly, the SIAer thinks that if I learn I’m the single clone who would have existed either way, then my credence in heads and tails should be equal. In clone coin toss crosstemporal, if I learn I’m the person before the coin toss, I should think heads and tails are equally likely. Before learning that I was the first person, I thought tails was 5x likelier than heads. The probability that I’d be first given the coin came up tails is 1/5, while it’s 1 given heads. So the probabilities cancel out—we’re back to a credence in heads of 50%.
So in short, the SIAer agrees that you should assign low epistemic probability to being whichever person you happen to be, assuming there are many people you could be. This is not an objection to SIA—it is consistent with it.
Now, here’s the inference that’s supposed to cancel out the SIA updating:
P(I’d be this clone)|heads=1
P(I’d be this clone)|tails=.2
I am this clone.
So my being this clone favors heads over tails by a factor of 5, cancelling out the greater probability of existing at all given tails.
But this is a mistake because the first step isn’t true. There is some chance that I’m one of the clones that would only exist given tails. If so, then the odds I’d be this clone if the coin came up heads was zero. Here’s a parallel case:
Rooms: There are five non-descript white rooms. A coin is flipped. If it comes up heads, you’re summoned into room 1. If it comes up tails, you’re summoned into a random one of the five rooms. Upon being summoned into a non-descript white room, what should your credence be that the coin came up tails?
The obvious answer is 1/2. You have no evidence either way. But here, one could likewise argue:
P(I’d be in this room)|heads=1
P(I’d be in this room)|tails=.2
I am in this room.
So my being in this room favors heads over tails by a factor of 5.
Clearly, that inference is wrong. The non-SIAer’s inference is wrong too in the same way. The right way to tabulate credences is the one described above, which I’ll repeat in a footnote.1 This implies the SIA result.
And what I’ve said so far closes the door to both ways to get out of the argument. It isn’t viable to assert that your existence would have happened either way, whether the coin came up tails or heads. Nor is it viable to think that something about the odds of you having whichever properties you have differing between heads and tails offsets the probabilistic boost. The SIA judgment is simply right.
The last argument was pretty complex and requires you to hold a lot of things in your head at once. This one is hopefully simpler. Consider:
Clone coin toss watcher: there are five white rooms, each with a pre-existing person called a watcher. A fair coin is flipped. If it comes up heads, one person is created in a random one of the five rooms. If it comes up tails, one person is created in all five rooms. After being created, what should your credence be that the coin came up heads?
SIA answers: 1/6, non-SIA views answer 1/2. But now here’s a question: what should the watcher’s credence be that the coin came up heads? The clear answer is: 1/6. After all, the watchers expected odds of only 1/5 that someone would appear in their room if the coin came up heads, while odds of 1 that someone would appear in their room if it came up tails. So, upon seeing someone appear in their room, they should think tails is 5x likelier than heads—because someone appearing in their room is 5x likelier if the coin comes up tails than if it comes up heads.2
So non-SIA views think your credence should be different from the watcher’s credence.
But this is weird. It seems like you and the watcher have the same evidence. After all, you and the watcher are given all the same information. You know all the things they know and vice versa. So it seems like you and the watcher should have the same credence. Here’s a principle to articulate what’s weird here:
Mandatory equality: if two agents have exclusively communicable evidence that they have each communicated to each other and this evidence makes some credence rationally mandatory for one of them, then their rationally mandatory credences will be equal.
[3]
In short, this principle says that if two agents are both rationally required by their evidence to have some credence, all the evidence going into this credence is the kind of thing that you could tell someone else about, and they both tell each other about all of their evidence, then they’re rationally required to have the same credence. There is a straightforward explanation of this: the agents have the same evidence, both knowing what the other knows. So if their credences are fixed by their evidence, then they must have the same credence.
Here’s another way to put the core idea: if your credences are different, presumably it will be because one of you is better informed than the other. But whichever is better informed, it seems, should simply defer to what the other person says. So you won’t be left with irreconcilably different credences.
This principle implies that your credence in the coin having come up heads should equal the watcher’s credence. The watcher’s credence should be 1/6. So yours should be too. SIA vindicated, haters mad!
Credit to for the thought behind this argument.
Suppose that a fair coin is flipped. If it comes up heads, a virus sweeps through the human population that renders 90% of future people non-sentient zombies for their whole lives (a zombie is someone like a normal person but who isn’t conscious).4 If it comes up tails, nothing of note happens—nobody is zombified.
Suppose you are born a normal person (that’s a dog-whistle for a non-zombie). What should your credence be that the coin came up heads? SIA answers: 1/11. After all, if the coin came up heads, odds are 90% that in my place would have been a non-sentient zombie—never having any experiences at all. Non-SIA views will standardly answer: 50%. After all, tails simply leads to the creation of more total conscious experiencers. So my existence is no evidence either way.5
This on its own is weird enough. But now imagine that the zombies would have, before being zombified, had a brief flicker of consciousness for ten seconds. If I don’t get zombified, then non-SIA views will agree that tails is 10x likelier than heads. After all, upon being created, in the first second of existence, pre-zombification, heads and tails will be equally likely. The odds I’d be zombified are 90% given heads, 0% given tails. So then I update by a factor of 10:1 in favor of tails over heads and conclude that tails is 10x likelier than tails.
This is an intuitively very weird asymmetry. Whether the zombies have a few brief seconds of consciousness seems irrelevant for whether I, upon finding myself non-zombified, should think the coin came up heads. So non-SIA views both get seemingly the wrong result and result in an odd evidential asymmetry—where your credences depend on whether zombification is immediate or there are a few brief seconds of consciousness. If the zombification happens immediately, before any experience, heads and tails are equally likely—if it happens after some experiences, then tails is likelier. Weird!
These arguments strike me as very strong. They join the 50 bazillion other very strong arguments for the self-indication assumption, collectively rendering it the most unfairly maligned view in philosophy!
Compartmentalized conditionalization is the view that anthropic updating depends only on uncentered evidence. So, if I have some experience, my evidence is simply “that experience was had somewhere in the universe.” Theories rise in probability relative to the odds that *someone *would have that exact pattern of experience if they were true—exactly how many people or what portion of people have them is irrelevant.
CC is, in my view, by far the worst of the three major anthropic theories. I explain why here and in 2017 some bright undergraduate named Daniel Kokotajlo wrote a clever undergrad thesis providing a strong objection to it—I wonder what ever became of him.
But anyways, I don’t think the watcher argument really works against CC. Or, well, it’s complicated. Let’s consider some different versions.
Version 1: the watchers all have the same experiences. So whether the coin comes up heads or tails, the same experiences will be had by the watchers. They’ll just be had by more if the coin comes up tails. In this case, after someone appears in their room, the watchers should still think heads and tails are equally likely. Their experience would be had either way. Thus, the watcher’s credences=the created people’s credences—they’re both 1/2.
Now, this is pretty weird. Remember, before the coin was flipped, the watchers all thought the probability of someone appearing in their room was 20% if the coin came up heads and 100% if it came up tails. So some event happened that was 5x as likely given that the coin came up tails as that it came up heads. Ordinarily if an event happens that’s N times likelier given theory A than B, it happening should raise the relative odds of A over B by a factor of N. This follows from Bayes theorem. So denying this is pretty costly. Still, it’s old news that CCers have to reject this kind of conditionalization. So this gives no *additional *reason to reject the view beyond what was already known.
Version 2: the watchers all have different experiences and so do the created people. In this cas…
