March 22, 2005
Power Slaw

united states income distribution

That's the most depressing power law curve I've ever seen [via Ben Hyde].

It looks like two straight lines, but it's actually an astronomically steep curve that shows just how inequitably income, and power, are distributed in the US. And Alternet reports that the curve for wealth (accumulated income) is much steeper even than the income curve shown above.

Posted by jjwiseman at March 22, 2005 11:08 PM

"inequitable income distribution"

inequitable, adj: not equitable, unfair. (

I'm always curious, when I see remarks like this, how the speaker would go about making the distribution more "equitable" and "fair".

Posted by: Larry Clapp on March 23, 2005 04:27 AM

Ben forgets that in the US it is possible to take the risks and exhert the effort necessary to join those in the vertical line.

His effort would be better spent generating wealth than stirring up a mob to take someone else's.

Posted by: Ed Symanzik on March 23, 2005 05:29 AM

Who cares? Why are you interested in diminishing the income *difference* between the 'poor' and the rich, instead of in raising their *abolute* income? You do know that envy is a relic from the stone age, when people lived in small groups, and in not utile any more in a modern catallactic economy?

Posted by: Illuminatus on March 23, 2005 05:45 AM

It's fascinating how hard it is to discuss this stuff without people trotting out all the groundless cliche'd arguments. I mean gee, I make a posting about how people aren't visualizing the long tail very well and I get accused of envy? Weird.

For heaven's sake, the other example given in my posting is the distribution of last names! The last example I posted in detail on my blog is the distribution of earthquakes.

If you want to architect your society to shape these distributions (and other measures like growth, mobility, heterogeneity, whatever) there are plenty of examples. Just sample various regions of the planet. The variations are wide. Vile design patterns appear to have very more severe distributions - communist countries, lawless low-government regions, dictatorships, fascist states, etc. Shop around, pick a functional model and labor for that.

Posted by: Ben Hyde on March 23, 2005 07:04 AM

This is a classic example of how to lie, or at least mislead, with statistics. The only information actually conveyed by this graph is "someone makes ~$180M, there are are more than 120M households, and almost all of those households make less than $1M per year". Well yes, actually. So what? A million dollars per year in income is rather a lot of purchasing power. Is it really that surprising, or even undesirable, to have the top earner in a country of ~300M makes ~200x the millionth biggest earner? Is earning less than that much per year a terrible hardship? I would tend to say no, and would add that there are lots of worse things than 120M households earning less than $1M per year-for example, 30M households earning less than $20K per year. I think both are true of the income distribution of the US.

If the vertical scale were changed to a reasonable dimension, like thousands of dollars, 2 things would happen:

1: A "square curve" would actually mean that the overwhelming majority of the nation was desparately poor, not that the overwhelming majority was not rich.

2: The curve would no longer be square.

This would be a net loss, if you were trying to make a largely content-free rhetorical point, and a net win, if you were trying to take a reasonable look at income distributions and poverty in america.

Posted by: matt knox on March 23, 2005 10:38 AM

Golly, forgetful, envy and now lying. I am a troubled dude!

The point of my posting, and some others I've made in this domain is that these power-law distributions are extremely hard to visualize. For example the distribution of first names is similarly distributed and I talk about that example here:

While a log-log chart is a very helpful view is hardly any help in letting people get useful intuitions about these things.

Now the suggestion that the vertical scale would be better in some larger unit, say thousands. All that does is have the effect of assure we ignore the wealthy. That might be fine if they didn't capture such a large proportion of the total economic output; because they do it seems a big mistake to make drawings that push them off the top of the screen an up into the stratosphere.

In 1970 the top 1% held 13% of the total wealth; in 1995 they held 38%. The trends are clear. The reasons are clear. In that drawing the area between the curve and the axis constitutes the total income generated by the economy. I find it mind boggling how much of it is on the left edge. It's not lying to attempt to make that clear.

Posted by: Ben Hyde on March 23, 2005 11:30 AM

Nice work, Ben.

It is amazing how spastic people get when they are suddenly challenged with hard data that does not fit with their world view.

Once people see the reality of unequal wealth distributions, they start to froth at the mouth about people taking away their "hard earned" money.

