Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Pascal's Mugging (2009) [pdf]

nickbostrom.com

Post reply on HN
Print view View original

51–60 of 71 posts

Re: Pascal's Mugging (2009) [pdf]

#51

Post by maest »

roenxi wrote: post #19
maest wrote: post #16

Earlier quoted context omitted.

I thought the "solution" for St Peteresburg paradox was to consider utility as a non-linear function of wealth. And this makes the series converge. Also, I don't find the Pascal's Mugger example convincing, as the probability that the mugger will return with the money is inversely proportional to the multiple they are promissing (for very large multiples this is because they have finite resources, but even at lower m…

> as the probability that the mugger will return with the money is... That can't be reasonably estimated though. Putting aside the fact that we can't really assert the relation you posit, there is also a finite probability that the mugger is some sort of illuminati member with the ability to create an arbitrary amount of money. Ie, there is some tiny-but-positive probability that he can create an arbitrary amount of…

It seems to me that the set of worlds where the mugger can return $X is strictly a subset of the set of worlds where the mugger can return $X+epsilon.

So the probability won't be "inversely proportional" in the strict sense, but it will be decreasing with X increasing.

Re: Pascal's Mugging (2009) [pdf]

#52

Post by YeGoblynQueenne »

Dylan16807 wrote: post #49
YeGoblynQueenne wrote: post #42

Earlier quoted context omitted.

Thanks, that's an interesting read. But I don't think it addresses my question: why shouldn't Pascal place the probability that the Mugger is an Operator from the Seventh dimension to _zero_ (rather than an infinitissemally small number)? The point is that, at the time when the Mugger declares himself to be an Operator from the Seventh Dimension who can offer large rewards etc, there is no evidence to suggest he's sa…

Probability zero is the same as saying that it would take infinite evidence to convince you. Even if someone provides amazingly convincing evidence, better than you've ever seen, a flat 0 or 1 eats it. > there is no evidence to suggest he's saying the truth. No evidence at all. Accordingly, the probability that he's telling the truth must be zero. I don't think that logic works. What if the claim was "I have a five d…

>> Probability zero is the same as saying that it would take infinite evidence to convince you.

That assumes I can't go back and change my earlier beliefs. But I don't see why that's necessary. If I have no evidence that X is true at time t, I assing a probability of 0 to it. If I acquire evidence that X is true at time t+1, I throw out the 0 and assign a higher probability to X.

The world changes all the time. Why am I condemned to hold on to obviously unsound beliefs for all eternity?

>> I don't think that logic works. What if the claim was "I have a five dollar bill in my pocket"?

That depends. I've seen five dollar bills coming out of peoples' pockets before (actually, I haven't because dollars are not common where I live but Ok). I don't have to assing a zero probability to that. I have some evidence that it's possible.

But I have no evidence that there even exists such a thing as a Seventh Dimension etc.

Re: Pascal's Mugging (2009) [pdf]

#53

Post by YeGoblynQueenne »

TeMPOraL wrote: post #50
YeGoblynQueenne wrote: post #42

Earlier quoted context omitted.

Thanks, that's an interesting read. But I don't think it addresses my question: why shouldn't Pascal place the probability that the Mugger is an Operator from the Seventh dimension to _zero_ (rather than an infinitissemally small number)? The point is that, at the time when the Mugger declares himself to be an Operator from the Seventh Dimension who can offer large rewards etc, there is no evidence to suggest he's sa…

As the saying goes, "zero and one are not probabilities". Like 'Dylan16807 says, they eat evidence. When doing maths, when transforming to log probabilities, 0 becomes -Infinity; when transforming to odds ratios, 1 goes to infinity. A longer explanation: https://www.lesswrong.com/posts/QGkYCwyC7wTDyt3yT/0-and-1-ar... . See also https://en.wikipedia.org/wiki/Cromwell%27s_rule , mentioned by 'edflsafoiewq.

