240 questions for your utility function
A game comparing intrinsic values can approximate a person’s utility function.
First joke: An economist can answer any question phrased in terms of money.
Second joke: An economist receives a call from his artist friend. The artist is flying in to town, would like to visit the economist, and needs to be picked up at the airport. The economist agrees, and pays a cab to pick up the artist. The artist arrives by cab and demands an explanation for this slight. The economist explains that the opportunity cost of personally performing the favor was higher than the cost of a cab. The artist then tears up a bush in the front lawn of the economist, explaining: “The whole point of being friends is to suffer together.”
Abstractions
Let’s begin with the assumption that human utility is complex. Specifically, the complexity of utility seems to come from the number of intrinsic goods, summarized by M. Zimmerman and quoted by W. Frankena as:
Life, consciousness, and activity; health and strength; pleasures and satisfactions of all or certain kinds; happiness, beatitude, contentment, etc.; truth; knowledge and true opinions of various kinds, understanding and wisdom; beauty, harmony, proportion in objects contemplated; aesthetic experience; morally good dispositions or virtues; mutual affection, love, friendship, cooperation; just distribution of goods and evils; harmony and proportion in ones’ own life; power and experiences of achievement; self-expression; freedom; peace, security; adventure and novelty; and good reputation, honor, esteem, etc.
This list of intrinsic goods makes intuitive sense to me, and I’ll return to it throughout the post. I’m predisposed to think that decisions become agonizing only with conflicting imperatives. My experience from Judgment & Decision Making class taught me that it’s relatively simple to calculate a rational choice for a complex decision like buying a car, provided an extraneous utility function.
I believe that the list of intrinsic values is the key. I believe that a human utility function can be succinctly and robustly described by 120 ratios, generated from pairwise comparisons of sixteen intrinsic values. The sixteen intrinsic values are a variation on Frankena’s list. The variation includes only two changes: the merger of “truth” with “knowledge… wisdom,” and the merger of “beauty...” and “aesthetic experience.” Sixteen intrinsic values yield 120 pairwise combinations: eg, “Truth, knowledge, and true opinions of various kinds, understanding and wisdom” and “ beauty, harmony, proportion in objects contemplated, aesthetic experience.” Compare these values. Do you value one more highly than the other? More accurately, to what degree do you value one more highly than the other? I believe that the degree to which you value one more than the other can be expressed as a ratio (ranging from the golden moderation of 1:1 all the way to the extremism of 1:0, and including everything in between, such as 7841:7853). Further research may introduce a curve to this description for more accuracy, but a ratio is the first step towards that. If a microeconomist had a list of 120 ratios between each value, she could describe a great deal of a rational agent’s behavior in a wide new variety of contexts.
Third joke (Eliezer’s): “Many commonly used priors are listed in the Handbook of Chemistry and Physics.”
Obviously, your utility function is not in the back of the book.
Applications
The real problem comes is that you don’t have access to your own utility function, and that your utility function changes in response to experience. Every advertiser and salesman holds this to be true: when a customer walks onto a car lot, the salesman proceeds with the assumption that she doesn’t know what she wants yet; when a viewer sees an advertisement on TV, she views an ad based on the assumption that her desires can be changed from outside. The second problem, the problem of a responsive utility function, seems more mathematically difficult, but fit for a Bayesian model. The first problem is only obscure due to a lack of self-examination. In Rumsfeldian terms, it is an “unknown known,” or something that you don’t know (explicitly) that you know (implicitly).
There are lots of ways to access “unknown knowns.” Most commonly, others notice truths about ourselves. (The bias of illusory superiority is well-demonstrated evidence for our lack of self-scrutiny. Rationalists have an imperative to counteract this experimentally demonstrated bias: an imperative to take the criticisms of others seriously.) Some sociopaths gather social information in a systemic, utilitarian way; the conniving character Bob Benson revealed this in a recent episode of Mad Men, observing, “You don’t respond well to gratitude.” But neither sociopaths nor society return information about our own values in a systemic way. Without a systemic approach, there’s little hope to integrate every aspect of your utility function. I believe I have a more systemic, analytical proposal that is nevertheless based on social insight.