There are a whole host of possible social and economic policy measures that could be explored which are quite far away from simply taking away money that people have "earned".

You hit it right on the head when you ask what a desirable income distribution looks like and how could we make that happen?

I wonder how many of the people frantically clutching their pile of money "earned" it by swimming to an uninhabited island and digging gold out of the ground with their bare hands.

I suspect that would be none of them. The rest "earned" their money by participating in a very large and very old social and economic system, built through the efforts of many, many people. It seems such an obvious point that it is sad it needs to be made. No person lives and works in isolation.

William Gates, Sr. on his support of estate taxes:

"But let me talk about values. We started off a long time ago in this country on the theme that it was not a good thing to have a small number of people at the top who were enormously wealthy, and I think we continue to believe that that's not a healthy situation...

...Well, beyond the leveling issue, there is a question of the role of taxation.
The business of being wealthy, if you look at it fairly, is a direct function of the contribution that government makes.

Government creates markets that are stable and can be regulated, it educates our children, it gives us law and order and a court system for resolving our disputes, it funds research that gave us the Internet and genomic research, which created huge fortunes, even the Air Force that flies over our heads and keeps us safe. It's those "freebies" that are created by tax dollars.

The fact is that their wealth, their comfort is largely to be credited to the circumstances in which they grew up."

His book:

Posted by: tensegritydan on March 23, 2005 11:56 AM

You are also forgetting that wealth is not 'distributed'; it must be 'produced'.

Posted by: Illuminatus on March 23, 2005 01:35 PM

The notion that wealth is distributed, is also a relic from prehistoric psychology.

Posted by: Illuminatus on March 23, 2005 01:37 PM

No, the real story is really here:
a log-log scale of the one you showed.

Posted by: Igor Carron on March 23, 2005 02:14 PM

I highly recommend "The Millionaire Mind" ( to debunk everything you thought you knew about millionaires.

For example, the book shows that only an insignificant percentage of millionaires got rich through inheritance. Also the book discusses the factors that contributed to the success of millionairs.

Note that, even if they did get rich through inheritance, this does not diminish the wealth of others.

Re: Envy. I was not reffering to *you*, I was reffering to Mr. Lemonodor, who selected the income distribution graph and called it "the most depressing power law curve I've ever seen". This is not an objective statement, but a value judgement.

Posted by: Illuminatus on March 23, 2005 02:18 PM


surely you'd agree that taxes are a means of wealth distribution?

perhaps its depressing because it would be hard to get to the top-left side of the curve
depressing because finding the best fit equation for the curve was very simple
depressing because he's at the top left part of the curve and realizes he has to interact with poor schmoes all day long
depressing because he's an anarcho-syndicalist who sees the violence inherent in the system

