Thank you a lot for posting this scenario. It’s instructive from the “heuristics and biases” point of view.
Imagine there are a trillion variants of Islam, differing by one paragraph in the holy book or something. At most one of them can be true. You pick one variant at random, test it with your machine and get 30 1′s in a row. Now you should be damn convinced that you picked the true one, right? Wrong. Getting this result by a fluke is 1000x more likely than having picked the true variant in the first place. Probability is unintuitive and our brains are mush, that’s all I’m sayin’.
I agree with this. But if the scenario happened in real life, you would not be picking a certain variant. You would be asking the vague question, “Is Islam true,” to which the answer would be yes if any one of those trillion variants, or many others, were true.
Yes, there are trillions of possible religions that differ from one another as much as Islam differs from Judaism, or whatever. But only a few of these are believed by human beings. So I still think I would convert after 30 1′s, and I think this would reasonable.
If a religion’s popularity raises your prior for it so much, how do you avoid Pascal’s Mugging with respect to the major religions of today? Eternity in hell is more than 2^30 times worse than anything you could experience here; why aren’t you religious already?
It doesn’t matter whether it raises your prior or not; eternity in hell is also more than 2^3000 times worse etc… so the same problem will apply in any case.
Elsewhere I’ve defended Pascal’s Wager against the usual criticisms, and I still say it’s valid given the premises. But there are two problematic premises:
1) It assumes that utility functions are unbounded. This is certainly false for all human beings in terms of revealed preference; it is likely false even in principle (e.g. the Lifespan Dilemma).
2) It assumes that humans are utility maximizers. This is false in fact, and even in theory most of us would not want to self-modify to become utility maximizers; it would be a lot like self-modifying to become a Babyeater or a Super-Happy.
Do you have an answer for how to avoid giving in to the mugger in Eliezer’s original Pascal’s Mugging scenario? If not, I don’t think your question is a fair one (assuming it’s meant to be rhetorical).
I don’t have a conclusive answer, but many people say they have bounded utility functions (you see Unknowns pointed out that possibility too). The problem with assigning higher credence to popular religions is that it forces your utility bound to be lower if you want to reject the mugging. Imagining a billion lifetimes is way easier than imagining 3^^^^3 lifetimes. That was the reason for my question.
My answer (for why I don’t believe in a popular religion as a form of giving in to a Pascal’s Mugging) would be that I’m simultaneously faced with a number of different Pascal’s Muggings, some of which are mutually exclusive, so I can’t just choose to give in to all of them. And I’m also unsure of what decision theory/prior/utility function I should use to decide what to do in the face of such Muggings. Irreversibly accepting any particular Mugging in my current confused state is likely to be suboptimal, so the best way forward at this point seems to be to work on the relevant philosophical questions.
That’s what I think too! You’re only the second other person I have seen make this explicit, so I wonder how many people have even considered this. Do you think more people would benefit from hearing this argument?
Do you think more people would benefit from hearing this argument?
Sure, why do you ask? (If you’re asking because I’ve thought of this argument but haven’t already tried to share it with a wider audience, it probably has to do with reasons, e.g., laziness, that are unrelated to whether I think more people would benefit from hearing it.)
I was considering doing a post on it, but there are many posts that I want to write, many of which require research, so I avoided implying that it would be done soon/ever.
Yes, there are trillions of possible religions that differ from one another as much as Islam differs from Judaism, or whatever. But only a few of these are believed by human beings.
Privileging the hypothesis! That they are believed by human beings doesn’t lend them probability.
Well, it does to the extent that lack of believers would be evidence against them. I’d say that Allah is considerably more probable than a similarly complex and powerful god who also wants to be worshiped and is equally willing to interact with humans, but not believed in by anyone at all. Still considerably less probable than the prior of some god of that general sort existing, though.
Well, it does to the extent that lack of believers would be evidence against them.
Agreed, but then we have the original situation, if we only consider the set of possible gods that have the property of causing worshiping of themselves.
Yes, there are trillions of possible religions that differ from one another as much as Islam differs from Judaism, or whatever. But only a few of these are believed by human beings.
Privileging the hypothesis! That they are believed by human beings doesn’t lend them probability.
No. It doesn’t lend probability, but it seems like it ought to lend something. What is this mysterious something? Lets call it respect.
Privileging the hypothesis is a fallacy.
Respecting the hypothesis is a (relatively minor) method of rationality.
We respect the hypotheses that we find in a math text by investing the necessary mental resources toward the task of finding an analytic proof. We don’t just accept the truth of the hypothesis on authority. But on the other hand, we don’t try to prove (or disprove) just any old hypothesis. It has to be one that we respect.
We respect scientific hypotheses enough to invest physical resources toward performing experiments that might refute or confirm them. We don’t expend those resources on just any scientific hypothesis. Only the ones we respect.
Does a religion deserve respect because it has believers? More respect if it has lots of believers? I think it does. Not privilege. Definitely not. But respect? Why not?
You can dispense with this particular concept of respect since in both your examples you are actually supplied with sufficient Bayesian evidence to justify evaluating the hypothesis, so it isn’t privileged. Whether this is also the case for believed in religions is the very point contested.