Games are analytical and social. Games are algorithms designed for semi-random human input. Games are the way to assess your own utility function. I propose what I call “The Trade-Off Game,” and it’s guaranteed to be the next fad sweeping the solar system.
To play the game, get a list of the sixteen intrinsic values and a couple friends. To play, you have to make up stories that dramatize the choice between two values that results in a marginal decision. Examples are below. The game is scored, but each player should also keep a log of his or her responses. (The log is actually the entire point: the ratios expressed in the log go towards the player’s complete utility function.) Each player scores a point for telling a story that dramatizes the marginal choice between values. (Fantastical stories involving utopias, magic, and advanced science are encouraged.) For each player who is stymied by the choice, or gives an answer that is exactly 50:50, the story-telling player scores another point. Take turns or don’t; play until it’s boring. But most of all, keep a log of value-ratios.
You can also play a solitaire version of the Trade-Off Game. For those of you playing alone at home, I encourage one more twist. Without social feedback, you may be vulnerable to your own biases, especially the framing bias. Therefore, compose two stories for each comparison: one in which you gain value A at the expense of value B, and one in which you gain value B at the expense of value A. The solitaire version of the Trade-Off Game doubles the number of questions, but 240 questions is a relatively small amount of self-interrogation for systemic insight into your aggregate set of values.
Examples
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Health and strength vs. Self-expression
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You are a dissident in a totalitarian state. You have passionately and publicly demonstrated in favor of free speech. Therefore agents of the regime ran your car off the road. Now you confined to a hospital bed. Your body is now a husk of what it once was. Your allies for free speech gather around you every day to carry your words to the outside world. If you choose, you may denounce your treatment, or the regime, or say whatever you choose. But when your allies are gone, the doctors tell you that they are all passionate supporters of the regime. For every day that you express yourself with your allies for free speech, they will add a day to your recovery, extending your sentence in a broken body. The doctors are thoroughly brainwashed, and you cannot possibly persuade them to join your cause. Neither can your allies, and they do not have the means to remove your body to a free hospital. You cannot leave on your strength unless the doctors sufficiently aid you. In each week, how many days will you spend speaking freely, and how many days will will you spend recovering your health? [Express all answers in ratios, eg, 3 ½ days of health to 3 ½ days of self-expression.]
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You are an Olympic athlete with a career-defining sponsorship from a major pharmaceutical corporation. They provide legal supplements that enable your world-class health, with a notable side-effect. The size of the supplement dosage proportionately limits your ability to transform your thoughts, feelings, and personality into language or art. You become indistinguishable from a schizophrenic person with an Apollonian body at the maximum daily dosage of 100 mg. At 50 mg, you are exactly halfway between your current physical state and bodily perfection, though you are exactly half as expressive as you are normally. Of course, 0 mg returns your health and powers of self-expression to their natural levels. How many milligrams of medication do you take each day? [Translate all answers into ratios between health and expression, eg 50 mg becomes 1 health : 1 expression.]
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Pleasures and satisfactions of all or certain kinds vs. Just distribution of goods and evils
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You are the favored child of an all-powerful magician. The magician can provide you with any pleasing experience, art, music, food, sensation, literature, &c. Every one of these experiences could be the most pleasing of your entire life. However, the magician has drawn power from the moral imbalance of the world. Each iota of pleasure that you surrender returns back to the world restore an iota of justice. The less pleasing your experience, the better the distribution of good and evil. You are set to live a life of feasts and orgies in a world where the cruelest monsters will be kings and the greatest heroes are miserable, abject slaves. If you reject everything that the wizard has given to you, you will live the life of an average person somewhere in global history, on a globe with the normal distribution of good and evil. How much of your own pleasures do you return in exchange for a more just world? [Express all answers in ratio format, eg 50⁄50 pleasure to justice.]
