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.
Just to be clear, you know that an exponential utility function (somewhat misleadingly ) doesn't actually imply that utility is exponential in wealth, right? Bill's claimed utility function doesn't exhibit increasing marginal utility, if that's what you're intuitively objecting to. It's 1-exp(-x), not exp(x).
Many people do find the constant absolute risk aversion implied by exponential utility functions unappealing, and prefer isoelastic utility functions that exhibit constant relative risk aversion, but it does have the advantage of tractability, and may be reasonable over some ranges.
Example of the "unappealingness" of constant absolute risk aversion. Say my u-curve were u(x) = 1-exp(-x/400K) over all ranges. What is my value for a 50-50 shot at 10M?
Answer: around $277K. (Note that it is the same for a 50-50 shot at $100M)
Given the choice, I would certainly choose a 50-50 shot at $10M over $277K. This is why over larger ranges, I don't use an exponential u-curve.
However, it is a good approximation over a range that contains almost all the decisions I have to make. Only for huge decisions to I need to drag out a more complicated u-curve, and they are rare.