Applying dutch book arguments to real life situations always goes way behind deduction and definitions, yes.
lets say “there is a need to assign probabilities to events, no probability can be less than 0 or more than 1 and probabilities of mutually exclusive events should add”.
A need? Are you talking about morality now?
Why are we saying this? You now speak of probabilities of events. Previously we were discussing epistemology which is about ideas. I object to assigning probabilities to the truth of ideas. Assigning them to events is OK when
1) the laws of physics are indeterministic (never, as far as we know)
2) we have incomplete information and want to make a prediction that would be deterministic except that we have to put several possibilities in some places, which leads to several possible answers. and probability is a reasonable way to organize thoughts about that.
So what?
Can you give an example of what you mean by “moral knowledge”?
Murder is immoral.
Being closed minded makes ones life worse because it sabotages improvement.
Can you give an example of what you mean by “moral knowledge”?
Murder is immoral.
Are you saying Popper would evaluate “Murder is immoral.” in the same way as “Atoms are made up of electrons and a nucleus.”? How would you test this? What would you consider a proof of it?
I prefer to leave such statements undefined, since people disagree too much on what ‘morality’ means. I am a moral realist to some, a relativist to others, and an error theorist to other others. I could prove the statement for many common non-confused definitions, though not for, for example, people who say ‘morality’ is synomnymous to ‘that which is commanded by God’, which is based on confusion but at least everyone can agree on when it is or isn’t true and not for error theorists, as both groups’ definitions make the sentence false.
Being closed minded makes ones life worse because it sabotages improvement.
In theory I could prove this sentence, but in practice I could not do this clearly, especially over the internet. It would probably be much easier for you to read the sequences, which get to this toward the end, but, depending on your answers to some of my questions, there may be an easier way to explain this.
Are you saying Popper would evaluate “Murder is immoral.” in the same way as “Atoms are made up of electrons and a nucleus.”?
Yes. One epistemology. All types of knowledge. Unified!
How would you test this?
You would not.
What would you consider a proof of it?
We don’t accept proofs of anything, we are fallibilists. We consider mathematical proofs to be good arguments though. I don’t really want to argue about those (unless you’re terribly interested. btw this is covered in the math chapter of The Fabric of Reality by David Deutsch). But the point is we don’t accept anything as providing certainty or even probableness. In our terminology, nothing provides justification.
What we do instead is explain our ideas, and to criticize mistakes, and in this way to improve our ideas. This, btw, creates knowledge in the same way as evolution (replication of ideas, with variation, and selection by criticism). That’s not a metaphor or analogy by literally true.
I prefer to leave such statements undefined, since people disagree too much on what ‘morality’ means.
Wouldn’t it be nice if you had an epistemology that helped you deal with all kinds of knowledge, so you didn’t have to simply give up on applying reason to important issues like what is a good life, and what are good values?
This, btw, creates knowledge in the same way as evolution (replication of ideas, with variation, and selection by criticism). That’s not a metaphor or analogy by literally true.
Well, biological evolution is a much smaller part of conceptspace than “replication, variation, selection” and now I’m realizing that you probably haven’t read A Human’s Guide to Words which is extremely important and interesting and, while you’ll know much of it, has things that are unique and original and that you’ll learn a lot from. Please read it.
I prefer to leave such statements undefined, since people disagree too much on what ‘morality’ means.
Wouldn’t it be nice if you had an epistemology that helped you deal with all kinds of knowledge, so you didn’t have to simply give up on applying reason to important issues like what is a good life, and what are good values?
I do apply reason to those things, I just don’t use the words ‘morality’ in my reasoning process because too many people get confused. It is only a word after all.
On a side note, I am staring to like what I hear of Popper. It seems to embody an understanding of the brain and a bunch of useful advice for it. I think I disagree with some things, but on grounds that seems like the sort of thing that is accepted as motivation for the theory self-modify. Does that make sense? Anyways, it’s not Popper’s fault that there are a set of theorems that in principle remove the need for other types of thought and in practice cause big changes in the way we understand and evaluate the heuristics that are necessary because the brain is fallible and computationally limited.
