To answer your question as I understand it: it does not make sense for me to be confident that the result of some unspecified operation performed on some unknown object will be 12. It does make sense to be confident that it won’t be 12. (I might, of course, be confident and wrong. It’s just unlikely.)
I consider the latter a more apposite analogy for the argument you challenge here. Being confident that an unspecified process (e.g., AGI) won’t value paperclips makes more sense than being confident that it will, in the same way that being confident that it won’t return “12” makes more sense than being confident than it will.
Perhaps we are using a different notion of ‘confidence’. The uses of that term that I am familiar with have a separate specific meaning apart from probability. Confidence to me implies meta-level knowledge about the potential error in one’s probability estimate, intervals, or something of that nature.
So in your analogy, I can’t be confident about any properties of an unspecified process. I can of course assign a low probability estimate to the proposition that this unspecified process won’t value paperclips purely from priors, but that will not be a high confidence estimate. The ‘process’ could be a paperclip factory for all I know.
If you then map this analogy back to the original SIAI frame, I assume that the ‘die’ maps loosely to AGI development, and the 12 is AGI’s values being human values. And then no, it does not make sense to be confident that the roll won’t be 12, given that we supposedly don’t know what kind of die it is. It very well could be a ‘die’ with only 12s.
Priors are really just evidence you have already accumulated, so in reality one is never in a state of complete ignorance.
For example, I know that AGI will be created by humans (high confidence), humans create things which they value or things which help fulfill their values, and that humans for reasons both anthropocentric and economic are more likely to thus create AGI that shares human values.
I don’t think it’s useful to talk about whether we can have confidence in statements about the outcome of an AGI process while we still disagree about whether we can have confidence in statements about the outcome of rolling a hundred-sided die.
So, OK. Given two statements, P1 (“my next roll of this hundred-sided die will not be 12”) and P2 (“my next roll of this hundred-sided die will be 12″), I consider it sensible to be confident of P1 but not P2, you don’t consider it sensible to be confident of either statement. This may be because of different uses of the term “confident”, or it might be something more substantive.
Would you agree that there’s a 99% chance of P1 being true, and a 99% chance of P2 being false, given a fair die toss?
If so, can you say more about the class of statements like P1, where I estimate a 99% chance of it being true but it’s inappropriate for me to be confident in it?
while we still disagree about whether we can have confidence in statements about the outcome of rolling a hundred-sided die.
Ok. I’ll attempt to illustrate confidence vs probability as I understand it.
Lets start with your example. Starting with the certain knowledge that there is an object which is a 100-sided die, you are correct to infer that P(roll(D) != 12 | D=100) = 99⁄100.
Further, you are correct (in this example) to have complete confidence in that estimate.
We can think of confidence as how closely one’s probability estimate approaches the true frequency if we iterated the experiment to infinity, or alternatively summed across the multiverse.
If we roll that die an infinite number of times, (or summed across the multiverse), the observed frequency of (roll(D) != 12 | D=100) is more or less guaranteed to converge to the probability estimate of 99%. This is thus a high confidence estimate.
But this high confidence is conditional on your knowledge (and really, your confidence in this knowledge) that there is a die, and the die has 100 sides, and the die is fair, and so on.
Now if you remove all this knowledge, the situation changes dramatically.
Imagine that you know only that there is a die, but not how many sides the die has. You could still make some sort of an estimate. You could guesstimate using your brain’s internal heuristics, which wouldn’t be so terrible, or you could research dice and make a more informed prior about the unknown number of sides.
From that you might make an informed estimate of 98.7% for P(roll(D) != 12 | D = ???), but this will be a low confidence estimate. In fact once we roll this unknown die a large number of times, we can be fairly certain that the observed frequency will not converge to 98.7%.
So that is the difference between probability and confidence, at least in intuitive english. There are several more concrete algorithmic schemes for dealing with confidence or epistemic uncertainty, but that’s the general idea. (We could even take it up a whole new meta level by considering probability distributions of probability functions (one for each possible die type), and this would be a more accurate model, but it is of course no more confident)
So, if I understand you correctly, and returning to my original question… given the statement “my next roll of this hundred-sided die will not be 12” (P1), and a bunch of background knowledge (K1) about how hundred-sided dice typically work, and a bunch of background knowledge (K2) relevant to how likely it is that my next roll of this hundred-dided die will be typical (for example, how likely this die is to be loaded), I could in principle be confident in P1.
However, since K2 is not complete, I cannot in practice be confident in P1.
The best I can do is make an informed estimate of the likelihood of P1, but this will be a low confidence estimate.
Have I correctly generalized your reasoning and applied it to the case I asked about?
Have I correctly generalized your reasoning and applied it to the case I asked about?
Yeah, kind of.
However, your P1 statement already implies the most important parts of K1 and K2; as just by inserting the adjective “hundred-sided” into P1 loads it with this knowledge. Beyond that the K1 and K2 stuff is cumbersome background detail that most human brains will have (but of course also necessary for understanding ‘dice’).