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You live in a utopia of justice: every human is completely free to be just or err, and society responds to each action with a completely proportionate sanction that eventually guides all people to a just life. Criminals are sternly but fairly corrected; heroes are satisfyingly praised to encourage the same virtues in all people. The price of this utopia is the complete eradication of all pleasure. There is no chocolate, and there is no orgasm. You have just discovered a simple recipe that can produce one of four things from chemicals found in every home: it can make either high fructose corn syrup, viagra, lysergic acid, or crack cocaine. Needless to say, these consumables will unleash pleasure and anarchy into your society. If they are universally distributed, society will totally crumble. Supposing that your recipe is discovered or shared, what proportion of the population do you believe should have access to the recipe? [Express all answers in ratio format, eg 1⁄3 of the population should be hippies.]
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Please fix the font type and size to be LW-standard, your post is hard to read. As a general advice, avoid serifs on screen.
General note to everyone: I recommend composing posts in something that converts easily to clean HTML. I always write my posts in markdown, then convert to HTML with the Markdown Dingus, then paste it into the HTML editor in the LW post editor.
By the way, why posts aren’t written like comments, in Markdown format? Could we consider adding markdown formatting as an option?
Do you have a solution for LaTeX?
I also use markdown, but have been doing ascii math because there’s no obvious and easy way to handle LaTeX.
I have a mathy post or two coming up that would enjoy trivial LaTeX.
Some of http://wiki.lesswrong.com/wiki/Comment_formatting#Using_LaTeX_to_render_mathematics is relevant.
Draft.in is another great option for this.
I’ve found Draft.in to be annoying. I may try it again in 6 months to see if they’ve improved it in the ways I care about.
Minor munchkin technique: If you have strong preferences for one font or another, it is possible in most web browsers, including Firefox, to tell your browser to respect your font choices and not allow web sites to override them. For instance I set Firefox to require a minimum 16 point font size. If it mattered to me, I could also also set all fonts to sans serif.
I find sans serif fonts annoying insofar as they fail to distinguish between different characters, such as l and I.
Ah: thesis, and then anti-thesis. This is where I come in with synthesis and say you’re both wrong, on average serif vs sans-serif may not matter at all for reader happiness on longform content.
Yep, VoI is not a Vol.
The way these are written, the answer will almost always be zero or one. What you need to do is ask what the trade-off should be to make it a hard question. How many days do you have to be confined to a hospital bed to make a day of self-expression not worth it? How badly must the supplement mangle your communication abilities before you stop taking it? How much moral imbalance is your happiness worth? How badly must pleasures corrupt society before you abandon them?
1.1:
All else being equal, I’d avoid expressing myself. If I can help stop the regime, it’s probably worth the hospital stay, but I’m not going to protest for fun.
1.2:
All else being equal, I wouldn’t take any supplements. I don’t really need to be any healthier. I’m just going to be on the computer all day anyway. Being unable to communicate normally would be a huge setback.
2.1:
All else being equal, I don’t care about justice. It can be useful to prevent crime and make people happy, but on its own it’s worthless.
2.2:
Does anarchy make people unhappy? If not, I’d give it to everyone.
That just contradicts the set-up of the question, which was:
So you need to consider a different scenario that you can identify with.
I’m going to do my job, and then play on the computer all day. Or are you asking how much I’d value physical ability if I valued physical ability?
The premise of the original question was that you are a top athlete who values competition and being top-ranked and winning. And you need the supplement to enable you to compete—it’s “career-defining” and “enables your world-class health”. Without the supplement, you won’t have your current career (or job).
Saying that you “don’t need to be any healthier” is just denying the setup of the question.
The real question is how much I value my health. If you tell me how much I value my health, then the original question goes unanswered.
As long as you’re telling me that I value my health, you might as well tell me how much, and just answer the question on your own.
You’re basically saying you can’t answer the question as posed, because it describes someone who is too different from yourself, and you value different things from that someone and don’t want to become like they are. Which is a perfectly valid position. It means the question’s scenario isn’t useful to you, and you can come up with a different one if you like.
However, your original comment is phrased as if it were an answer to the original question, which it really isn’t.
It was an answer to the question that the original question was posed to answer.
Also, it’s quite common to have thought experiments where you’re told to assume all else is equal, even though the assumption is insane. I can’t just assume that I’m not going to go to jail for murdering the guy on the track. I merely assumed that I care about my physical ability the same as I do in real life. It might go against the premise of the question, but it’s the sort of “assume all else is equal” thing you’re generally supposed to do with these questions.