Wei Dai likes thinking about how to deal with questions outside of Bayesianism’s current domain of applicability, so he might be interested in this.
lets say “there is a need to assign probabilities to events, no probability can be less than 0 or more than 1 and probabilities of mutually exclusive events should add”.
A need? Are you talking about morality now?
Interpret this as a need in order to achieve some specified goal in order to keep this part the debate out of morality. A paperclip maximizer, for example would obviously need to not pay 200 paperclips for a lottery with a maximum payout of 100 paperclips in order to achieve its goals. Furthermore, this applies to any consequentialist set of preferences.
Why are we saying this? You now speak of probabilities of events.
So you assume morality (the “specified goal”). That makes your theory amoral.
Well there’s a bit more than this, but it’s not important right now. One can work toward any goal just by assuming it as a goal.
Why is there a need to assign probabilities to theories? Popperian epistemology functions without doing that.
Because of the Dutch book arguments. The probabilities can be inferred from the choices. I’m not sure if the agent’s probability distribution can be fully determined from a finite set of wagers, but it can be definitely be inferred to an arbitrary degree of precision by adding enough wagers.
Can you give an example of how you use a Dutch book argument on a non-gambling topic? For example, if I’m considering issues like whether to go swimming today, and what nickname to call my friend, and I don’t assign probabilities like “80% sure that calling her Kate is the best option”, how do I get Dutch Booked?
First you hypothetically ask what would happen if you were asked to make bets on whether calling her Kate would result in world X (with utility U(X)). Do this for all choices and all possible worlds. This gives you probabilities and utilities. You then take a weighted average, as per the VNM theorem.
You don’t get to decide utilities so much as you have to figure out what they are. You already have a utility function, and you do your best to describe it . How do you weight the things you value relative to each other?
This takes observation, because what we think we value often turns out not to be a good description of our feelings and behavior.
By criticizing them. And conjecturing improvements which meet the challenges of the criticism. It is the same method as for improving all other knowledge.
In outline it is pretty simple. You may wonder things like what would be a good moral criticism. To that I would say: there’s many books full of examples, why dismiss all that? There is no one true way of arguing. Normal arguments are ok, I do not reject them all out of hand but try to meet their challenges. Even the ones with some kind of mistake (most of them), you can often find some substantive point which can be rescued. It’s important to engage with the best versions of theories you can think of.
BTW once upon a time I was vaguely socialist. Now I’m a (classical) liberal. People do change their fundamental moral values for the better in real life. I attended a speech by a former Muslim terrorist who is now a pro-Western Christian (walid shoebat).
I’ve changed my social values plenty of times, because I decided different policies better served my terminal values. If you wanted to convince me to support looser gun control, for instance, I would be amenable to that because my position on gun control is simply an avenue for satisfying my core values, which might better be satisfied in a different way.
If you tried to convince me to support increased human suffering as an end goal, I would not be amenable to that, unless it turns out I have some value I regard as even more important that would be served by it.
This is what Popper called the Myth of the Framework and refuted in his essay by that name. It’s just not true that everyone is totally set in their ways and extremely closed minded, as you suggest. People with different frameworks learn from each other.
One example is children learn. They are not born sharing their parents framework.
You probably think that frameworks are genetic, so they are. Dealing with that would take a lengthy discussion. Are you interested in this stuff? Would you read a book about it? Do you want to take it seriously?
I’m somewhat skeptical b/c e.g. you gave no reply to some of what I said.
I think a lot of the reason people don’t learn other frameworks, in practice, is merely that they choose not to. They think it sounds stupid (before they understand what it’s actually saying) and decide not to try.
When did I suggest that everyone is set in their ways and extremely closed minded? As I already pointed out, I’ve changed my own social values plenty of times. Our social frameworks are extremely plastic, because there are many possible ways to serve our terminal values.
I have responded to moral arguments with regards to more things than I could reasonably list here (economics, legal codes, etc.) I have done so because I was convinced that alternatives to my preexisting social framework better served my values.
