Like the word "rational" is sometimes used instead of "optimal" or "good", words "utility function" are probably used to mean "good" or "our values" or something like that.
Therefore, analogically to the suggestion of only using the word 'rational' when talking about cognitive algorithms and thinking techniques, we should only use the words 'utility function' when talking about computer programs. When speaking about humans, "good / better / the best" probably expresses what we need well enough.
It seems worth reflecting on the fact that the point of the foundational LW material discussing utility functions was to make people better at reasoning about AI behavior and not about human behavior.
I think part of Eliezer's point was also to introduce decision theory as an ideal for human rationality. (See http://lesswrong.com/lw/my/the_allais_paradox/ for example.) Without talking about utility functions, we can't talk about expected utility maximization, so we can't define what it means to be ideally rational in the instrumental sense (and we also can't justify Bayesian epistemology based on decision theory).
So I agree with the problem stated here, but "let's stop talking about utility functions" can't be the right solution. Instead we need to emphasize more that having the wrong values is often worse than being irrational, so until we know how to obtain or derive utility functions that aren't wrong, we shouldn't try to act as if we have utility functions.
It's more than a metaphor; a utility function is the structure any consistent preference ordering that respects probability must have. It may or may not be a useful conceptual tool for practical human ethical reasoning, but "just a metaphor" is too strong a judgment.
a utility function is the structure any consistent preference ordering that respects probability must have.
This is the sort of thing I mean when I say that people take utility functions too seriously. I think the von Neumann-Morgenstern theorem is much weaker than it initially appears. It's full of hidden assumptions that are constantly violated in practice, e.g. that an agent can know probabilities to arbitrary precision, can know utilities to arbitrary precision, can compute utilities in time to make decisions, makes a single plan at the beginning of time about how they'll behave for eternity (or else you need to take into account factors like how the agent should behave in order to acquire more information in the future and that just isn't modeled by the setup of vNM at all), etc.
The biggest problematic unstated assumption behind applying VNM-rationality to humans, I think, is the assumption that we're actually trying to maximize something.
To elaborate, the VNM theorem defines preferences by the axiom of completeness, which states that for any two lotteries A and B, one of the following holds: A is preferred to B, B is preferred to A, or one is indifferent between them.
So basically, a “preference” as defined by the axioms is a function that (given the state of the agent and the state of the world in general) outputs an agent’s decision between two or more choices. Now suppose that the agent’s preferences violate the Von Neumann-Morgenstern axioms, so that in one situation it prefers to make a deal that causes it to end up with an apple rather than an orange, and in another situation it prefers to make a deal that causes it to end up with an orange rather than an apple. Is that an argument against having circular preferences?
By itself, it's not. It simply establishes that the function that outputs the agent’s actions behaves differently in different situations. Now the normal way to establish that this is bad is to assume that all choices are between monetar...
Essentially every post would have been better if it had included some additional thing. Based on various recent comments I was under the impression that people want more posts in Discussion so I've been experimenting with that, and I'm keeping the burden of quality deliberately low so that I'll post at all.
"a utility function is the structure any consistent preference ordering that respects probability must have."
Yes, but humans still don't have one. It's not even clear they can make themselves have one.
I don't think I have much to add to this discussion that you guys aren't already going to have covered, except to note that Qiaochu definitely understands what a utility function is and all of the standard arguments for why they "should" exist, so his beliefs are not a function of not having heard these arguments (just noting this because this thread and some of the siblings seem to be trying to explain basic concepts to Qiaochu that I'm confident he already knows, and I'm hoping that pointing this out will speed up the discussion).
There's a problem with discussing ethics in terms of UFs, which is that no attempt is made to separate morally relevant preferences from others. Which is a wider issue than UFs. There may be some further issue with UFs.
The problem partly is in utility functions being used as both: a) as a metaphor and b) as an exact mathematical tool with exact properties.
a) can be used to elucidate terminal values in a discussion or to structure and focus a discussion away from vague concepts in ethics. But as a metaphor it cannot be used to derive anything with strength. b) on the other hand can strictly only be used where the preconditions are satisfied. Mixing a) and b) means committing the mathematical fallacy: Believing that to have formulated something in an exact way solves the issue in practice.