I’m having trouble understanding this. The 120 ratios are independent? Don’t ratios multiply? That is, a/c = (a/b)/(c/b). There’s also the question of how these goods can be quantified, and why you think the ratios are constant. It seems to me that if the goods can be quantified and the ratios are constant, then there are only 15 parameters, not 120.
They ought to for a perfectly rational being, but humans aren’t.
Whether ratios multiply is a mathematical question, not a psychological one, so your comment doesn’t make sense. The only relevance human rationality has is whether ratios are an accurate model for humans. Furthermore, the OP said “If a microeconomist had a list of 120 ratios between each value, she could describe a great deal of a rational agent’s behavior in a wide new variety of contexts.” so humans are being modeled as rational beings, both explicitly (the OP outright says it) and implicitly (the use of ratios implies a certain level of rationality, no pun intended).
Once you choose a model, you can only model systems as being consistent with your model. If you model people as having a well defined utility function, then you are modeling them as having preference ratios that multiply. If the ratio between the utilitons that A gives you and the utilitons B gives you is X, and the ratio between the utilitons that B gives you and the utilitons C gives you is Y, then the ratio between the utilitons that A gives you and the utilitons C gives you must be XY. If U(A)/U(B) = X and U(B)/U(C) = Y, then U(A)/U(C) = XY. Saying “Well, people are irrational, so their utility function might not make sense” isn’t a valid response to this. U(A) is a real number, so it must follow the rules of real numbers. The fact that it the domain of U is a set of things that doesn’t have to follow those rules doesn’t change the fact that its codomain does have to follow those rules.
If you want to propose some other model, maybe come up with some mathematical structure that doesn’t follow these rules, then you are welcome to try. But you should be clear in properly formalizing this model, and not put it in terms of things that have to follow rules that your model doesn’t follow.
Good point.
1.1.: I would maybe speak out once, then shut up until I’m out of the hospital.
1.2.: Probably somewhere about 80 mg a day for a few weeks right before the most important competitions (once or twice per year), and 20 mg a day the rest of the time.
2.1.: Can’t I sell some of the stuff daddy gives me and give it to GiveWell-recommended charities or something? :-) Jokes aside, maybe about 80%/20%.
2.2.: “The price of this utopia is the complete eradication of all pleasure” is a contradiction for any reasonable value of “utopia” and “pleasure”.
These are not values, these are categories into which more specific values tend to fall. Two people with the same category-weightings may have completely different values, if they choose different things within those categories. Furthermore, some people value things in some of these things negatively; eg, some people actively dislike novelty and adventure. In fact, humans can value anything that they can describe in words.
I was hopeful that there would actually be 240 questions, presumably as a linked quiz/survey or something.
For the questions that are already there; 1.1: 100% self-expression 1.2: 100% health
2:1: I’m not sure, and not for unselfish reasons. I know pleasure being desirable is basically the most fundamental thing about utility functions but the idea of eliminating hedonic adaptation so as to live a life of constant happiness significantly greater than just baseline contentment actually scared me when Eliezer discussed it at one point in the sequences. Because of this fear, I wouldn’t answer 100%. Any inbetween seems unsatisfactory—if I was at the 90%-as-good-as-the-best-possible-feast/orgy/LAN party, I would have to wonder about the actual best possible, and want more. Thus, I would choose 100% justice, ignoring the wizard completely. 2.2: 100% pleasure.
I don’t think the questions perfectly encapsulate a trade-off between one value and another, and I think the hypotheticals might either need to be refined, or a much larger sampling of hypotheticals that make these trade-offs happen.
Also, I don’t think everyone’s values perfectly match the sixteen you give. To me, the list seems more like a collection of applause lights than an actual list of intrinsic values, and I expect a real list of things intrinsically valued by a specific human’s utility function would be much messier, with some values being very broad things that encompass/cause several of the equivalent values in the list, and some being ridiculously specific additions or exceptions. And I would expect every human’s to be different, except when abstracted to the point of maybe-uselessness.