Valuing strict gun control, to pick an example, is not genetically coded for. A person might have various inborn tendencies which will affect how they’re likely to feel about gun control; they might have innate predispositions towards authoritarianism or libertarianism, for instance, that will affect how they form their opinion. A person who valued freedom highly enough might support little or no gun control even if they were convinced that it would result in a greater loss of life. You would have a hard time finding anyone who valued freedom so much that they would support looser gun control if they were convinced it would destroy 90% of the world population, which gives you a bit of information about how they weight their preferences.
If you wanted to convince me to support more human suffering instead of more human happiness, you would have to appeal to something else I value even more that would be served by this. If you could argue that my preference for happiness is arbitrary, that preference for suffering is more natural, even if you could demonstrate that the moral goodness of human suffering is intrinsically inscribed on the fabric of the universe, why should I care? To make me want to make humans unhappy, you’d have to convince me there’s something else I want enough to make humans unhappy for its sake.
I also don’t feel I’m being properly understood here; I’m sorry if I’m not following up on everything, but I’m trying to focus on the things that I think meaningfully further the conversation, and I think some of your arguments are based on misapprehensions about where I’m coming from. You’ve already made it clear that you feel the same, but you can take it as assured that I’m both trying to understand you and make myself understood.
When did I suggest that everyone is set in their ways and extremely closed minded?
You suggested it about a category of ideas which you called “core values”.
If you wanted to convince me to support more human suffering instead of more human happiness, you would have to appeal to something else I value even more
You are saying that you are not open to new values which contradict your core values. Ultimately you might replace all but the one that is the most core, but never that one.
You are saying that you are not open to new values which contradict your core values. Ultimately you might replace all but the one that is the most core, but never that one.
That’s more or less correct. To quote one of Eliezer’s works of ridiculous fanfiction, “A moral system has room for only one absolute commandment; if two unbreakable rules collide, one has to give way.”
If circumstances force my various priorities into conflict, some must give way to others, and if I value one thing more than anything else, I must be willing to sacrifice anything else for it. That doesn’t necessarily make it my only terminal value; I might have major parts of my social framework which ultimately reduce to service to another value, and they’d have to bend if they ever came into conflict with a more heavily weighted value.
Well in the first half, you get Dutch booked in the usual way. It’s not necessarily actually happening, but there still must be probabilities that you would use if it were. In the second half, if you don’t follow the procedure (or an equivalent one) you violate at least one VNM axiom.
If you violate axiom 1, there are situations in which you don’t have a preferred choice—not as is “both are equally good/bad” but as in your decision process does not give an answer or gives more than one answer. I don’t think I’d call this a decision process.
If you violate axiom 2, there are outcomes L, M and N such that you’d want to switch from L to M and then from M to N, but you would not want to switch from L to N.
Axiom 3 is unimportant and is just there to simplify the math.
For axiom 4, imagine a situation where a statement with unknown truth-value, X, determines whether you get to choose between two outcomes, L and M, with L < M, or have no choice in accepting a third outcome, N. If you violate the axiom, there is a situation like this where, if you were asked for your choice before you know X (it will be ignored if X is false), you would pick L, even though L < M.
Do any of these situations describe your preferences?
And I’m still curious how the utilities are decided. By whim?
If your decision process is not equivalent to one that uses the previously described procedure, there are situations where something like one of the following will happen.
I ask you if you want chocolate or vanilla ice cream and you don’t decide. Not just you don’t care which one you get or you would prefer not to have ice cream, but you don’t output anything and see nothing wrong with that.
You prefer chocolate to vanilla ice cream, so you would willingly pay 1c to have the vanilla ice cream that you have been promised upgraded to chocolate. You also happen to prefer strawberry to chocolate, so you are willing to pay 1c to exchange a promise of a chocolate ice cream for a promise of a strawberry ice cream. Furthermore, it turn out you prefer vanilla to strawberry, so whenever you are offered a strawberry ice cream, you gladly pay a single cent to change that to an offer of vanilla, ad infinitum.
N/A
You like chocolate ice cream more than vanilla ice cream. Nobody knows if you’ll get ice cream today, but you are asked for your choice just in case, so you pick vanilla.
Let’s consider (2). Suppose someone was in the process of getting Dutch Booked like this. It would not go on ad infinitum. They would quickly learn better. Right? So even if this happened, I think it would not be a big deal.
