Post Your Utility Function

A lot of rationalist thinking about ethics and economy assumes we have very well defined utility functions - knowing exactly our preferences between states and events, not only being able to compare them (I prefer X to Y), but assigning precise numbers to every combinations of them (p% chance of X equals q% chance of Y). Because everyone wants more money, you should theoretically even be able to assign exact numerical values to positive outcomes in your life.

I did a small experiment of making a list of things I wanted, and giving them point value. I must say this experiment ended up in a failure - thinking "If I had X, would I take Y instead", and "If I had Y, would I take X instead" very often resulted in a pair of "No"s. Even thinking about multiple Xs/Ys for one Y/X usually led me to deciding they're really incomparable. Outcomes related to similar subject were relatively comparable, those in different areas in life were usually not.

I finally decided on some vague numbers and evaluated the results two months later. My success on some fields was really big, on other fields not at all, and the only thing that was clear was that numbers I assigned were completely wrong.

This leads me to two possible conclusions:

  • I don't know how to draw utility functions, but they are a good model of my preferences, and I could learn how to do it.
  • Utility functions are really bad match for human preferences, and one of the major premises we accept is wrong.

Anybody else tried assigning numeric values to different outcomes outside very narrow subject matter? Have you succeeded and want to share some pointers? Or failed and want to share some thought on that?

I understand that details of many utility functions will be highly personal, but if you can share your successful ones, that would be great.

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Utility functions are really bad match for human preferences, and one of the major premises we accept is wrong.

They may be a bad descriptive match. But in prescriptive terms, how do you "help" someone without a utility function?

To help someone, you don't need him to have an utility function, just preferences. Those preferences do have to have some internal consistency. But the consistency criteria you need to in order to help someone seem strictly weaker than the ones needed to establish an utility function. Among the von Neumann-Morgenstern axioms, maybe only completeness and transitivity are needed.

For example, suppose I know someone who currently faces choices A and B, and I know that if I also offer him choice C, his preferences will remain complete and transitive. Then I'd be helping him, or at least not hurting him, if I offered him choice C, without knowing anything else about his beliefs or values.

Or did you have some other notion of "help" in mind?

Furthermore, utility functions actually aren't too bad as a descriptive match when you are primarily concerned about aggregate outcomes. They may be almost useless when you try to write one that describes your own choices and preferences perfectly, but they are a good enough approximation that they are useful for understanding how the choices of individuals aggregate: see the discipline of economics. This is a good place for the George Box quote: "All models are wrong, but some are useful."

They may be a bad descriptive match. But in prescriptive terms, how do you "help" someone without a utility function?

Isn't "helping" a situation where the prescription is derived from the description? Are you suggesting we lie about others' desires so we can more easily claim to help satisfy them?

Helping others can be very tricky. I like to wait until someone has picked a specific, short term goal. Then I decide whether to help them with that goal, and how much.

Isn't "helping" a situation where the prescription is derived from the description?

Not necessarily. There are lots of plausible moral theories under which individuals' desires don't determine their well-being.

I think Eliezer is simply saying: "I can't do everything, therefore I must decide where I think the marginal benefits are greatest. This is equivalent to attempting to maximize some utility function."

Derivation of prescription from description isn't trivial.

That's the difference between finding the best plan, and conceding for a suboptimal plan because you ran out of thought.

I agree with both those statements, but I'm not completely sure how you're relating them to what I wrote.

Do you mean that the difficulty of going from a full description to a prescription justifies using this particular simpler description instead?

It might. I doubt it because utility functions seem so different in spirit from the reality, but it might. Just remember it's not the only choice.

A simple utility function can be descriptive in simple economic models, but taken as descriptive, such function doesn't form a valid foundation for the (accurate) prescriptive model.

On the other hand, when you start from an accurate description of human behavior, it's not easy to extract from it a prescriptive model that could be used as a criterion for improvement, but utility function (plus prior) seems to be a reasonable format for such a prescriptive model if you manage to construct it somehow.

In that case, we disagree about whether the format seems reasonable (for this purpose).

You want a neuron dump? I don't have a utility function, I embody one, and I don't have read access to my coding.

I'm not sure I embody one! I'm not sure that I don't just do whatever seems like the next thing to do at the time, based on a bunch of old habits and tendencies that I've rarely or never examined carefully.