By including “hundred-sided’ in the analogy, you are importing a ton of implicit confidence in the true probability distribution in question. Your ‘analogy’ assumes you already know the answer with complete confidence.
That analogy would map to an argument (for AI risk) written out in labyrinthine explicit well grounded detail, probably to the point of encoding complete tested/proven working copies of the entire range of future AGI designs.
In other words, your probability estimate in the dice analogy is only high confidence because of the confidence in understanding how dice work, and that the object in question actually is a hundred sided die.
We don’t have AGI yet, so we can’t understand them in the complete engineering sense that we understand dice. Moreover, stuart above claimed we don’t even understand how AGI will be built.
However, your P1 statement already implies the most important parts of K1 and K2; as just by inserting the adjective “hundred-sided” into P1 loads it with this knowledge.
I disagree.
For example, I can confirm that something is a hundred-sided die by the expedient of counting its sides. But if a known conman bets me $1000 that P1 is false, I will want to do more than count the sides of the die before I take that bet. (For example, I will want to roll it a few times to ensure it’s not loaded.) That suggests that there are important facts in K2 other than the definition of a hundred-sided die (e.g., whether the die is fair, whether the speaker is a known conman, etc.) that factor into my judgment of P1.
In other words, your probability estimate in the dice analogy is only high confidence because of the confidence in understanding how dice work, and that the object in question actually is a hundred sided die.
And a bunch of other things, as above. Which is why I mentioned K1 and K2 in the first place.
...your probability estimate in the dice analogy is only high confidence …
Wait, what?
First, nowhere in here have I made a probability estimate. I’ve made a prediction about what will happen on the next roll of this die. You are inferring that i made that prediction on the basis of a probability estimate, and you admittedly have good reasons to infer that.
Second… are you now saying that I can be confident in P1? Because when I asked you that in the first place you answered no. I suspect I’ve misunderstood you somewhere.
First, nowhere in here have I made a probability estimate. I’ve made a prediction about what will happen on the next roll of this die. You are inferring that i made that prediction on the basis of a probability estimate, and you admittedly have good reasons to infer that.
Yes. I have explained (in some amount of detail) what I mean by confidence, such that it is distinct from probability, as relates to prediction.
And yes, as a human you are in fact constrained (in practice) to making predictions based on internal probability estimates (based on my understanding of neuroscience).
Confidence, like probability, is not binary.
You can have fairly high confidence in the implied probability of P1 given K1 and K2, and likewise little confidence in a probability estimate of P1 in the case of a die of unknown dimension—this should be straightforward.
Second… are you now saying that I can be confident in P1? Because when I asked you that in the first place you answered no. I suspect I’ve misunderstood you somewhere.
Yes, and the mistake is on my part: wow that first comment was a partial brainfart. I was agreeing with you, and meant to say yes but … I’ll edit in a comment to that effect.
OK, I think I understand you now. Thanks.
To answer your question as I understand it: it does not make sense for me to be confident that the result of some unspecified operation performed on some unknown object will be 12.
It does make sense to be confident that it won’t be 12. (I might, of course, be confident and wrong. It’s just unlikely.)
I consider the latter a more apposite analogy for the argument you challenge here. Being confident that an unspecified process (e.g., AGI) won’t value paperclips makes more sense than being confident that it will, in the same way that being confident that it won’t return “12” makes more sense than being confident than it will.
Perhaps we are using a different notion of ‘confidence’. The uses of that term that I am familiar with have a separate specific meaning apart from probability. Confidence to me implies meta-level knowledge about the potential error in one’s probability estimate, intervals, or something of that nature.
So in your analogy, I can’t be confident about any properties of an unspecified process. I can of course assign a low probability estimate to the proposition that this unspecified process won’t value paperclips purely from priors, but that will not be a high confidence estimate. The ‘process’ could be a paperclip factory for all I know.
If you then map this analogy back to the original SIAI frame, I assume that the ‘die’ maps loosely to AGI development, and the 12 is AGI’s values being human values. And then no, it does not make sense to be confident that the roll won’t be 12, given that we supposedly don’t know what kind of die it is. It very well could be a ‘die’ with only 12s.
Priors are really just evidence you have already accumulated, so in reality one is never in a state of complete ignorance.
For example, I know that AGI will be created by humans (high confidence), humans create things which they value or things which help fulfill their values, and that humans for reasons both anthropocentric and economic are more likely to thus create AGI that shares human values.
I don’t think it’s useful to talk about whether we can have confidence in statements about the outcome of an AGI process while we still disagree about whether we can have confidence in statements about the outcome of rolling a hundred-sided die.
So, OK.
Given two statements, P1 (“my next roll of this hundred-sided die will not be 12”) and P2 (“my next roll of this hundred-sided die will be 12″), I consider it sensible to be confident of P1 but not P2, you don’t consider it sensible to be confident of either statement. This may be because of different uses of the term “confident”, or it might be something more substantive.
Would you agree that there’s a 99% chance of P1 being true, and a 99% chance of P2 being false, given a fair die toss?