Let’s say they did learn better. How would they do this—changing their utility function? Someone with a utility function like this really does prefer B+1c to A, C+1c to B, and A+1c to C. Even if they did change their utility function, the new one would either have a new hole or it would obey the results of the VNM-theorem.
So Bayes teaches: do not disobey the laws of logic and math.
Still wondering where the assigning probabilities to truths of theories is.
OK. So what? There’s more to life than that. That’s so terribly narrow. I mean, that part of what you’re saying is right as far as it goes, but it doesn’t go all that far. And when you start trying to apply it to harder cases—what happens? Do you have some Bayesian argument about who to vote for for president? Which convinced millions of people? Or should have convinced them, and really answers the questions much better than other arguments?
Still wondering where the assigning probabilities to truths of theories is.
Well the Dutch books make it so you have to pick some probabilities. Actually getting the right prior is incomplete, though Solomonoff induction is most of the way there.
OK. So what? There’s more to life than that. That’s so terribly narrow. I mean, that part of what you’re saying is right as far as it goes, but it doesn’t go all that far.
Where else are you hoping to go?
And when you start trying to apply it to harder cases—what happens? Do you have some Bayesian argument about who to vote for for president? Which convinced millions of people? Or should have convinced them, and really answers the questions much better than other arguments?
In principle, yes. There’s actually a computer program called AIXItl that does it. In practice I use approximations to it. It probably could be done to a very higher degree of certainty. There are a lot of issues and a lot of relevant data.
Well the Dutch books make it so you have to pick some probabilities.
Can you give an example? Use the ice cream flavors. What probabilities do you have to pick to buy ice cream without being dutch booked?
Where else are you hoping to go?
Explanatory knowledge. Understanding the world. Philosophical knowledge. Moral knowledge. Non-scientific, non-emprical knowledge. Beyond prediction and observation.
In principle, yes.
How do you know if your approximations are OK to make or ruin things? How do you work out what kinds of approximations are and aren’t safe to make?
The way I would do that is by understanding the explanation of why something is supposed to work. In that way, I can evaluate proposed changes to see whether they mess up the main point or not.
Endo, I think you are making things more confusing by combining issues of Bayesianism with issues of utility. It might help to keep them more separate or to be clear when one is talking about one, the other, or some hybrid.
I use the term Bayesianism to include utility because (a) they are connected and (b) a philosophy of probabilities as abstract mathematical constructs with no applications doesn’t seem complete; it needs an explanation of why those specific objects are studied. How do you think that any of this caused or could cause confusion?
Well, it empirically seems to be causing confusion. See curi’s remarks about the ice cream example. Also, one doesn’t need Bayesianism to include utility and that isn’t standard (although it is true that they do go very well together).
Let’s consider (2). Suppose someone was in the process of getting Dutch Booked like this. It would not go on ad infinitum. They would quickly learn better. Right? So even if this happened, I think it would not be a big deal.
So the argument is now not that that suboptimal issues don’t exist but that they aren’t a big deal? Are you aware that the primary reason that this involves small amounts of ice cream is for convenience of the example? There’s no reason these couldn’t happen with far more serious issues (such as what medicine to use).
I know. I thought it was strange that you said “ad infinitum” when it would not go on forever. And that you presented this as dire but made your example non-dire.
But OK. You say we must consider probabilities, or this will happen. Well, suppose that if I do something it will happen. I could notice that, criticize it, and thus avoid it.
How can I notice? I imagine you will say that involves probabilities. But in your ice cream example I don’t see the probabilities. It’s just preferences for different ice creams, and an explanation of how you get a loop.
And what I definitely don’t see is probabilities that various theories are true (as opposed to probabilities about events which are ok).
But OK. You say we must consider probabilities, or this will happen. Well, suppose that if I do something it will happen. I could notice that, criticize it, and thus avoid it.
Yes, but the Bayesian avoids having this step. For any step you can construct a “criticism” that will duplicate what the Bayesian will do. This is connected to a number of issues, including the fact that what constitutes valid criticism in a Popperian framework is far from clear.
But in your ice cream example I don’t see the probabilities. It’s just preferences for different ice creams, and an explanation of how you get a loop.
