Friday, October 17, 2008

No Such Thing As Utility Functions

One of the most fundamental concepts in economics is the "utility function" that is supposed to represent a person's desires and their relative value to each other. Of course, this is crap (distant rumble as the entire edifice of mainstream economics goes down) but let us reflect here on why it is crap.

A person's desires are not well-ordered like the real numbers. It's not the case that you can always tell that one thing is more important than another thing. Being tortured may be less desirable than chocolate ice cream, but is having a nail driven through your hand more or less desirable than being kneed in the groin?

It's not even the case that there is no relationship between some pairs of desires, like the (knee in groin, nail in hand) pair. Rather, the relationship may or may not exist and may or may not fluctuate over time or due to externalities. You may prefer to have a nail driven through your hand one day and be kicked in the groin the next. All depending on whether you had chocolate ice cream that morning.

So people's desires are not well-ordered and they are not even partially-ordered. They are rather extremely disordered and so form an edset - to contrast with poset. Now the question is, what does an edset have to do with a utility "function"? The answer is: not a fucking thing. As should be immediately and blindingly obvious to anyone familiar with programming.

A function is a set of relations between two sets or between a set and itself, with each relation mapping to a unique value. A "utility function" is not a function since utility(knee in groin, nail in hand) maps to every possible value in the range of the function (less, equal, more) and also to no value at all.

The economist will counter by claiming that if people have no persistent utility functions then it's simple enough to take a snapshot of their desires at any one point in time and treat this as a utility function. However, this is moronic because the "utility function" so generated will invariably be 99.99% blank. Maybe there is a way to rescue the notion using a probability distribution of value for each desire (to represent randomness from internal and external sources) but this would rapidly become intractable.

More substantively, the utility "function" of an edset encodes little to no information. It is primarily white noise. What is of interest is not "less" or "more" or "equal" or whatever. What is of importance is the edset itself. This should be familiar to programmers because I am saying no more than that describing people's desires isn't well suited to a functional approach at all but rather requires an object-oriented approach.

Of course, the reason economists cling to this functional approach is because first it sounds more mathematical. Economists are suckers for anything that makes them sound more authoritative, the scum. And secondly because they are holding onto a Utilitarian past where you can pretend that utility(knee in groin) = -10.0. Such precision!

This makes it the 273rd umm 274th? reason why mainstream economists are morons and the whole field should be thrown in a rubbish bin. Along with anthropology and ... I am actually drawing a blank here since I can think of no other fields in academe that equals these in loathesomeness. Oh wait, philosophy. Phew, I was afraid my sense of righteousness was waning.

Oh yeah, there's a better name than 'edset', it's 'value system'. I really don't like 'desire' since it sounds too earthy and sensual. Of course, value has the dual problem of sounding too abstract and cerebral, but I can live with that better. And desire has the problem that satisfied desires are no longer desires, whereas value doesn't have that problem.

8 comments:

futurebird said...

I think you mean they are not "totally ordered" --becuase if they are not "well ordered" it makes no sense to mention partial orders.

Richard Kulisz said...

I wrote this:

> So people's desires are not well-ordered and they are not even partially-ordered.

Did you think I did not mean it?

tigerthink said...

>Being tortured may be less desirable than chocolate ice cream, but is having a nail driven through your hand more or less desirable than being kneed in the groin?

I'd rather be kneed in the groin. Obvious question. Furthermore, if you're having trouble deciding which of two things is better, that can easily be attributed to the low resolution of your experience simulator and doesn't say anything about the validity of utilitarianism.

>It's not even the case that there is no relationship between some pairs of desires, like the (knee in groin, nail in hand) pair. Rather, the relationship may or may not exist and may or may not fluctuate over time or due to externalities. You may prefer to have a nail driven through your hand one day and be kicked in the groin the next. All depending on whether you had chocolate ice cream that morning.

Whether external factors influence the value of various actions over time has nothing to do with whether it is useful to treat those values as if they could be represented by numbers.

>Maybe there is a way to rescue the notion using a probability distribution of value for each desire (to represent randomness from internal and external sources) but this would rapidly become intractable.

Saying that doing this sort of math would be difficult is different than saying that it's not useful to pretend that the value of various results can be treated as if they can be represented by numbers.

Richard Kulisz said...

Tigerthink, it ISN'T useful to pretend that people's values are totally ordered, well-ordered or even partially ordered. It's a vicious lie that REDUCES your understanding of the human mind.

Furthermore, the conceit that totally ordering one's values is at all desirable, that it is "rational" to do this, is extremely destructive and anti-human. Not to mention that it just isn't possible so anyone who tries is just deluding themselves and insulting truth.

Bob-E said...