A priori, with no other evidence one way or another, a belief held by human beings is more likely to be true than not. If Ann says she had a sandwich for lunch, then her words are evidence that she actually had a sandwich for lunch.
Of course, we have external reason to doubt lots of things that human beings claim and believe, including religions. And a religion does not become twice as credible if it has twice as many adherents. Right now I believe we have good reason to reject (at least some of) the tenets of all religious traditions.
But it does make some sense to give some marginal privilege or respect to an idea based on the fact that somebody believes it, and to give the idea more credit if it’s very durable over time, or if particularly clever people believe it. If it were any subject but religion—if it were science, for instance—this would be an obvious point. Scientific beliefs have often been wrong, but you’ll be best off giving higher priors to hypotheses believed by scientists than to other conceivable hypotheses.
Also… if you haven’t been to Australia, is it privileging the hypothesis to accept the word of those who say that it exists? There are trillions of possible countries that could exist that people don’t believe exist...
And don’t tell me they say they’ve been there… religious people say they’ve experienced angels etc. too.
And so on. People’s beliefs in religion may be weaker than their belief in Austrialia, but it certainly is not privileging a random hypothesis.
Your observations (of people claiming to having seen an angel, or a kangaroo) are distinct from hypotheses formed to explain those observations. If in a given case, you don’t have reason to expect statements people make to be related to facts, then the statements people make taken verbatim have no special place as hypotheses.
“You don’t have reason to expect statements people make to be related to facts” doesn’t mean that you have 100% certainty that they are not, which you would need in order to invoke privileging the hypothesis.
Now you are appealing to impossibility of absolute certainty, refuting my argument as not being that particular kind of proof. If hypothesis X is a little bit more probable than many others, you still don’t have any reason to focus on it (and correlation could be negative!).
In principle the correlation could be negative but this is extremely unlikely and requires some very strange conditions (for example if the person is more likely to say that Islam is true if he knows it is false than if he knows it is true).
I disagree; given that most of the religions in question center on human worship of the divine, I have to think that Pr(religion X becomes known among humans | religion X is true) > Pr(religion X does not become known among humans | religion X is true). But I hate to spend time arguing about whether a likelihood ratio should be considered strictly equal to 1 or equal to 1 + epsilon when the prior probabilities of the hypotheses in question are themselves ridiculously small.
Thank you a lot for posting this scenario. It’s instructive from the “heuristics and biases” point of view.
Imagine there are a trillion variants of Islam, differing by one paragraph in the holy book or something. At most one of them can be true. You pick one variant at random, test it with your machine and get 30 1′s in a row. Now you should be damn convinced that you picked the true one, right? Wrong. Getting this result by a fluke is 1000x more likely than having picked the true variant in the first place. Probability is unintuitive and our brains are mush, that’s all I’m sayin’.
I agree with this. But if the scenario happened in real life, you would not be picking a certain variant. You would be asking the vague question, “Is Islam true,” to which the answer would be yes if any one of those trillion variants, or many others, were true.
Yes, there are trillions of possible religions that differ from one another as much as Islam differs from Judaism, or whatever. But only a few of these are believed by human beings. So I still think I would convert after 30 1′s, and I think this would reasonable.
If a religion’s popularity raises your prior for it so much, how do you avoid Pascal’s Mugging with respect to the major religions of today? Eternity in hell is more than 2^30 times worse than anything you could experience here; why aren’t you religious already?
It doesn’t matter whether it raises your prior or not; eternity in hell is also more than 2^3000 times worse etc… so the same problem will apply in any case.
Elsewhere I’ve defended Pascal’s Wager against the usual criticisms, and I still say it’s valid given the premises. But there are two problematic premises:
1) It assumes that utility functions are unbounded. This is certainly false for all human beings in terms of revealed preference; it is likely false even in principle (e.g. the Lifespan Dilemma).
2) It assumes that humans are utility maximizers. This is false in fact, and even in theory most of us would not want to self-modify to become utility maximizers; it would be a lot like self-modifying to become a Babyeater or a Super-Happy.
Do you have an answer for how to avoid giving in to the mugger in Eliezer’s original Pascal’s Mugging scenario? If not, I don’t think your question is a fair one (assuming it’s meant to be rhetorical).
I don’t have a conclusive answer, but many people say they have bounded utility functions (you see Unknowns pointed out that possibility too). The problem with assigning higher credence to popular religions is that it forces your utility bound to be lower if you want to reject the mugging. Imagining a billion lifetimes is way easier than imagining 3^^^^3 lifetimes. That was the reason for my question.
My answer (for why I don’t believe in a popular religion as a form of giving in to a Pascal’s Mugging) would be that I’m simultaneously faced with a number of different Pascal’s Muggings, some of which are mutually exclusive, so I can’t just choose to give in to all of them. And I’m also unsure of what decision theory/prior/utility function I should use to decide what to do in the face of such Muggings. Irreversibly accepting any particular Mugging in my current confused state is likely to be suboptimal, so the best way forward at this point seems to be to work on the relevant philosophical questions.