Ice cream is an analogy. It might not be a great one since it is connected to preferences (which sometimes gets confused with Bayesianism). The analogy isn’t a great one. It might make more sense to just go read Cox’s theorem and translate to yourself what the assumptions mean about an approach.
what constitutes valid criticism in a Popperian framework is far from clear.
Anything which is not itself criticized.
Ice cream is an analogy.
Could you pick any real world example you like, where the probabilities needed to avoid dutch book aren’t obvious, and point them out? To help concretize the idea for me.
Could you pick any real world example you like, where the probabilities needed to avoid dutch book aren’t obvious, and point them out
Well, I’m not sure, in that I’m not convinced that Dutch Booking really does occur much in real life other than in the obvious contexts. But there are a lot of contexts it does occur in. For example, a fair number of complicated stock maneuvers can be thought of essentially as attempts to dutch book other players in the stock market.
Applying dutch book arguments to real life situations always goes way behind deduction and definitions, yes.
A need? Are you talking about morality now?
Why are we saying this? You now speak of probabilities of events. Previously we were discussing epistemology which is about ideas. I object to assigning probabilities to the truth of ideas. Assigning them to events is OK when
1) the laws of physics are indeterministic (never, as far as we know)
2) we have incomplete information and want to make a prediction that would be deterministic except that we have to put several possibilities in some places, which leads to several possible answers. and probability is a reasonable way to organize thoughts about that.
So what?
Murder is immoral.
Being closed minded makes ones life worse because it sabotages improvement.
Are you saying Popper would evaluate “Murder is immoral.” in the same way as “Atoms are made up of electrons and a nucleus.”? How would you test this? What would you consider a proof of it?
I prefer to leave such statements undefined, since people disagree too much on what ‘morality’ means. I am a moral realist to some, a relativist to others, and an error theorist to other others. I could prove the statement for many common non-confused definitions, though not for, for example, people who say ‘morality’ is synomnymous to ‘that which is commanded by God’, which is based on confusion but at least everyone can agree on when it is or isn’t true and not for error theorists, as both groups’ definitions make the sentence false.
In theory I could prove this sentence, but in practice I could not do this clearly, especially over the internet. It would probably be much easier for you to read the sequences, which get to this toward the end, but, depending on your answers to some of my questions, there may be an easier way to explain this.
Yes. One epistemology. All types of knowledge. Unified!
You would not.
We don’t accept proofs of anything, we are fallibilists. We consider mathematical proofs to be good arguments though. I don’t really want to argue about those (unless you’re terribly interested. btw this is covered in the math chapter of The Fabric of Reality by David Deutsch). But the point is we don’t accept anything as providing certainty or even probableness. In our terminology, nothing provides justification.
What we do instead is explain our ideas, and to criticize mistakes, and in this way to improve our ideas. This, btw, creates knowledge in the same way as evolution (replication of ideas, with variation, and selection by criticism). That’s not a metaphor or analogy by literally true.
Wouldn’t it be nice if you had an epistemology that helped you deal with all kinds of knowledge, so you didn’t have to simply give up on applying reason to important issues like what is a good life, and what are good values?
Fine, what would you consider an argument for it?
Eliezer and I probably agree with you.
Well, biological evolution is a much smaller part of conceptspace than “replication, variation, selection” and now I’m realizing that you probably haven’t read A Human’s Guide to Words which is extremely important and interesting and, while you’ll know much of it, has things that are unique and original and that you’ll learn a lot from. Please read it.
I do apply reason to those things, I just don’t use the words ‘morality’ in my reasoning process because too many people get confused. It is only a word after all.
On a side note, I am staring to like what I hear of Popper. It seems to embody an understanding of the brain and a bunch of useful advice for it. I think I disagree with some things, but on grounds that seems like the sort of thing that is accepted as motivation for the theory self-modify. Does that make sense? Anyways, it’s not Popper’s fault that there are a set of theorems that in principle remove the need for other types of thought and in practice cause big changes in the way we understand and evaluate the heuristics that are necessary because the brain is fallible and computationally limited.
Wei Dai likes thinking about how to deal with questions outside of Bayesianism’s current domain of applicability, so he might be interested in this.