I get up in the morning. I go to work. I come home. I spend more time reading the internets (both at work and at home) than I probably should -- on occasion I spend most of the day reading the internets, one way or another, and while I'm doing so have a vague but very real thought that I would prefer to be doing something else, and yet I continue reading the internets.

I eat more or less the same breakfast and the same lunch most days, just out of habit. Do I enjoy these meals more than other options? Almost certainly not. It's just habit, it's easy, I do it without thinking. Does this mean that I have a utility function that values what's easy and habitual over what would be enjoyable? Or does it mean that I'm not living in accord with my utility function?

In other words, is the sentence "I embody a utility function" intended to be tautological, in that by definition, any person's way of living reveals/embodies their utility function (a la "revealed preferences" in economics), or is it supposed to be something more than that, something to aspire to that many people fail at embodying?

If "I embody a utility function" is aspirational rather than tautological -- something one can fail at -- how many people reading this believe they have succeeded or are succeeding in embodying their utility function?

I've put a bit of thought into this over the years, and don't have a believable theory yet. I have learned quite a bit from the excercise, though.

1) I have many utility functions. Different parts of my identity or different frames of thought engage different preference orders, and there is no consistent winner. I bite this bullet: personal identity is a lie - I am a collective of many distinct algorithms. I also accept that Arrow’s impossibility theorem applies to my own decisions.

2) There are at least three dimensions (time, intensity, and risk) to my utility curves. None of these are anywhere near linear - the time element seems to be hyperbolic in terms of remembered happiness for past events, and while I try to keep it sane for future events, that's not my natural state, and I can't do it for all my pieces with equal effectiveness.

3) They change over time (which is different than the time element within the preference space). Things I prefer now, I will not necessarily prefer later. The meta-utility of balancing this possibly-anticipated change against the timeframe of the expected reward is very high, and I can sometimes even manage it.

Here's one data point. Some guidelines have been helpful for me when thinking about my utility curve over dollars. This has been helpful to me in business and medical decisions. It would also work, I think, for things that you can treat as equivalent to money (e.g. willingness-to-pay or willingness-to-be-paid).

  1. Over a small range, I am approximately risk neutral. For example, a 50-50 shot at $1 is worth just about $0.50, since the range we are talking about is only between $0 and $1. One way to think about this is that, over a small enough range, there isn't much practical difference between a curve and a straight line approximating that curve. Over the range -$10K and +$20K I am risk neutral.

  2. Over a larger range, my utility curve is approximately exponential. For me, between -$200K and +$400K, my utility curve is fairly close to u(x) = 1 - exp (-x/400K). The reason is that, for me, changing my wealth by a relatively small amount won't radically change my risk preference, and that implies an exponential curve. Give me $1M and my risk preferences might change, but within the above range, I pretty much would make the same decisions.

  3. Outside that range, it gets more complicated than I think I should go into here. In short, I am close to logarithmic for gains and exponential for losses, with many caveats and concerns (e.g. avoiding the zero illusion. My utility curve should not have any sort of "inflection point" around my current wealth; there's nothing special about that particular wealth level).

(1) and (2) can be summarized with one number, my risk tolerance of $400K. One way to assess this for yourself is to ask "Would I like a deal with a 50-50 shot at winning $X versus losing $X/2?" The X that makes you indifferent between having the deal and not having the deal is approximately your risk tolerance. I recommend acting risk neutral for deals between $X/20 and minus $X/40, and use an exponential utility function between $X and minus $X/2. If the numbers get too large, thinking about them in dollars per year instead of total dollars sometimes helps. For example, $400K seems large, but $20K per year forever may be easier to think about.

Long, incomplete answer, but I hope it helps.

How have you come to these conclusions?

For example:

The reason is that, for me, changing my wealth by a relatively small amount won't radically change my risk preference, and that implies an exponential curve

Is that because there have been points in time when you have made 200K and 400K respectively and found that your preferences didn't change much. Or is that simply expected utility?

For the specific quote: I know that, for a small enough change in wealth, I don't need to re-evaluate all the deals I own. They all remain pretty much the same. For example, if you told me a had $100 more in my bank account, I would be happy, but it wouldn't significantly change any of my decisions involving risk. For a utility curve over money, you can prove that that implies an exponential curve. Intuitively, some range of my utility curve can be approximated by an exponential curve.

Now that I know it is exponential over some range, I needed to figure out which exponential and over what range does it apply. I assessed for myself that I am indifferent between having and not having a deal with a 50-50 chance of winning $400K and