Arthur: Old woman!
Dennis: MAN!
Arthur: Man, sorry. What knight lives in that castle over there?
Dennis: I'm 37.
Arthur: What?
Dennis: I'm 37! I'm not old!
Arthur: Well, I can't just call you "man".
Dennis: You could say "Dennis".
Arthur: I didn't know you were called Dennis.
Dennis: Well you didn't bother to find out, did you?
Arthur: I did say I'm sorry about the old woman thing, but from behind you looked...
Dennis: What I object is to you automatically treat me like an inferior.
Arthur: Well, I am king.
Dennis: Oh, king, eh - very nice. And how'd you get that, then? By exploiting the workers! By hanging on to outdated imperialist dogma which perpetuates the economic and social differences in our society. If there's ever going to be any progress...
Woman: Dennis, Dennis! There's some lovely filth down here. Oh, how'd you do?
Arthur: How'd you do good lady? I am Arthur, king of the Britons. Whose castle is that?
Woman: King of the who?
Arthur: The Britons.
Woman: Who are the Britons?
Arthur: Well, we all are. We are all Britons and I am your king.
Woman: I didn't know we had a king. I thought we were an autonomous collective.
Dennis: You're foolin' yourself. We're living in a dicatorship! A self-perpetuating autocracy in which the working class...
Woman: Oh there you go bringing class into it again!
Dennis: That's what it's all about! If only people would realize...
Arthur: Please, please good people. I am in haste. Who lives in that castle?
Woman: No one lives there.
Arthur: Then who is your lord?
Woman: We don't have a lord.
Arthur: What?!
Dennis: I told you. We're an anarcho-syndicalist commune. We take it in turns to act as sort of executive officer for the week.
Arthur: Yes.
Dennis: But all the decisions of that officer have to be ratified at a special biweekly meeting...
Arthur: Yes, I see. a simple majority. In the case of purely internal affairs...
Arthur: Be quiet.
Dennis:...require two thirds majority. In the case of old ladys...
Arthur: Be quiet! I order you to be quiet!
Woman: Order, eh? Who does he think he is?
Arthur: I am your king!
Woman: Well, I didn't vote for you.
Arthur: You don't vote for kings.
Woman: Well, how did you become King, then?
Arthur: The Lady of the Lake,... [Angel chorus begins singing in background] her arm clad in the purest shimmering samite, held aloft Excalibur from the bosom of the water signifying by Divine Providence that I, Arthur, was to carry Excalibur. [Angel chorus ends] That is why I am your king!
Dennis: Listen. Strange women lying in ponds distributing swords is no basis for a system of government. Supreme executive power derives from a mandate from the masses, not from some farcical aquatic ceremony.
Arthur: Be quiet!
Dennis: óbut you can't expect to wield supreme executive power just 'cause some watery tart threw a sword at you!
Arthur: Shut up!
Dennis: I mean, if I went 'round saying I was an emperor just because some moistened bint had lobbed a scimitar at me, they'd put me away!
Arthur: Shut up, will you? Shut up!
Dennis: Ah, now we see the violence inherent in the system!
Arthur: Shut up!
Dennis: Oh! Come and see the violence inherent in the system! Help! Help! I'm being repressed!
Arthur: Bloody peasant!
Dennis: Oh, what a give-away. Did you hear that? Did you hear that, eh? That's what I'm on about. Did you see him repressing me? You saw it, didn't you?

Posted by: paul on March 23, 2005 02:44 PM

larry clapp -

Design an equitable distribution of wealth (not method for or whatever) before you are born, not knowing whether you'd be born a white male to middle or upper class parents in the US, or a woman in saudi, farmer in China, or one of the other 6.4 billion backgrounds you could choose from people living today

Posted by: paul on March 23, 2005 03:03 PM

I don't think Ben is troubled, but rather that his graph sacrifices content for impact. The square curve looks really scary, but looking at the scale, one notes that it does not really say anything about poor people. It says something about at least one very rich individual (namely, that he gets something like 100x the income of the millionth highest earner in the US.), but nothing about the people 'below'. In fact, this curve doesn't even show that there ARE any poor. This graph would look exactly the same in 2 very different instances:

1: the other 99% of the US has an income of around $1-3M

2: the other 99% has an income of $0

2: would indicate a horrendous inequality and terrible hardship for most of the US, while 1: looks pretty close to paradise-everyone is rich!

Had I done the graph, I would have had the vertical scale denominated in thousands. Then I lose the arresting apperance of the square curve, and I cannot distinguish between someone who makes $200K and $200M, but on the other hand, I would now show that there are a very large number of people who are terribly poor, which Ben's graph does not do.

I did not complain that the graph conveyed information that I did not like-I complained that it did not convey as much as it could have, with a better choice of scale. The fact that he chose his scale as he did seems to suggest that he is troubled by the fact that there are people who are very wealthy, and not by the fact that there are many more who are very poor. That seems odd.

Posted by: matt knox on March 23, 2005 04:28 PM

I have never used Lisp before, but whenever someone mentions it, I'm willing to be closedminded, defensive and verifiably lie. Java and XML have proven themselves to be the best; many brilliant people use them. Just plain technological darwinism. Java and XML have problems, but everything is worse.

Anyway, some may enjoy this following link. Technerds and other professionals apparently form a third economic class, which views capitalists as obstacles to attaining genius (as we see in Dilbert, Paul Graham's recent book, etc), and workers as.. dumb.