Interpret this as a need in order to achieve some specified goal in order to keep this part the debate out of morality. A paperclip maximizer, for example would obviously need to not pay 200 paperclips for a lottery with a maximum payout of 100 paperclips in order to achieve its goals. Furthermore, this applies to any consequentialist set of preferences.
Not sure why I wrote that. Substitute ‘theories’.
So you assume morality (the “specified goal”). That makes your theory amoral.
Why is there a need to assign probabilities to theories? Popperian epistemology functions without doing that.
Well there’s a bit more than this, but it’s not important right now. One can work toward any goal just by assuming it as a goal.
Because of the Dutch book arguments. The probabilities can be inferred from the choices. I’m not sure if the agent’s probability distribution can be fully determined from a finite set of wagers, but it can be definitely be inferred to an arbitrary degree of precision by adding enough wagers.
Can you give an example of how you use a Dutch book argument on a non-gambling topic? For example, if I’m considering issues like whether to go swimming today, and what nickname to call my friend, and I don’t assign probabilities like “80% sure that calling her Kate is the best option”, how do I get Dutch Booked?
First you hypothetically ask what would happen if you were asked to make bets on whether calling her Kate would result in world X (with utility U(X)). Do this for all choices and all possible worlds. This gives you probabilities and utilities. You then take a weighted average, as per the VNM theorem.
How do I get Dutch Booked for not doing that?
And I’m still curious how the utilities are decided. By whim?
You don’t get to decide utilities so much as you have to figure out what they are. You already have a utility function, and you do your best to describe it . How do you weight the things you value relative to each other?
This takes observation, because what we think we value often turns out not to be a good description of our feelings and behavior.
From our genes? And the goal is just to figure out what it is, but not change it for the better?
Can you explain how you would change your fundamental moral values for the better?
By criticizing them. And conjecturing improvements which meet the challenges of the criticism. It is the same method as for improving all other knowledge.
In outline it is pretty simple. You may wonder things like what would be a good moral criticism. To that I would say: there’s many books full of examples, why dismiss all that? There is no one true way of arguing. Normal arguments are ok, I do not reject them all out of hand but try to meet their challenges. Even the ones with some kind of mistake (most of them), you can often find some substantive point which can be rescued. It’s important to engage with the best versions of theories you can think of.
BTW once upon a time I was vaguely socialist. Now I’m a (classical) liberal. People do change their fundamental moral values for the better in real life. I attended a speech by a former Muslim terrorist who is now a pro-Western Christian (walid shoebat).
I’ve changed my social values plenty of times, because I decided different policies better served my terminal values. If you wanted to convince me to support looser gun control, for instance, I would be amenable to that because my position on gun control is simply an avenue for satisfying my core values, which might better be satisfied in a different way.
If you tried to convince me to support increased human suffering as an end goal, I would not be amenable to that, unless it turns out I have some value I regard as even more important that would be served by it.
This is what Popper called the Myth of the Framework and refuted in his essay by that name. It’s just not true that everyone is totally set in their ways and extremely closed minded, as you suggest. People with different frameworks learn from each other.
One example is children learn. They are not born sharing their parents framework.
You probably think that frameworks are genetic, so they are. Dealing with that would take a lengthy discussion. Are you interested in this stuff? Would you read a book about it? Do you want to take it seriously?
I’m somewhat skeptical b/c e.g. you gave no reply to some of what I said.
I think a lot of the reason people don’t learn other frameworks, in practice, is merely that they choose not to. They think it sounds stupid (before they understand what it’s actually saying) and decide not to try.
When did I suggest that everyone is set in their ways and extremely closed minded? As I already pointed out, I’ve changed my own social values plenty of times. Our social frameworks are extremely plastic, because there are many possible ways to serve our terminal values.
I have responded to moral arguments with regards to more things than I could reasonably list here (economics, legal codes, etc.) I have done so because I was convinced that alternatives to my preexisting social framework better served my values.