Yes! Thank you for saying this clearly and distinctly.
Real-world objects are never perfect spheres or other mathematical entities. However, math is quite useful for modeling them. But the way we decide which math is the right math to use to model a particular sort of object is through repeated experiment. And sometimes the trajectory through spacetime of a given object (say, a gold coin of a certain mass) is best modeled by certain math (e.g. ballistics) and sometimes by other very different math (e.g. economics).
Utility functions belong to the math, not the territory.
It seems worth reflecting on the fact that the point of the foundational LW material discussing utility functions was to make people better at reasoning about AI behavior and not about human behavior.
For value extrapolation problem, you need to consider both what an AI could do with a goal (how to use it, what kind of thing it is), and which goal represents humane values (how to define it).
I still think there's too much confusion between ethics-for-AI and ethics-for-humans discussions here. There's no particular reason that a conceptual apparatus suited for the former discussion should also be suited for the latter discussion.
For practical purposes I agree that it does not help a lot to talk about utility functions. As the We Don't Have a Utility Function article points out, we simply do not know our utility functions but only vague terminal values. However, as you pointed out yourself that does not mean that we do not "have" a utility function at all.
The soft (and hard) failure seems to be a tempting but unnecessary case of pseudo-rationalization. Still, the concept of an agent "having" (maybe in the sense of "acting in a complex way towards optimizing...
On the one hand, you are correct regarding philosophy for humans: we do ethics and meta-ethics to reduce our uncertainty about our utility functions, not as a kind of game-tree planning based on already knowing those functions.
On the other hand, the Von-Neumann-Morgenstern Theorem says blah blah blah blah.
On the third hand, if you have a mathematical structure we can use to make no-Dutch-book decisions that better models the kinds of uncertainty we deal with as embodied human beings in real life, I'm all ears.
I don't think Dutch book arguments matter in practice. An easy way to avoid being Dutch booked is to refuse bets being offered to you by people you don't trust.
Can you give some specific examples of people misusing utility functions? Or if you don't want to point fingers, can you construct examples similar to those you've seen people use?
To the extent that we care about causing people to become better at reasoning about ethics, it seems like we ought to be able to do better than this.
What would you propose as an alternative?
The biggest problematic unstated assumption behind applying VNM-rationality to humans, I think, is the assumption that we're actually trying to maximize something.
To elaborate, the VNM theorem defines preferences by the axiom of completeness, which states that for any two lotteries A and B, one of the following holds: A is preferred to B, B is preferred to A, or one is indifferent between them.
So basically, a “preference” as defined by the axioms is a function that (given the state of the agent and the state of the world in general) outputs an agent’s decision between two or more choices. Now suppose that the agent’s preferences violate the Von Neumann-Morgenstern axioms, so that in one situation it prefers to make a deal that causes it to end up with an apple rather than an orange, and in another situation it prefers to make a deal that causes it to end up with an orange rather than an apple. Is that an argument against having circular preferences?
By itself, it's not. It simply establishes that the function that outputs the agent’s actions behaves differently in different situations. Now the normal way to establish that this is bad is to assume that all choices are between monetary payouts, and that an agent with inconsistent preferences can be Dutch Booked and made to lose money. An alternative way, which doesn't require us to assume that all the choices are between monetary payouts, is to construct a series of trades between resources that leaves us with less resources than when we started.
Stated that way, this sounds kinda bad. But then there are things that kind of fit that description, but which we would intuitively think of as good. For instance, some time back I asked:
Suppose someone has a preference to have sex each evening, and is in a relationship with someone what a similar level of sexual desire. So each evening they get into bed, undress, make love, get dressed again, get out of bed. Repeat the next evening.
How is this different from having exploitable circular preferences? After all, the people involved clearly have cycles in their preferences - first they prefer getting undressed to not having sex, after which they prefer getting dressed to having (more) sex. And they're "clearly" being the victims of a Dutch Book, too - they keep repeating this set of trades every evening, and losing lots of time because of that.
