Saturday, December 29, 2007

Why are law professors (and everybody else) unhappy?
Tom Smith

First of all, let me reassure you that I am not unhappy.  Indeed, in the immortal words of Mater, "I'm happier thanna tornader inna trailer park!"  That said, Paul Caron (via Instapundit) asks why law professors are "edgy," by which he seems to mean discontented.  I confess I want to use this observation to float a very general idea I have, which I suspect is so good that it is almost certainly not original.  And it may not even be that good.  In my defense, I will say that this blog post is much shorter than any law review article.

My observation on the general cause of much discontent not just among law professors, but among humans in general, of which the former are, albeit controversially, a subset, can be presented in two pictures.  First, here is a picture of the distribution of intelligence, at least as measured by a standard IQ test, in the US population:


Second, here is a picture of income distribution in the US:


This is not going where you think.  I am not going to suggest or complain that law professors, who are so smart, are paid less than real estate promoters or whoever, who are not.  (Though this completely irrelevant picture I stumbled upon is interesting.)  Rather, I call your attention to the very different shape of these graphs.  Intelligence is normally distributed.  It is spread out in the population according to our old friend, the bell curve, which smarter people call a Gaussian distribution.  Income, on the other hand, is not normally distributed.  It is distributed much more like a power law distribution, which is illustrated in the context of web page linkages below (because that's the easiest context in which to find a handy picture to steal on the web):


I like the picture above better because it illustrates the "long tail" webbies are familiar with more clearly.  But if you moved the axes around on the income distribution picture, you would see that income distribution also follows a highly skewed (darn skewed!) distribution, much more like a power law distribution than a normal distribution.  (See also this dated but still cool income distribution poster.)

Why is this, and why the big difference?  The highly skewed income distribution is due to (I simplify of course) the phenomenon popularly rued as the rich getting richer, while the poor just plod along.  It ain't just an old wives' tail.  Success breeds success, opportunities more opportunities and so on. 

Now, compare this to IQ distribution.  But do not think about just IQ.  Instead, consider all the traits, abilities, blessings, good breaks, and so on, that we think ought to result in rewards.  My claim is certainly not that social rewards ought to track IQ distribution.  But I do think that the agglomeration of things that we tend to think ought to be rewarded in an academic career and in any other, are statistically much the same.  That is, they are the result of the interaction of many, independent, or at least not very closely related factors.  For law professors, you have intelligence, interest in the law (not always inversely related), absence of hideously bad looks, a decent speaking voice, and so on and so on.  The point is, there are more than a few.  Whenever you have a number of independent factors at work producing the results you are measuring, under the central limit theorem you tend to get a normal distribution.  I happen to think this is very cool, but that is beside the point.

My overall point then is that there is a deep mismatch between how deserts are distributed and how rewards end up, and that these distributions are as close to inevitable as things get.  In any dynamic process where there are repeated games, and success builds on success, and that is certainly true where you have professional reputations or anything similar, you are going to have a highly skewed distribution.  On the other hand, the factors that in some sense ought to lead to success are going to be normally distributed.  This means in any profession, very broadly conceived of, there are going to be a lot of discontented people, not only in the long tail, but towards of the middle of rewards curve (if you can even say it has a middle).  You are also going to have a few people basking in more than they (in some sense) deserve, but this is not to say they are not entitled to it, by the rules of the game, under which you are rewarded for having been rewarded.

I think a lot of discontent among law professors and everybody else results from thinking that we ought in some sense be rewarded according to where we are on the normal distribution (which measures things like talent plus work ethic plus creativity etc.) when instead we are living in a world which produces that long slide of a fat tailed distribution.

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Tom Smith


I have a somewhat discontented younger colleague to whom I repeatedly sing the song that Life is not an IQ test.

Posted by: dearieme | Dec 29, 2007 4:38:03 PM

Great creative post; but the answer is, of course, that social rewards go to those who provide social needs. So the reason Bill Gates gets $60B is that he made 6.5B eartlings lives uncountable times better by creating and suprvising a common computer language. This is especially true when it comes to the provision of staples. You can have all the talent/virtue in the world, but if you dig ditches (or teach law) you are not really providing anything so very much marginally more than the next ditch digger or law professor candidate. And it's a good system that generally speaking and often despite themselves, provides the poorest what they need most either cheaply or for free via welfare, etc.