If so, can you say more about the class of statements like P1, where I estimate a 99% chance of it being true but it’s inappropriate for me to be confident in it?
Ok. I’ll attempt to illustrate confidence vs probability as I understand it.
Lets start with your example. Starting with the certain knowledge that there is an object which is a 100-sided die, you are correct to infer that P(roll(D) != 12 | D=100) = 99⁄100.
Further, you are correct (in this example) to have complete confidence in that estimate.
We can think of confidence as how closely one’s probability estimate approaches the true frequency if we iterated the experiment to infinity, or alternatively summed across the multiverse.
If we roll that die an infinite number of times, (or summed across the multiverse), the observed frequency of (roll(D) != 12 | D=100) is more or less guaranteed to converge to the probability estimate of 99%. This is thus a high confidence estimate.
But this high confidence is conditional on your knowledge (and really, your confidence in this knowledge) that there is a die, and the die has 100 sides, and the die is fair, and so on.
Now if you remove all this knowledge, the situation changes dramatically.
Imagine that you know only that there is a die, but not how many sides the die has. You could still make some sort of an estimate. You could guesstimate using your brain’s internal heuristics, which wouldn’t be so terrible, or you could research dice and make a more informed prior about the unknown number of sides.
From that you might make an informed estimate of 98.7% for P(roll(D) != 12 | D = ???), but this will be a low confidence estimate. In fact once we roll this unknown die a large number of times, we can be fairly certain that the observed frequency will not converge to 98.7%.
So that is the difference between probability and confidence, at least in intuitive english. There are several more concrete algorithmic schemes for dealing with confidence or epistemic uncertainty, but that’s the general idea. (We could even take it up a whole new meta level by considering probability distributions of probability functions (one for each possible die type), and this would be a more accurate model, but it is of course no more confident)
OK.
So, if I understand you correctly, and returning to my original question… given the statement “my next roll of this hundred-sided die will not be 12” (P1), and a bunch of background knowledge (K1) about how hundred-sided dice typically work, and a bunch of background knowledge (K2) relevant to how likely it is that my next roll of this hundred-dided die will be typical (for example, how likely this die is to be loaded), I could in principle be confident in P1.
However, since K2 is not complete, I cannot in practice be confident in P1.
The best I can do is make an informed estimate of the likelihood of P1, but this will be a low confidence estimate.
Have I correctly generalized your reasoning and applied it to the case I asked about?
Yeah, kind of.
However, your P1 statement already implies the most important parts of K1 and K2; as just by inserting the adjective “hundred-sided” into P1 loads it with this knowledge. Beyond that the K1 and K2 stuff is cumbersome background detail that most human brains will have (but of course also necessary for understanding ‘dice’).
By including “hundred-sided’ in the analogy, you are importing a ton of implicit confidence in the true probability distribution in question. Your ‘analogy’ assumes you already know the answer with complete confidence.
That analogy would map to an argument (for AI risk) written out in labyrinthine explicit well grounded detail, probably to the point of encoding complete tested/proven working copies of the entire range of future AGI designs.
In other words, your probability estimate in the dice analogy is only high confidence because of the confidence in understanding how dice work, and that the object in question actually is a hundred sided die.
We don’t have AGI yet, so we can’t understand them in the complete engineering sense that we understand dice. Moreover, stuart above claimed we don’t even understand how AGI will be built.
I disagree.
For example, I can confirm that something is a hundred-sided die by the expedient of counting its sides.
But if a known conman bets me $1000 that P1 is false, I will want to do more than count the sides of the die before I take that bet. (For example, I will want to roll it a few times to ensure it’s not loaded.)
That suggests that there are important facts in K2 other than the definition of a hundred-sided die (e.g., whether the die is fair, whether the speaker is a known conman, etc.) that factor into my judgment of P1.
And a bunch of other things, as above. Which is why I mentioned K1 and K2 in the first place.
Wait, what?
First, nowhere in here have I made a probability estimate. I’ve made a prediction about what will happen on the next roll of this die. You are inferring that i made that prediction on the basis of a probability estimate, and you admittedly have good reasons to infer that.
Second… are you now saying that I can be confident in P1? Because when I asked you that in the first place you answered no. I suspect I’ve misunderstood you somewhere.
Yes. I have explained (in some amount of detail) what I mean by confidence, such that it is distinct from probability, as relates to prediction.
And yes, as a human you are in fact constrained (in practice) to making predictions based on internal probability estimates (based on my understanding of neuroscience).
Confidence, like probability, is not binary.
You can have fairly high confidence in the implied probability of P1 given K1 and K2, and likewise little confidence in a probability estimate of P1 in the case of a die of unknown dimension—this should be straightforward.
Yes, and the mistake is on my part: wow that first comment was a partial brainfart. I was agreeing with you, and meant to say yes but … I’ll edit in a comment to that effect.
Ah!
I feel much better now.
I should go through this discussion again and re-evaluate what I think you’re saying based on that clarification before I try to reply .