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.
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).
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.
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.
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:
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?