Posted by: The Objective Historian | Dec 29, 2007 6:33:36 PM

This is a very fascinating mathematical issue, which is actually a little beyond me (or at least beyond the amount of work I want to put into understanding it). When a particular outcome (i.e., income) is the product of two independent qualities (e.g., musical ability and good looks, or intelligence and hard work), the resulting distribution can be highly skewed even if distributions of the underlying qualities themselves are not. Take a look at Laurence R. Iannaccone, "Skewness Explained," 36 Journal for the Scientific Study of Religion 141 (1997).

Posted by: y81 | Dec 29, 2007 7:17:56 PM

The problem is that income is earned, not distributed. "Income distribution" presupposes that there is some authority that is in charge of "distributing" income. There isn't.

From over 60 years of observation in various places around the world, I have come to the conclusion that one indisputable ingredient in gaining a high income is the willingness to work hard.

That's not something that I'm interested in doing, thus I am not rich.

One other ingredient is, of course, the ability to do something well that others either cannot or will not.

Posted by: John D | Dec 29, 2007 7:30:07 PM

We live in a society in which many things are demonstrated as being desirable by being 'rewarded' with money. This is very good in some ways (it tends to reward most those who figure out how to deliver that which the system rewards, so, as long as the goals/rewards system is useful this reward system is 'good') and perversely bad in others (if the system rewards 'celebrity' then Paris Hilton gets 'undeservedly' even more wealthy).

However, if we remove the notion of money as the marker and merely refer to 'resources' rewarded for fulfilling systemic goals, we find, I think, that *all* systems reward those who fulfill the system's goals with resources. In *some* systems the rewards/resources are, indeed, 'distributed'. Think the old USSR, Cuba, Zimbabwe, Saddam's Iraq and so on.

I find it more than a bit odd that those in our system who decry the 'unfairness' of the current system goals/rewards fail to see that if one wants systemic 'distribution' rather than 'earning' then you must inevitably end up with a tyrannical system of reward distribution. Hardly a change for the better in my book.

And, we would probably end up with a great many more 'edgy' or unhappy individuals (see above countries for examples).

Posted by: JorgXMcKie | Dec 29, 2007 8:13:17 PM

It has been a long time since my college stats class, but that income distribution sure looks like a Rayleigh distribution ( to me. You get a Rayleigh distribution (not a normal distribution) when you have a measurement that is a function of several independent normally distributed parameters.

If income is a function of IQ, work ethic, atractiveness, etc, then a Rayleigh distribution seems like a good model and the difference in shape between the IQ curve and the income curve makes perfect sense.

Posted by: Richard Clark | Dec 29, 2007 9:52:01 PM

Tom, what you're looking at is an artifact of your choice of IQ and annual income as measures of intelligence and financial status, respectively. Had you instead defined intelligence in terms of total accumulated intellectual achievements, and financial status in terms of percentile rank on the income scale, then you could have used the resulting graphs to rail bitterly against the obscene hyper-egalitarianism of a society where true intellectual giants, with earth-shattering achievements to their names, and complete mental midgets of no accomplishment whatsoever compete for position on a completely uniform income distribution with a fixed maximum.

Perhaps what you really mean is that people like to *think* of intelligence as distributed IQ-style--that is, not all that unevenly distributed (and presumably with themselves not really all that far from the top handful on the curve)--and of financial status as directly proportional to number of dollars earned--that is, very unevenly distributed indeed (presumably with themselves much, much farther away from the top handful than they believe they ought to be). If so, then you may have just discovered the human phenomena of vanity, greed and envy--but I don't think these really have anything to do with those graphs you're so excited about.

Posted by: Dan Simon | Dec 29, 2007 10:53:38 PM

Beware of comparing a distribution having a positive and negative range with one having only a positive range. The normal distribution (Gaussian) abscissa can take on positive or negative values. The test that produces the IQ distribution is designed to have a mean of 100 and a standard deviation of 15. It could have been designed to produce a mean of 0 with below average IQs having a negative value. At any rate, it is symmetric. The distribution of income can only lie in the positive range and is unlikely to be symmetric. However, it turns out that the tail of the income distribution above $77,500 is approximated by the normal distribution greater than one standard deviation. It could also be approximated by a gamma, log normal or a number of other distributions. The point is: income is an apple and smarts is an orange.

