The correct answer is to update in favor of Tails if you know that you were randomly selected to be created and not update otherwise. If there was no random sampling involved, if Bob was planning to create you no matter what, then your existence tells nothing about the outcome of the coin toss - you simply observe event "At least one person was created", not "I was randomly selected from N attempts".
However, SIA just assumes that you are always randomly sampled. This is sometimes true. But not always. You need to actually investigate the casual history that led to your existence to know which case is which. Therefore SIA is wrong in a general case.
You should have addressed my example from the comments to the previous post:
On Tails only your biological parents are infertile since 1970, on Heads everyone in the world except your parents is infertile since 1970.
It is an actually interesting case where SIA contradict common sense and so it allows us to distinguish between two types of reasoning about such problems.
Oh wait oops sorry I forgot that I used different case names in this article and in the paper.
What do you mean by if you were randomly selected? The scenario is as was stated: a million were created if tails, 1 if heads.
//On Tails only your biological parents are infertile since 1970, on Heads everyone in the world except your parents is infertile since 1970.//
No, that's completely false. You have reason to think there are more people with your current evidence. Once you know the distinction between your parents and others, other people don't have your current evidence.
> What do you mean by if you were randomly selected?
Exactly that. Did Bob have a list of possible people to create, from which he was randomly choosing people until he happened to create me or did he intention to create me in particular no matter the outcome of the coin toss. The actual algorithm, according to which Bob was acting, determines whether I'm supposed or not supposed to update. Or, more generally, what are the specifics of the causal process that led to my existence
> No, that's completely false. You have reason to think there are more people with your current evidence. Once you know the distinction between your parents and others, other people don't have your current evidence.
I don't understand what are you denying here. Are you saying that SIA does not privilege the world with more people anymore as soon as the information about your parents is available? Can you formally specify the bayesian update? Let there be 3 steps: according to which you learn new facts about the setting:
1. A fair coin was tossed
2. If coin is Heads everyone except 2 people are infertile, otherwise only two people are infertile.
It worked the same way creating people normally works. He didn't keep creating until he created you--he made people at random.
//I don't understand what are you denying here. Are you saying that SIA does not privilege the world with more people anymore as soon as the information about your parents is available? //
Yes. SIA says you should think there are more people who, based on your current evidence, it's epistemically possible you might be. That doesn't apply to parents other than you. SIA says you should reason as if randomly selected from the set of all possible people. The theory that more people exist starts out more likely, but then updating on who my parents are, and them being infertile, cancels out the update. SIA gives you no reason to think other people exist in greater numbers once you know who you are and that they are not you.
> He didn't keep creating until he created you--he made people at random.
Well then in this particular case I agree with SIA. As I've already mentioned, occasionally it's correct - specifically when it's assumption that people are made at random is satisfied.
> It worked the same way creating people normally works.
It doesn't seem plausible at all that people existences can be approximated as random sampling in a general case. That's kind of the whole problem. SIA just assumes that it's the case without any justifications.
> The theory that more people exist starts out more likely, but then updating on who my parents are, and them being infertile, cancels out the update.
Does it simply cancels out the update or updates in the opposite direction? Could you show me a formal example of bayesian update with actual numbers? Say, there are 100 times more people if the coin is Tails but only on Heads your biological parents are fertile.
As you say, regardless of anthropics, in the the super-prolific case I have reason to favor tails. One reason for this is that the probability of Randi getting pregnant at all (or carrying through to term, or whatever) is higher on the tails outcome than on the heads outcome*. In the divine case, the existence of the causal processes that successfully lead to even a single example of a human being created are the same. The causal process is just "God decides to directly create at least one person," and that has probability 1 of happening/succeeding on both coin outcomes, given omnipotence. Of course, you can modify the scenario so that God's actions might fail to create anyone based on more intermediary processes, but then we can appeal to a similar sort of non-anthropic evidence as in the other example.
