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.
It makes sense however you mention that you test it against your intuitions. My first reaction would be to say that this is introducing a biased variable which is not based on a reasonable calculation.
That may not be the case as you may have done so many complicated calculations such that your unconscious "intuitions" may give your conscious the right answer. However from the millionaires biographies I have read and rich people I have talked to a better representation of money and utility according to them is logarithmic rather than exponential. This would indicate to me that the relationship between utility and money would be counter-intuitive for those who have not experienced those levels which are being compared.
I have not had the fortune to experience anything more than a 5 figure income so I cannot reasonably say how my preferences would be modeled. I can reasonably believe that I would be better off at 500K than 50K through simple comparison of lifestyle between myself and a millionaire. I cannot make an accurate enough estimation of my utility and as a result I would not be prepared to make a estimation of what model would best represent it because the probability of that being accurate is likely the same as coin flipping.
Ed: I had a much better written post but an errant click lost the whole thing - time didn't allow the repetition of the better post.
As I said in my original post, for larger ranges, I like logarithmic-type u-curves better than exponential, esp. for gains. The problem with e.g. u(x)=ln(x) where x is your total wealth is that you must be indifferent between your current wealth and a 50-50 shot of doubling vs. halving your wealth. I don't like that deal, so I must not have that curve.
Note that a logarithmic curve can be approximated by a straight line for some small range around your current wealth. It can also be approximated by an exponential for a larger range. So even if I were purely... (read more)