Posted by: Jaybee | Dec 29, 2007 11:47:50 PM

Some responses FWIW:
Jaybee: point taken, and I concede I'm comparing apples and oranges and crudely at that. But I do think there is something to the intuition that people think the size of their apples ought to be correlated with the size their oranges when in fact these sizes are inevitably distributed very differently.

Dan: I don't think it is just a matter of definition that intelligence or ability are normally distributed. Probably you could define something called total intellectual achievement that would not be normally distributed, such as number of recognized awards that would appear on a CV, in a database of CVs, that would be highly skewed. But I don't see what the point would be of doing that, unless your claim is that this measure corresponds to something. I'm saying that the set of attributes that people think ought to determine their total rewards in their careers are (something like) normally distributed, while the rewards themselves are far from normally distributed. As you point out, I could have said something different and far less plausible than that, and I'm glad I didn't. Nor am I railing bitterly against anything. In fact, I was afraid my post would come across as smug. I do agree that what I am talking about has much to do with human greed, envy and vanity, which are interests of mine. No doubt the things that excite me are often puzzling to others, and I habitually pay little attention to well-intentioned advice not to get excited about my own ideas. If you have an idea I should be excited about, I would be happy to hear it. But while my statistics are very crude, I do think there is something quite interesting in the idea that perceived deserts are and inevitably will be very differently distributed than rewards.

Richard: the idea that income has a Rayleigh distribution is very interesting. Undoubtedly there is a literature on this that some economist could enlighten us about. If it is, however, I think my point may still hold, that rewards distribution is highly skewed compared to perceived deserts distribution.

y81: Thanks. I will try to find that. It could be that is the very thing I am noticing. I wish I had the math chops to really understand it, but I agree it is very interesting.

TOH and dearime: I agree that Bill Gates has made huge contributions to human productivity. Without starting a whole new argument, however, I also think he has profited enormously from some market effects that don't have a lot to do with making products better. Personally, the awfulness of Word has done a lot to convince me that there is something to network externality as a market failure argument. I think in fact he is a good example of what I am talking about. Lots of computer scientists resent his success because they are smarter than he is and could have or have created better products, but due to historical path type reasons, they won't be nearly as successful. Life certainly is not an IQ contest, but intelligence is a pretty good predictor of future success. This probably makes really smart but not very successful people feel worse.

Posted by: Tom Smith | Dec 30, 2007 3:51:52 AM

Tom Smith:

Quite right; and beta-max they say was better than VHS. The market does not get perfect results, just, it would seem, better results than a Politburo. My point regarding Gates was merely general in that the relatively free market's purpose is to provide huge incentives for people to provide the basic needs of the vast majority of mankind faster, more affordably, and better. I'd give you another concept: society might prefer every hyper-genius in the world dedicated themselves to a cure for cancer rather than be law professors, corporate lawyers, investment bankers, etc. By luck and talent and work, one of those hyper-geniuses might develop that wonder drug and become 10 times wealthier than Gates; not necessarily smarter than the other hyper-geniuses. But the system we have of the big prize going to the one who helps mankind most as far as day-to-day living is very effective. To paraphrase Churchill: the relatively free market, with certain socialist adjustments depending on the predelictions of the electorate (US v. Scandinavian models), is a horrible economic system; it's just better at providing for BOTH the least amongst us and us generally than any other. The poor in the Western world live better than anywhere and at any time in world history BECAUSE we have this system that rewards provision of social needs far in excess of rewarding talent however considered. So my answer to disgruntled law professors is this: don't be a law professor if you want to be rewarded with income ... use your genius to work on a cure for cancer or a 300 mpg car with range and power or a educational system that effectively and statistically inbues young men and women with the best of human virtues or a something that society needs ... not something that they prefer to do: teach law.


Posted by: The Objective Historian | Dec 30, 2007 6:21:40 AM

I thought of this summary:

However unjust one thinks it is the way talent and hard work are rewarded by our Western system (e.g., law professors making $100,000), the unjustness is miniscule compared to the bounty our system provides us all, particularly the least amongst us. A Western system, i.e., a hybrid socialist-free market, that does so better than any other. So when disgruntled, stroll your campus - in particular - and the area beyond; see what USA is like compared to the 2007 Malawi or 1970 USSR or 1250 France. The real reward for our way of life so valuable as to be invaluable and is invisibly conferred to a law professor and all of us and so easy to ignore. There is poverty and misery, but those are for the overwhelmingly most part caused by self-inflicted poverty-conducive behavior and consequent to our regard for civil liberties and privacy. A law professor might not make as much as you think you ought to given his or her talent and hard work, but you do so in a civil and prosperous society that does do it's best to care for the young, the old, and the ill in the context of ordered liberty ... we ought to be very grateful.