Yes, I get the arithmetic, thank you. What I don't get is why I'm forced to perform it in the way that you say. Why do I have to hold on to that 0 probabilty no matter what happens? Clearly it's much more reasonable to change my mind given that the world has changed and assign a non-zero probability to an event for which I now have evidence. Why would I not?

>> See also https://en.wikipedia.org/wiki/Cromwell%27s_rule, mentioned by 'edflsafoiewq.

How about the statement "Hillary Clinton is the President of the United States"? What probability should I assign to that? I know that the PotUS is Donald Trump. Does Cromwell's Rule mean that I have to believe that Hillary Clinton is the PotUS at least a little, because otherwise I will never be able to believe it if she ever gets elected president?

Re: Pascal's Mugging (2009) [pdf]

#54

Post by [deleted] »

Dylan16807 wrote: post #49
YeGoblynQueenne wrote: post #42

Earlier quoted context omitted.

Thanks, that's an interesting read. But I don't think it addresses my question: why shouldn't Pascal place the probability that the Mugger is an Operator from the Seventh dimension to _zero_ (rather than an infinitissemally small number)? The point is that, at the time when the Mugger declares himself to be an Operator from the Seventh Dimension who can offer large rewards etc, there is no evidence to suggest he's sa…

Probability zero is the same as saying that it would take infinite evidence to convince you. Even if someone provides amazingly convincing evidence, better than you've ever seen, a flat 0 or 1 eats it. > there is no evidence to suggest he's saying the truth. No evidence at all. Accordingly, the probability that he's telling the truth must be zero. I don't think that logic works. What if the claim was "I have a five d…

[deleted]

Re: Pascal's Mugging (2009) [pdf]

#55

Post by Dylan16807 »

YeGoblynQueenne wrote: post #52
Dylan16807 wrote: post #49

Earlier quoted context omitted.

Probability zero is the same as saying that it would take infinite evidence to convince you. Even if someone provides amazingly convincing evidence, better than you've ever seen, a flat 0 or 1 eats it. > there is no evidence to suggest he's saying the truth. No evidence at all. Accordingly, the probability that he's telling the truth must be zero. I don't think that logic works. What if the claim was "I have a five d…

>> Probability zero is the same as saying that it would take infinite evidence to convince you. That assumes I can't go back and change my earlier beliefs. But I don't see why that's necessary. If I have no evidence that X is true at time t, I assing a probability of 0 to it. If I acquire evidence that X is true at time t+1, I throw out the 0 and assign a higher probability to X. The world changes all the time. Why a…

> If I acquire evidence that X is true at time t+1, I throw out the 0 and assign a higher probability to X.

> The world changes all the time. Why am I condemned to hold on to obviously unsound beliefs for all eternity?

Normally when you update a probability, how much you change it is based on the strength of the evidence. If your probability of something is ultra-low, and you see an event that's a million times more likely if that thing is true, your new probability is roughly a million times higher. And for a probability that's sufficiently close to 0 or 1, that pit is basically impossible to climb out of.

Do you have an alternate method to suggest? What's the calculation you would use? Note that "I'm seeing this with my own eyes" should only give you so much change, because you might have accidentally taken a whole bunch of hallucinogens.

> But I have no evidence that there even exists such a thing as a Seventh Dimension etc.

If you're setting a hard cutoff based on the silly Seventh Dimension stuff, then you still fall for the version where I come to your house and sign a document giving you a giant pile of money. That's how mortgages and business deals work every day after all.

> How about the statement "Hillary Clinton is the President of the United States"? What probability should I assign to that? I know that the PotUS is Donald Trump. Does Cromwell's Rule mean that I have to believe that Hillary Clinton is the PotUS at least a little, because otherwise I will never be able to believe it if she ever gets elected president?

Not for that reason. But you have to factor in the chance that you got confused, or your brain is failing to make new memories and it's actually 2022, or you just woke up from a really detailed dream about the wrong president.

Re: Pascal's Mugging (2009) [pdf]

#56

Post by YeGoblynQueenne »

Dylan16807 wrote: post #55
YeGoblynQueenne wrote: post #52

Earlier quoted context omitted.