* This still only gives me absurdly weak evidence for tails, since the probability of at least one pregnancy happening on heads and tails are both pretty close to 1. But I don't see a problem with this.
It's not intuitively crazy in part because there's no "discontinuity." The better your evidence that you resulted from causal process X, and the better your evidence that causal process X would've successfully gone through either way the coin lands, the worse evidence you have favoring heads or tails. In the limit, where we assume perfect knowledge of a perfectly reliable causal process (God's deliberate intervention to create a conscious mind like my own), the evidence for the coin's outcome is non-existent.
In a more realistic scenario, where we only have imperfect-but-strong evidence of the divine setup, we will in fact have evidence for tails, and maybe this is what your (or some people's) intuition ultimately draws from.
It's crazy that the process by which people are created matters to how they should anthropically reason. SIAers claim that it's likelier your specific mind is created if there are more total minds created.
It seems completely uncontroversially true that the process by which people are created matters. The other commenter above gave an example that illustrates this perfectly. ("If heads means everyone before my birth but my parents got near-perfect contraception, and tails means my parents alone got near-perfect contraception, I should infer from the known sexually reproductive mechanism of my creation that the coin landed heads despite fewer people being created.")
OK, that makes sense, but then I'm not sure I understand what the original issue is. It's not the specific causal process that's important per se (although I guess I misleadingly phrased it that way, sorry), it's the probability that it generates a mind with my evidence, together with the probability of being generated by competing epistemically possible processes. Some causal processes like the in contraception case generate minds like mine with certain probabilities, while others like in the divine case generate it with certain other probabilities, and it seems completely natural to me that this would then inform my probabilistic reasoning about what happened before my birth. If the probabilities are all the same/isomorphic, then yes, the specifics of the causal process don't matter.
> Bob’s coin toss
The correct answer is to update in favor of Tails if you know that you were randomly selected to be created and not update otherwise. If there was no random sampling involved, if Bob was planning to create you no matter what, then your existence tells nothing about the outcome of the coin toss - you simply observe event "At least one person was created", not "I was randomly selected from N attempts".
However, SIA just assumes that you are always randomly sampled. This is sometimes true. But not always. You need to actually investigate the casual history that led to your existence to know which case is which. Therefore SIA is wrong in a general case.
You should have addressed my example from the comments to the previous post:
On Tails only your biological parents are infertile since 1970, on Heads everyone in the world except your parents is infertile since 1970.
It is an actually interesting case where SIA contradict common sense and so it allows us to distinguish between two types of reasoning about such problems.
Bob's coin toss is not a case that I gave. Which case do you think the probabilistic reasoning should change at?
I'm confused. How it's not a case that you gave if I took it from your post?
Oh wait oops sorry I forgot that I used different case names in this article and in the paper.
What do you mean by if you were randomly selected? The scenario is as was stated: a million were created if tails, 1 if heads.
//On Tails only your biological parents are infertile since 1970, on Heads everyone in the world except your parents is infertile since 1970.//
No, that's completely false. You have reason to think there are more people with your current evidence. Once you know the distinction between your parents and others, other people don't have your current evidence.
> What do you mean by if you were randomly selected?
Exactly that. Did Bob have a list of possible people to create, from which he was randomly choosing people until he happened to create me or did he intention to create me in particular no matter the outcome of the coin toss. The actual algorithm, according to which Bob was acting, determines whether I'm supposed or not supposed to update. Or, more generally, what are the specifics of the causal process that led to my existence
> No, that's completely false. You have reason to think there are more people with your current evidence. Once you know the distinction between your parents and others, other people don't have your current evidence.
I don't understand what are you denying here. Are you saying that SIA does not privilege the world with more people anymore as soon as the information about your parents is available? Can you formally specify the bayesian update? Let there be 3 steps: according to which you learn new facts about the setting:
1. A fair coin was tossed
2. If coin is Heads everyone except 2 people are infertile, otherwise only two people are infertile.
3. These two people are your biological parents
It worked the same way creating people normally works. He didn't keep creating until he created you--he made people at random.