In response, I was told that
The circular preferences that go against the axioms of utility theory, and which are Dutch book exploitable, are not of the kind "I prefer A to B at time t1 and B to A at time t2", like the ones of your example. They are more like "I prefer A to B and B to C and C to A, all at the same time".
The couple, if they had to pay a third party a cent to get undressed and then a cent to get dressed, would probably do it and consider it worth it---they end up two cents short but having had an enjoyable experience. Nothing irrational about that. To someone with the other "bad" kind of circular preferences, we can offer a sequence of trades (first A for B and a cent, then C for A and a cent, then B for C and a cent) after which they end up three cents short but otherwise exactly as they started (they didn't actually obtain enjoyable experiences, they made all the trades before anything happened). It is difficult to consider this rational.
But then I asked that, if we accept this, then what real-life situation does count as an actual circular preference in the VNM sense, given that just about every potential circularity that I can think of is the kind "I prefer A to B at time t1 and B to A at time t2"? And I didn't get very satisfactory replies.
Intuitively, there are a lot of real-life situations that feel kind of like losing out due to inconsistent preferences, like someone who wants to get into a relationship when he's single and then wants to be single when he gets into a relationship, but there our actual problem is that the person spends a lot of time being unhappy, rather than with the fact that he makes different choices in different situations. Whereas with the couple, we think that's fine because they get enjoyment from the "trades".
The general problem that I'm trying to get at is that in order to hold up VNM rationality as a normative standard, we would need to have a meta-preference: a preference over preferences, stating that it would be better to have preferences that lead to some particular outcomes. The standard Dutch Book example kind of smuggles in that assumption by the way that it talks about money, and thus makes us think that we are in a situation where we are only trying to maximize money and care about nothing else. And if you really are trying to only maximize a single concrete variable or resource and care about nothing else, then you really should try to make sure that your choices follow the VNM axioms. If you run a betting office, then do make sure that nobody can Dutch Book you.
But we don't have such a clear normative standard for life in general. It would be reasonable to try to construct an argument for why the couple having sex were rational but the person who kept vacillating about being in a relationship was irrational by suggesting that the couple got happiness whereas the other person was unhappy... but we also care about other things than just happiness (or pleasure) and thus aren't optimizing just for pleasure either. And unless you're a hedonistic utilitarian, you're unlikely to say that we should optimize only for pleasure either.
So basically, if you want to say that people should be VNM-rational, then you need to have some specific set of values or goals that you think people should strive towards. If you don't have that, then VNM-rationality is basically irrelevant aside for the small set of special cases where people really do have a clear explicit goal that's valued above other things.
Now suppose that the agent’s preferences violate the Von Neumann-Morgenstern axioms, so that in one situation it prefers to make a deal that causes it to end up with an apple rather than an orange, and in another situation it prefers to make a deal that causes it to end up with an orange rather than an apple. Is that an argument against having circular preferences?
I'm not sure I follow in what sense this is a violation of the vNM axioms. A vNM agent has preferences over world-histories; in general one can't isolate the effect of having an apple vs. having an orange without looking at how that affects the entire future history of the world.
I think we should stop talking about utility functions.
In the context of ethics for humans, anyway. In practice I find utility functions to be, at best, an occasionally useful metaphor for discussions about ethics but, at worst, an idea that some people start taking too seriously and which actively makes them worse at reasoning about ethics. To the extent that we care about causing people to become better at reasoning about ethics, it seems like we ought to be able to do better than this.
The funny part is that the failure mode I worry the most about is already an entrenched part of the Sequences: it's fake utility functions. The soft failure is people who think they know what their utility function is and say bizarre things about what this implies that they, or perhaps all people, ought to do. The hard failure is people who think they know what their utility function is and then do bizarre things. I hope the hard failure is not very common.
It seems worth reflecting on the fact that the point of the foundational LW material discussing utility functions was to make people better at reasoning about AI behavior and not about human behavior.