Posted by: Tayssir John Gabbour on March 23, 2005 04:46 PM

Incidentally, I'm not talking about anyone discussing here, just something I frequently notice when people discuss economics, programming, or a few other subjects which have enormous reality distortion fields constructed around them. ;)

Posted by: Tayssir John Gabbour on March 23, 2005 04:54 PM

Are you joking, or serious? (if you are joking, then sorry for my being tired and dumb.) There is a pretty tenuous connection between popularity and most kinds of "fitness"-Dvorak is a demonstrably better keyboard layout for typing (although it lags badly if the goal is to develop RSI), and common lisp is demonstrably better at rapid prototyping than C or java, but qwerty keyboards and java are overwhelmingly more popular for those respective purposes.

Posted by: matt knox on March 23, 2005 06:42 PM

Oh, just being a sarcastic jerk. ;) I'm likening reactions to economic issues, to the kneejerk reactions of programmers upon hearing about Lisp. I've frequently heard people lie repeatedly and verifiably about Lisp, in an attempt to dismiss it; it's not conscious lying, but they repeat such verifiably wrong things with fervor, that it should be considered a form of lying.

People do the same with discussions of economic models. I'm not saying anyone here frothed at the mouth, just that it happens often in other places, and there's a small tinge of that defensiveness even in this discussion.

For example, I thought your first post was certainly thoughtful and looked at detail. But I also think it had an element of dismissing this graph's point... which is that this power graph was unusual in how fast it sloped downwards. Now, taken constructively, your criticism gives an idea for a second graph, which perhaps would be more informative. But I think this birds-eye graph was certainly fair in itself. Graphs are often useful to show, at a quick glance, that something is interesting enough to look more deeply at.

But alone, in today's ideological and hostile discourse, I suppose this little graph would be called propaganda.

Posted by: Tayssir John Gabbour on March 24, 2005 01:52 AM


I didn't say I had a plan, or that Any Idiot could easily redesign the world economy, I just wondered if the person speaking about inequitable distribution had a plan. I'll grant you, I did have a hint of sarcasm in mind when I posted that, but I also honestly wanted to know. (Actually, I guess that's not entirely true -- I suspect I could find out if I *really* wanted to know. I guess mostly I'm curious whether the speaker had a plan at all or just felt like indulging in some anxious hand-wringing. "Gosh, things are awful. Someone should do something!" Great! What?)

How about "from each according to his ability, to each according to his need"? ;) Okay, *maybe* an interesting idea, but difficult to implement in practice.

How about "You exist. We guarantee you nothing. You will be distributed randomly over the planet. You may seek to add meaning to your existence in any way you choose. Note that some may choose differently than you."

Hmmm, I guess both of those would qualify as systems, not distributions.

Actually, specifying an equitable distribution seems like the easy part: everyone has nothing, or everyone has an equal share of everything, or everyone gets a random birth placement and gets to work their way up (or down) from there. Designing the system to achieve the first is easy: Nuclear Weapons at 50 paces. The second is very hard, and not actually very equitable, anyway. The third -- gosh -- seems a lot like what we actually have.

Posted by: Larry Clapp on March 24, 2005 05:18 AM

So all this time I've been working under the illusion that wealth is earned, and now I find that it's in fact distributed. Where do I sign up for my disbursements?

Posted by: Andreas Yankopolus on March 25, 2005 11:31 AM

actually there is something I did not know about pareto's law here:


Posted by: Igor Carron on March 25, 2005 01:59 PM

"working under the illusion that wealth is earned" I wrote about that 'illusion' a few years ago here - - the actual facts of what the statistics are for getting rich are apparently extremely foggy; but being born well seems to dominate everything else.

Posted by: Ben Hyde on March 27, 2005 11:44 AM

As you mention, picking good parents dominates just about everything, whether it's obtaining wealth or becoming an NBA star. Sure, the chances of me ever equalling the net worth with which Paris Hi1ton was born are slim to none, but applying myself in the right direction (i.e., earning wealth) seems like a more responsible approach than waiting for the government to take money from someone else and give it to me (i.e., distributing wealth). Our system is somewhat unfair, but the alternatives strike me as worse.

There's also my uncle's sage advice as one potential quick fix: "You can marry more money in five minutes than you can make in a lifetime."

Posted by: Andreas Yankopolus on March 30, 2005 08:06 AM

Government certainly does have powerful tools to shape that curve.

Posted by: Ben Hyde on April 1, 2005 11:08 AM
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