Valuing strict gun control, to pick an example, is not genetically coded for. A person might have various inborn tendencies which will affect how they’re likely to feel about gun control; they might have innate predispositions towards authoritarianism or libertarianism, for instance, that will affect how they form their opinion. A person who valued freedom highly enough might support little or no gun control even if they were convinced that it would result in a greater loss of life. You would have a hard time finding anyone who valued freedom so much that they would support looser gun control if they were convinced it would destroy 90% of the world population, which gives you a bit of information about how they weight their preferences.
If you wanted to convince me to support more human suffering instead of more human happiness, you would have to appeal to something else I value even more that would be served by this. If you could argue that my preference for happiness is arbitrary, that preference for suffering is more natural, even if you could demonstrate that the moral goodness of human suffering is intrinsically inscribed on the fabric of the universe, why should I care? To make me want to make humans unhappy, you’d have to convince me there’s something else I want enough to make humans unhappy for its sake.
I also don’t feel I’m being properly understood here; I’m sorry if I’m not following up on everything, but I’m trying to focus on the things that I think meaningfully further the conversation, and I think some of your arguments are based on misapprehensions about where I’m coming from. You’ve already made it clear that you feel the same, but you can take it as assured that I’m both trying to understand you and make myself understood.
You suggested it about a category of ideas which you called “core values”.
You are saying that you are not open to new values which contradict your core values. Ultimately you might replace all but the one that is the most core, but never that one.
That’s more or less correct. To quote one of Eliezer’s works of ridiculous fanfiction, “A moral system has room for only one absolute commandment; if two unbreakable rules collide, one has to give way.”
If circumstances force my various priorities into conflict, some must give way to others, and if I value one thing more than anything else, I must be willing to sacrifice anything else for it. That doesn’t necessarily make it my only terminal value; I might have major parts of my social framework which ultimately reduce to service to another value, and they’d have to bend if they ever came into conflict with a more heavily weighted value.
Well in the first half, you get Dutch booked in the usual way. It’s not necessarily actually happening, but there still must be probabilities that you would use if it were. In the second half, if you don’t follow the procedure (or an equivalent one) you violate at least one VNM axiom.
If you violate axiom 1, there are situations in which you don’t have a preferred choice—not as is “both are equally good/bad” but as in your decision process does not give an answer or gives more than one answer. I don’t think I’d call this a decision process.
If you violate axiom 2, there are outcomes L, M and N such that you’d want to switch from L to M and then from M to N, but you would not want to switch from L to N.
Axiom 3 is unimportant and is just there to simplify the math.
For axiom 4, imagine a situation where a statement with unknown truth-value, X, determines whether you get to choose between two outcomes, L and M, with L < M, or have no choice in accepting a third outcome, N. If you violate the axiom, there is a situation like this where, if you were asked for your choice before you know X (it will be ignored if X is false), you would pick L, even though L < M.
Do any of these situations describe your preferences?
I’ll let Desrtopa handle this.
Can you give a concrete example. What happens to me? Is it that I get an outcome which is less ideal than was available?
If your decision process is not equivalent to one that uses the previously described procedure, there are situations where something like one of the following will happen.
I ask you if you want chocolate or vanilla ice cream and you don’t decide. Not just you don’t care which one you get or you would prefer not to have ice cream, but you don’t output anything and see nothing wrong with that.
You prefer chocolate to vanilla ice cream, so you would willingly pay 1c to have the vanilla ice cream that you have been promised upgraded to chocolate. You also happen to prefer strawberry to chocolate, so you are willing to pay 1c to exchange a promise of a chocolate ice cream for a promise of a strawberry ice cream. Furthermore, it turn out you prefer vanilla to strawberry, so whenever you are offered a strawberry ice cream, you gladly pay a single cent to change that to an offer of vanilla, ad infinitum.
N/A
You like chocolate ice cream more than vanilla ice cream. Nobody knows if you’ll get ice cream today, but you are asked for your choice just in case, so you pick vanilla.
Let’s consider (2). Suppose someone was in the process of getting Dutch Booked like this. It would not go on ad infinitum. They would quickly learn better. Right? So even if this happened, I think it would not be a big deal.
Let’s say they did learn better. How would they do this—changing their utility function? Someone with a utility function like this really does prefer B+1c to A, C+1c to B, and A+1c to C. Even if they did change their utility function, the new one would either have a new hole or it would obey the results of the VNM-theorem.