Based on the way you described a utility function I would hate them too and therefore hate economics since modern economics are based on utility functions. My understanding of utility functions if that they were never meant to be taken seriously as precise measurements of the "utility" that an individual actually gets from a good or service. A utility function is meant for constructing theoretical understanding of how humans value goods/services. In other words how humans are willing to substitute one for another determines the 'kind' of good in question and is really just a fancy way of explaining everyday observations that many people see as common sense. I never met anyone actually try to derive an actual utility for anyone , but understanding that in general the "utility function" between two goods for most people tends to be U = x1^2 + x2 can be useful because it shows that the individuals in question would be worse off with one less x1 than x2. Economics does not claim to be able to derive yours and anyone's utility function, but given the right data it can derive an approximation of how a population of people values x1 compared to x2 'on the average'. These studies help to better allocate scarce resources but just like you have a problem with mediocre programmers I have problem with mediocre economists. Unfortunately I have found there simply isn't enough economists who know how to do real research let alone interpret the results of that research (since much of it's credibility extends no further than statistical inference and simple axioms). You obviously would not be surprised to learn that many do not even do real research and make important forecasts based solely on their own feelings. This is no different than people deciding to become life-long lottery players b/c they heard of some lucky person who won it twice despite thousands of lottery games being played each day. I admit economics is imprecise (and any good economist will admit this) but I think it is more scientific approach than many other sources of knowledge that far too many people rely on.

Richard Kulisz said...

On the meta-level, I know you don't want to commit yourself to defending utility functions but the fact remains that the defense you're using is cliche' and pathetic. It doesn't matter if the originators of the concept meant it seriously or not, because it is an independent fact of reality that it IS being taken seriously.

Just like the Central Dogma of Biology was taken utterly seriously until it was overturned and then the fuckers revised history to claim they never meant it seriously as some kind of intellectually dishonest pathetic face-saving exercise!

And when I say utility functions are taken seriously, I don't mean among the fanatical nutbars, right-libertarians in this case (a disease common among economists), but also among "decision theorists". This is proven by the fact the Condorcet Criterion for voting is widely assumed to be obvious and desirable, whereas I consider it utterly fucking absurd and ludicrous.

The whole concept of utility functions presupposes that information about what people want can be found wholly in human brains. This is NOT TRUE! It presupposes that such information is complete. This is ALSO NOT TRUE. It presupposes that such information is formalizable. This is ALSO NOT TRUE!

What then is there to redeem this intellectually bankrupt concept?

On the level, the concept of utility functions is contradicted by reality. As I have already stated, humans make decisions about conflicting desires by making relative comparisons. And ONLY relative comparisons, not absolute comparisons. The graph of these comparisons is SPARSE. This means that in practice, a decision resolving a conflict between A and Z is mostly contingent on happenstance, on the order you encounter B through Y in reality. This is unpredictable which means that a resolution between A and Z is made RANDOMLY.

This is PROVEN by the fact that cycles of pairwise comparisons such that A > B > C > A are COMMON. Not just in humans but in nature. And there is no meaningful understanding of "function" that would allow you to describe mechanisms that output random results based on happenstance as "functions".

I happen to have a really good theoretical grasp on how emotions work in actual human beings. The concepts I use to explain human emotions are the same concepts that must underly human decisions. I know this because there just isn't that much space in a human mind. So even though I have only the faintest clue how human decisions are actually made, I can tell you authoritatively that decision theory has FUCK ALL to do with any ACTUAL human decisions. *NO* concept found in decision theory occurs in a human brain.

Trying to use utility functions to give a "theoretical understanding" of human desires OR human decision making is analogous to trying to use the PCB contamination levels in eskimo pee to give a theoretical understanding of the CERN particle accelerators. THEY HAVE NOTHING TO DO WITH EACH OTHER!

Richard Kulisz said...

I apologize for going off tangent since this wasn't addressing your points. It's merely addressing the points I made in this blog post. Or the points I had in mind at the time.

To address your claim that utility functions are useful analytical (in the sense of totally made up and approximate) tools by certain economists studying large populations and diverse markets ...

I find myself not having an opinion on the matter chiefly due to the fact that I don't think that segment of economists is significant.

It took me a solid 15 minutes of head-scratching to think of any applications for what you describe. I came up with food and other goods consumption based on demographic projections under various economic scenarios.

I grant you this is rather important for high level policy planning, especially in the agricultural sectors of developing countries. For highly industrialized countries, it seems less important.

The other sector that requires long term planning is energy, especially electricity. And there I have difficulty taking projections seriously unless they're based on ridiculously complex models.

Richard Kulisz said...

I do find it interesting that you defend such an esoteric field of economics, a very empirical one too, and reject the credibility of any other. I happen to agree with your judgement on both those issues.

What I'm dubious on is the usefulness of the economics field you describe towards actual policy. It seems to me that policy can be, is, and should be made on other grounds than what you describe.

In the case of agricultural policy, this is driven in the USA by crony politics and corporate lobbying. When it should be driven by world food prices (bad), geo-politics (worse), and world grain reserves (abysmal).

In the case of energy policy, this is driven by crony politics and anti-industrial eco-zealotry. When it should be driven by reliability of supply, technological upgrading, cost-effectiveness, and elimination of undesirable side-effects.

You don't need to resort to utility functions of any kind to compare nuclear to coal or natural gas. Nuclear is a clear winner on simple arithmetical grounds. When simple arithmetic isn't being used to make policy decisions, what use are complicated analytical-statistical models?