//I don't understand what are you denying here. Are you saying that SIA does not privilege the world with more people anymore as soon as the information about your parents is available? //
Yes. SIA says you should think there are more people who, based on your current evidence, it's epistemically possible you might be. That doesn't apply to parents other than you. SIA says you should reason as if randomly selected from the set of all possible people. The theory that more people exist starts out more likely, but then updating on who my parents are, and them being infertile, cancels out the update. SIA gives you no reason to think other people exist in greater numbers once you know who you are and that they are not you.
> He didn't keep creating until he created you--he made people at random.
Well then in this particular case I agree with SIA. As I've already mentioned, occasionally it's correct - specifically when it's assumption that people are made at random is satisfied.
> It worked the same way creating people normally works.
It doesn't seem plausible at all that people existences can be approximated as random sampling in a general case. That's kind of the whole problem. SIA just assumes that it's the case without any justifications.
> The theory that more people exist starts out more likely, but then updating on who my parents are, and them being infertile, cancels out the update.
Does it simply cancels out the update or updates in the opposite direction? Could you show me a formal example of bayesian update with actual numbers? Say, there are 100 times more people if the coin is Tails but only on Heads your biological parents are fertile.
As you say, regardless of anthropics, in the the super-prolific case I have reason to favor tails. One reason for this is that the probability of Randi getting pregnant at all (or carrying through to term, or whatever) is higher on the tails outcome than on the heads outcome*. In the divine case, the existence of the causal processes that successfully lead to even a single example of a human being created are the same. The causal process is just "God decides to directly create at least one person," and that has probability 1 of happening/succeeding on both coin outcomes, given omnipotence. Of course, you can modify the scenario so that God's actions might fail to create anyone based on more intermediary processes, but then we can appeal to a similar sort of non-anthropic evidence as in the other example.
* This still only gives me absurdly weak evidence for tails, since the probability of at least one pregnancy happening on heads and tails are both pretty close to 1. But I don't see a problem with this.
I just think it's intuitively crazy to accept the inference rule in the first three cases but reject it in the fourth.
It's not intuitively crazy in part because there's no "discontinuity." The better your evidence that you resulted from causal process X, and the better your evidence that causal process X would've successfully gone through either way the coin lands, the worse evidence you have favoring heads or tails. In the limit, where we assume perfect knowledge of a perfectly reliable causal process (God's deliberate intervention to create a conscious mind like my own), the evidence for the coin's outcome is non-existent.
In a more realistic scenario, where we only have imperfect-but-strong evidence of the divine setup, we will in fact have evidence for tails, and maybe this is what your (or some people's) intuition ultimately draws from.
It's crazy that the process by which people are created matters to how they should anthropically reason. SIAers claim that it's likelier your specific mind is created if there are more total minds created.
It seems completely uncontroversially true that the process by which people are created matters. The other commenter above gave an example that illustrates this perfectly. ("If heads means everyone before my birth but my parents got near-perfect contraception, and tails means my parents alone got near-perfect contraception, I should infer from the known sexually reproductive mechanism of my creation that the coin landed heads despite fewer people being created.")
Because more people *with your evidence* are likely to be created.
OK, that makes sense, but then I'm not sure I understand what the original issue is. It's not the specific causal process that's important per se (although I guess I misleadingly phrased it that way, sorry), it's the probability that it generates a mind with my evidence, together with the probability of being generated by competing epistemically possible processes. Some causal processes like the in contraception case generate minds like mine with certain probabilities, while others like in the divine case generate it with certain other probabilities, and it seems completely natural to me that this would then inform my probabilistic reasoning about what happened before my birth. If the probabilities are all the same/isomorphic, then yes, the specifics of the causal process don't matter.