>> Probability zero is the same as saying that it would take infinite evidence to convince you. That assumes I can't go back and change my earlier beliefs. But I don't see why that's necessary. If I have no evidence that X is true at time t, I assing a probability of 0 to it. If I acquire evidence that X is true at time t+1, I throw out the 0 and assign a higher probability to X. The world changes all the time. Why a…

> If I acquire evidence that X is true at time t+1, I throw out the 0 and assign a higher probability to X. > The world changes all the time. Why am I condemned to hold on to obviously unsound beliefs for all eternity? Normally when you update a probability, how much you change it is based on the strength of the evidence. If your probability of something is ultra-low, and you see an event that's a million times more…

>> Do you have an alternate method to suggest? What's the calculation you would use? Note that "I'm seeing this with my own eyes" should only give you so much change, because you might have accidentally taken a whole bunch of hallucinogens.

I don't understand. How would it happen that I've accidentally taken a whole bunch of hallucinogens? I never go near that kind of stuff.

>> Not for that reason. But you have to factor in the chance that you got confused, or your brain is failing to make new memories and it's actually 2022, or you just woke up from a really detailed dream about the wrong president.

I don't see how that would happen either. Why would my brain fail to make new memories? Why are you saying that this might be the case?

I think this is just enhancing the deep unreality of what you are proposing. If we need to assume that I'm in some kind of weird mental state that I have no reason to be in for your whole proposition to make sense then I really don't see the point of it, other than perhaps an interesting theoretical game.

Re: Pascal's Mugging (2009) [pdf]

#57

Post by Dylan16807 »

YeGoblynQueenne wrote: post #56
Dylan16807 wrote: post #55

Earlier quoted context omitted.

> If I acquire evidence that X is true at time t+1, I throw out the 0 and assign a higher probability to X. > The world changes all the time. Why am I condemned to hold on to obviously unsound beliefs for all eternity? Normally when you update a probability, how much you change it is based on the strength of the evidence. If your probability of something is ultra-low, and you see an event that's a million times more…

>> Do you have an alternate method to suggest? What's the calculation you would use? Note that "I'm seeing this with my own eyes" should only give you so much change, because you might have accidentally taken a whole bunch of hallucinogens. I don't understand. How would it happen that I've accidentally taken a whole bunch of hallucinogens? I never go near that kind of stuff. >> Not for that reason. But you have to fa…

You can't come up with a one in a billion scenario that you would accidentally take a hallucinogen?

You never ever have a dream that seems real for a few moments?

And failing to make new memories would be a specific but possible injury.

We're supposed to be working with very low probabilities here. That's the whole point of the thought experiment. If you're going to round anything below one-in-a-million to exactly zero then that's your prerogative, and it works in everyday life, but it's objectively wrong; it would falsely reject the idea of lightning strikes and winning the lottery.

> I think this is just enhancing the deep unreality of what you are proposing.

You didn't even reply to the part about removing all the silly stuff and cutting it down to just "guy offers to sign a document for lots of money"...

Re: Pascal's Mugging (2009) [pdf]

#58

Post by roenxi »

maest wrote: post #51
roenxi wrote: post #19

Earlier quoted context omitted.

> as the probability that the mugger will return with the money is... That can't be reasonably estimated though. Putting aside the fact that we can't really assert the relation you posit, there is also a finite probability that the mugger is some sort of illuminati member with the ability to create an arbitrary amount of money. Ie, there is some tiny-but-positive probability that he can create an arbitrary amount of…

It seems to me that the set of worlds where the mugger can return $X is strictly a subset of the set of worlds where the mugger can return $X+epsilon. So the probability won't be "inversely proportional" in the strict sense, but it will be decreasing with X increasing.

At some point it converges to some constant probability. The probability of providing an "almost impossible" - say $9^^^^9 - is almost precisely equal to the probability of providing $9^^^^9+1. This is because any mechanism that can provide the first can also provide the second.