That’s what I think too! You’re only the second other person I have seen make this explicit, so I wonder how many people have even considered this. Do you think more people would benefit from hearing this argument?
Sure, why do you ask? (If you’re asking because I’ve thought of this argument but haven’t already tried to share it with a wider audience, it probably has to do with reasons, e.g., laziness, that are unrelated to whether I think more people would benefit from hearing it.)
I was considering doing a post on it, but there are many posts that I want to write, many of which require research, so I avoided implying that it would be done soon/ever.
Oddly, I think you meant “Pascal’s Wager”.
Pascal’s Mugging. Pascal’s Wager with something breaking symmetry (in this case observed belief of others).
Yes, I suppose it is technically a Pascal’s Mugging. I think Pascal thought he was playing Pascal’s Mugging though.
I don’t think Pascal recognized any potential symmetry in the first place, or he would have addressed it properly.
Privileging the hypothesis! That they are believed by human beings doesn’t lend them probability.
Well, it does to the extent that lack of believers would be evidence against them. I’d say that Allah is considerably more probable than a similarly complex and powerful god who also wants to be worshiped and is equally willing to interact with humans, but not believed in by anyone at all. Still considerably less probable than the prior of some god of that general sort existing, though.
Agreed, but then we have the original situation, if we only consider the set of possible gods that have the property of causing worshiping of themselves.
This whole discussion is about this very point. Downvoted for contradicting my position without making an argument.
Your position statement didn’t include an argument either, and the problem with it seems rather straightforward, so I named it.
I’ve been arguing with Sewing Machine about it all along.
No. It doesn’t lend probability, but it seems like it ought to lend something. What is this mysterious something? Lets call it respect.
Privileging the hypothesis is a fallacy. Respecting the hypothesis is a (relatively minor) method of rationality.
We respect the hypotheses that we find in a math text by investing the necessary mental resources toward the task of finding an analytic proof. We don’t just accept the truth of the hypothesis on authority. But on the other hand, we don’t try to prove (or disprove) just any old hypothesis. It has to be one that we respect.
We respect scientific hypotheses enough to invest physical resources toward performing experiments that might refute or confirm them. We don’t expend those resources on just any scientific hypothesis. Only the ones we respect.
Does a religion deserve respect because it has believers? More respect if it has lots of believers? I think it does. Not privilege. Definitely not. But respect? Why not?
You can dispense with this particular concept of respect since in both your examples you are actually supplied with sufficient Bayesian evidence to justify evaluating the hypothesis, so it isn’t privileged. Whether this is also the case for believed in religions is the very point contested.
No, it’s a method of anti-epistemic horror.
Yes, this seems right.
A priori, with no other evidence one way or another, a belief held by human beings is more likely to be true than not. If Ann says she had a sandwich for lunch, then her words are evidence that she actually had a sandwich for lunch.
Of course, we have external reason to doubt lots of things that human beings claim and believe, including religions. And a religion does not become twice as credible if it has twice as many adherents. Right now I believe we have good reason to reject (at least some of) the tenets of all religious traditions.
But it does make some sense to give some marginal privilege or respect to an idea based on the fact that somebody believes it, and to give the idea more credit if it’s very durable over time, or if particularly clever people believe it. If it were any subject but religion—if it were science, for instance—this would be an obvious point. Scientific beliefs have often been wrong, but you’ll be best off giving higher priors to hypotheses believed by scientists than to other conceivable hypotheses.
Also… if you haven’t been to Australia, is it privileging the hypothesis to accept the word of those who say that it exists? There are trillions of possible countries that could exist that people don’t believe exist...
And don’t tell me they say they’ve been there… religious people say they’ve experienced angels etc. too.
And so on. People’s beliefs in religion may be weaker than their belief in Austrialia, but it certainly is not privileging a random hypothesis.
Your observations (of people claiming to having seen an angel, or a kangaroo) are distinct from hypotheses formed to explain those observations. If in a given case, you don’t have reason to expect statements people make to be related to facts, then the statements people make taken verbatim have no special place as hypotheses.
“You don’t have reason to expect statements people make to be related to facts” doesn’t mean that you have 100% certainty that they are not, which you would need in order to invoke privileging the hypothesis.
Why do you have at most 99.999999999% certainty that they are not? Where does that number one-minus-a-billionth come from?
The burden of proof is on the one claiming a greater certainty (although I will justify this later in any case.)
Now you are appealing to impossibility of absolute certainty, refuting my argument as not being that particular kind of proof. If hypothesis X is a little bit more probable than many others, you still don’t have any reason to focus on it (and correlation could be negative!).
In principle the correlation could be negative but this is extremely unlikely and requires some very strange conditions (for example if the person is more likely to say that Islam is true if he knows it is false than if he knows it is true).
Begging the question!
I disagree; given that most of the religions in question center on human worship of the divine, I have to think that Pr(religion X becomes known among humans | religion X is true) > Pr(religion X does not become known among humans | religion X is true). But I hate to spend time arguing about whether a likelihood ratio should be considered strictly equal to 1 or equal to 1 + epsilon when the prior probabilities of the hypotheses in question are themselves ridiculously small.