So Bayes teaches: do not disobey the laws of logic and math.
Still wondering where the assigning probabilities to truths of theories is.
OK. So what? There’s more to life than that. That’s so terribly narrow. I mean, that part of what you’re saying is right as far as it goes, but it doesn’t go all that far. And when you start trying to apply it to harder cases—what happens? Do you have some Bayesian argument about who to vote for for president? Which convinced millions of people? Or should have convinced them, and really answers the questions much better than other arguments?
Well the Dutch books make it so you have to pick some probabilities. Actually getting the right prior is incomplete, though Solomonoff induction is most of the way there.
Where else are you hoping to go?
In principle, yes. There’s actually a computer program called AIXItl that does it. In practice I use approximations to it. It probably could be done to a very higher degree of certainty. There are a lot of issues and a lot of relevant data.
Can you give an example? Use the ice cream flavors. What probabilities do you have to pick to buy ice cream without being dutch booked?
Explanatory knowledge. Understanding the world. Philosophical knowledge. Moral knowledge. Non-scientific, non-emprical knowledge. Beyond prediction and observation.
How do you know if your approximations are OK to make or ruin things? How do you work out what kinds of approximations are and aren’t safe to make?
The way I would do that is by understanding the explanation of why something is supposed to work. In that way, I can evaluate proposed changes to see whether they mess up the main point or not.
Endo, I think you are making things more confusing by combining issues of Bayesianism with issues of utility. It might help to keep them more separate or to be clear when one is talking about one, the other, or some hybrid.
I use the term Bayesianism to include utility because (a) they are connected and (b) a philosophy of probabilities as abstract mathematical constructs with no applications doesn’t seem complete; it needs an explanation of why those specific objects are studied. How do you think that any of this caused or could cause confusion?
Well, it empirically seems to be causing confusion. See curi’s remarks about the ice cream example. Also, one doesn’t need Bayesianism to include utility and that isn’t standard (although it is true that they do go very well together).
Yes I see what you mean.
I think it goes a bit beyond this. Utility considerations motivate the choice of definitions. I acknowledge that they are distinct things, though.
The consequences could easily be thousands of lives or more in case of sufficiently important decisions.
So the argument is now not that that suboptimal issues don’t exist but that they aren’t a big deal? Are you aware that the primary reason that this involves small amounts of ice cream is for convenience of the example? There’s no reason these couldn’t happen with far more serious issues (such as what medicine to use).
I know. I thought it was strange that you said “ad infinitum” when it would not go on forever. And that you presented this as dire but made your example non-dire.
But OK. You say we must consider probabilities, or this will happen. Well, suppose that if I do something it will happen. I could notice that, criticize it, and thus avoid it.
How can I notice? I imagine you will say that involves probabilities. But in your ice cream example I don’t see the probabilities. It’s just preferences for different ice creams, and an explanation of how you get a loop.
And what I definitely don’t see is probabilities that various theories are true (as opposed to probabilities about events which are ok).
I didn’t say that (I’m not endoself).
Yes, but the Bayesian avoids having this step. For any step you can construct a “criticism” that will duplicate what the Bayesian will do. This is connected to a number of issues, including the fact that what constitutes valid criticism in a Popperian framework is far from clear.
Ice cream is an analogy. It might not be a great one since it is connected to preferences (which sometimes gets confused with Bayesianism). The analogy isn’t a great one. It might make more sense to just go read Cox’s theorem and translate to yourself what the assumptions mean about an approach.
OK, my bad. So many people. I lose track.
Anything which is not itself criticized.
Could you pick any real world example you like, where the probabilities needed to avoid dutch book aren’t obvious, and point them out? To help concretize the idea for me.
Well, I’m not sure, in that I’m not convinced that Dutch Booking really does occur much in real life other than in the obvious contexts. But there are a lot of contexts it does occur in. For example, a fair number of complicated stock maneuvers can be thought of essentially as attempts to dutch book other players in the stock market.
Koth already had an amusing response to that.
Someone here told me it does. Maybe you can go argue with him for me ;-)
I agree.