Technically one will be a subset of the other but it will be like the sum of an infinite series where the differences are so small that there is a limiting asymptotic on the value of the sum is 0. The probability will converge to the value of "probability an entity can provide arbitrary compensation".

Re: Pascal's Mugging (2009) [pdf]

#59

Post by YeGoblynQueenne »

Dylan16807 wrote: post #57
YeGoblynQueenne wrote: post #56

Earlier quoted context omitted.

>> Do you have an alternate method to suggest? What's the calculation you would use? Note that "I'm seeing this with my own eyes" should only give you so much change, because you might have accidentally taken a whole bunch of hallucinogens. I don't understand. How would it happen that I've accidentally taken a whole bunch of hallucinogens? I never go near that kind of stuff. >> Not for that reason. But you have to fa…

You can't come up with a one in a billion scenario that you would accidentally take a hallucinogen? You never ever have a dream that seems real for a few moments? And failing to make new memories would be a specific but possible injury. We're supposed to be working with very low probabilities here. That's the whole point of the thought experiment. If you're going to round anything below one-in-a-million to exactly ze…

But I'm not hallucinating and I'm not dreaming either.

Also, I don't know why you're saying I'd round anything below one-in-a-million to zero. I wouldn't. But would assign zero probability to a mugger being an Operator from the Sevent Dimension because that's a patently absurd idea that I see no good reason to grace even with the slightest degree of belief.

I mean, if you take what you are saying here at face value I actually have to assume that there is a probability that there exists a Seventh Dimension with magikcally powerful Operators inhabiting it. In real life, not just in the context of Pascal's Wager. Because I can't assign zero probability to anything.

That just doesn't make any sense at all.

>> You didn't even reply to the part about removing all the silly stuff and cutting it down to just "guy offers to sign a document for lots of money"...

Apologies. I didn't understand what you meant with that and I didn't want to clutter the comment space with more clarifying questions.

Re: Pascal's Mugging (2009) [pdf]

#60

Post by Dylan16807 »

YeGoblynQueenne wrote: post #59
Dylan16807 wrote: post #57

Earlier quoted context omitted.

You can't come up with a one in a billion scenario that you would accidentally take a hallucinogen? You never ever have a dream that seems real for a few moments? And failing to make new memories would be a specific but possible injury. We're supposed to be working with very low probabilities here. That's the whole point of the thought experiment. If you're going to round anything below one-in-a-million to exactly ze…

But I'm not hallucinating and I'm not dreaming either. Also, I don't know why you're saying I'd round anything below one-in-a-million to zero. I wouldn't. But would assign zero probability to a mugger being an Operator from the Sevent Dimension because that's a patently absurd idea that I see no good reason to grace even with the slightest degree of belief. I mean, if you take what you are saying here at face value I…

> But I'm not hallucinating and I'm not dreaming either.

You've never been unsure if something actually happened for a moment? Because even if you only spend a few moments like that per month, we can assign it a probability.

> I mean, if you take what you are saying here at face value I actually have to assume that there is a probability that there exists a Seventh Dimension with magikcally powerful Operators inhabiting it. In real life, not just in the context of Pascal's Wager. Because I can't assign zero probability to anything.

You don't think there's any chance that you fundamentally misunderstand the universe and that there are powerful secrets being actively hidden from you? It doesn't have to be real 'magic', just something too beyond your understanding. I think there's some chance of that. I'd say less than 1% and more than 1 in a googolplex, to put some amusingly loose bounds on it. And then you have to factor in the chance the guy picks you in particular to mess with, but that's not an unreasonably large number.

> Apologies. I didn't understand what you meant with that and I didn't want to clutter the comment space with more clarifying questions.

You're objecting so specifically to the seventh dimension stuff, I thought it would be simpler to cut all that out. The point of the thought experiment is just a very likely but very positive act. And the way to have a productive conversation is to respond to the strongest form of the argument. So in that version, you can't just declare that the person in front of you isn't a rich guy screwing around and giving money to people that accept, because the probability of that is clearly not zero.

Post reply on HN