Posted by: The Objective Historian | Dec 30, 2007 7:11:40 AM

OK, I'm starting to be obnoxious, I know:

But the real reward for being smart is being smart; that's something money cannot buy.


Posted by: The Objective Historian | Dec 30, 2007 7:14:23 AM

"comparing apples and oranges": a friend likes to say that comparing apples and oranges is perfectly sensible. He thinks that we should not, however, compare apples and Tuesday.

Posted by: dearieme | Dec 30, 2007 7:53:01 AM

For the purpose of this subject matter, in the distributive scheme of things, these smart people worked hard to place themselves in a very specific part of the curve and knew exactly how that choice would be "rewarded."

Perhaps the professors are disgruntled because they only take account of the value of the income they receive without the other benefits: tenure (little risk of job loss makes up for a lot of foregone salary), comfortable work setting, less-than-strenuous work, vacation time, retirement benefits, whatever . . .

In addition, through outside work and consulting, the professors can supplement that salary, proactively increase their monetary income and move to the right on the X-axis. Presumably, this would reduce their disgruntlement and "edginess" assuming they were not adverse to work and effort. I recall several of my law professors had some sort of professional practice (legal or consulting) apart from teaching.

Furthermore, through complacency, it is easy to be less than satisfied, but they are forgetting that the salary and non-monetary benefits derived from that occupation were not exactly a secret. Since they are so smart, presumably they know how much they will make and where the income ceiling is. They could use those same smarts to find more lucrative jobs and happiness. Ultimately, the "edginess" probably springs from the desire for others to provide them more money for no additional value.

Posted by: dmb | Dec 30, 2007 1:22:39 PM

Tom, I don't think your measure of either "deserts" or "rewards" is nearly as natural and universal as you seem to think. Consider the tail which is of most interest to you: is the difference between the intellectual potential of someone with an IQ three standard deviations away from the mean and that of someone with an IQ four standard deviations away from the mean, really much smaller than the difference between the material conditions of a person with an income three standard deviations from the mean, and one with an income four standard deviations from the mean? I'd say the reverse assertion is far more plausible.

On the other hand, to a particular sort of person--one with a very high estimate of his or her own intelligence, and a strongly competitive drive for financial success, the practically insignificant difference between very rich and ultra-rich may loom a lot larger than the difference between good smarts and real brilliance, even if the latter is much more important to the rest of the world. It wouldn't surprise me at all if very successful law students--say, those who become law professors-- or those who read their blogs, were relatively likely to fall into that category. But if so, then it's their own particular brand of vanity, greed and envy at work, not any widely accepted measure of "deserts" and "rewards".

Now, let's change the playing field and see what happens. Suppose we measure "deserts" in terms of athletic ability, and "rewards" (for men, at least) in terms of number of sexual partners per year. Now law professors and their blog readers--at least, the sports fans among them--probably have no difficulty recognizing the huge significance of the difference in athletic ability between even very talented amateur athletes and the top few professionals. Likewise, they probably tend to see the difference between Wilt Chamberlain-level promiscuity and ordinary handsome-jock levels as pretty unimportant.

However, I expect that to at least some testosterone-soaked fourth-string college athletes, the difference in athletic skill between themselves and the professional elite seems negligible, whereas the difference between dozens and hundreds of sex partners a year is huge and maddening. Again, though, vanity and envy (and in this case, lust) play a major role in that assessment.

People are, of course, entitled to measure "deserts" and "rewards" as they please. But if their measures are so heavily dependent on their own vices, then it's hard to blame the mathematical properties of the measures, rather than the vices that went into selecting them, for any conclusions drawn from them.

Posted by: Dan Simon | Dec 30, 2007 2:40:16 PM

Well put . . . but I wonder, is intelligence really "distributed" according to a bell curve, or are the tests simply set up so as to provide that distribution? In practice I think there are a heck of a lot more dumb folks than really smart ones. But you're certainly right that the rewards are infinitely more skewed than the talent, and that may indeed have something to say about happiness or lack of it.

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