Why Average Incomes Tell Us Nothing About Real World Inequality

When the experts tell us that average incomes have risen, what does that actually tell us? Not much that’s useful in understanding real world politics and the inequities of economic life. I know that most of us understand averages, now don’t we? What’s there to explain? Well, let’s have a look at average incomes.

Incomes can be looked at using three measures of central tendency: the mean (the average), the median and the mode. For a technical explanation of these terms see: https://statistics.laerd.com/statistical-guides/measures-central-tendency-mean-mode-median.php.

Each of these measures has its advantages and disadvantages.  If we take a population and want to figure out their average height, it’s simple: measure each individual in the population, add the heights of all of them together and divide by the number of individuals measured. It’s unlikely that all people in a population would be of the same stature, and it doesn’t tell us anything about the range of heights. It’s always good to know what the range is otherwise there’s no way of judging just how variable the heights are in a population. Same goes for incomes. Scenario A below is of a fictitious population of income earners that each earns $100 thousand dollars each per year. That makes the total incomes earned by the group $1 million dollars and the average is $100 thousand. If you know where such a world exists, please let me know.

Scenario A  
Income Earner Income $ % of total income
Income earner 1 100,000 10
Income earner 2 100,000 10
Income earner 3 100,000 10
Income earner 4 100,000 10
Income earner 5 100,000 10
Income earner 6 100,000 10
Income earner 7 100,000 10
Income earner 8 100,000 10
Income earner 9 100,000 10
Income earner 10 100,000 10
Total Income 1,000,000 100
Average Income 100,000  

Now, let’s consider Scenario B below. The total income of all ten earners is still $1 million and the average is still $100 thousand. What’s changed? The distribution. In this scenario, the highest income earner brought in $200 thousand while the lowest earner brought in $45 thousand. That’s a significant difference and means that there is substantial income inequality but if a government wanted to obfuscate rather than clarify the issue, it might want to argue that average incomes haven’t changed. What are you worried about?

Scenario B  
Income Earner Income $ % of total income
Income earner 1 200,000 20.00
Income earner 2 150,000 15.00
Income earner 3 130,000 13.00
Income earner 4 100,000 10.00
Income earner 5 95,000 9.50
Income earner 6 85,000 8.50
Income earner 7 75,000 7.50
Income earner 8 65,000 6.50
Income earner 9 55,000 5.50
Income earner 10 45,000 4.50
Total Income 1,000,000 100.00
Average Income 100,000  

Now, consider this third scenario. The total incomes are still $1 million, the average is still $100 thousand. However, in this scenario, the highest income earner is taking in 72.7 of the total income. This scenario pushes income inequality to a much greater degree.

Scenario C  
Income Earner Income $ % of total income
Income earner 1 726,990 72.70
Income earner 2 85,000 8.50
Income earner 3 45,000 4.50
Income earner 4 20,430 2.04
Income earner 5 20,430 2.04
Income earner 6 20,430 2.04
Income earner 7 20,430 2.04
Income earner 8 20,430 2.04
Income earner 9 20,430 2.04
Income earner 10 20,430 2.04
Total Income 1,000,000 100.00
Average Income 100,000  

Now, think of a situation where aggregate incomes rise, but the lowest earners retain their share of earnings at 2.04 percent. Now the government can say: What are you worried about? Your income hasn’t changed at all and the country is getting richer. Silly you. Maybe you should just work a little harder.

Calculating median income isn’t much more helpful. The median income is the point where half the incomes are above and half below. That will tell us if a population distribution is changing in broad terms, but the median income in scenario C is $20,430.00. What does that tell you about the distribution of incomes in this population.

Calculating the modal income is interesting. The modal income is the one that appears most often in a distribution. In scenario C, the modal income is clearly $20,430.00. That’s the income most people make. It still doesn’t shed much light on the inequality in a distribution.

So, we always need more than a measure of central tendency to tell us what’s really going on in the world in terms of income inequality. If the government, or the head of the Bank of Canada for example, tells you that average incomes are rising, know that you’re not being told the whole story.

If you’re not concerned about these things, never mind.

Note: this post was inspired by a section of Robert Sapolsky’s book: Why Zebras don’t get ulcers.

 

Which is better, Up or Down? North or South? Left or right?

Which is better, up or down? North or south? Left or right?

Well, technically, up and down are just words. Most of us think of them as neutral words that simply indicate orientation in space. They are that, but they also contain a political and moral side that is undeniable.

Left and right. Are they just words that indicate a direction from a fixed point in space but they also carry a load of political and moral baggage.

The reality is that left and right are not just neutral words that simply indicate direction. They are packed with poIitical and moral referents. In politics, we refer to socialist, communist and anarchist parties, movements and ideas as those occupying the left-wing of the political spectrum. We identify liberal and conservative ideas, parties and movements as more or less right-wing unless of course you’re a con troll. For con trolls (conservative internet trolls) everything on the left side of Ayn Rand is evil. This is all highly significant because of the qualities we normally attach to the words left and right without really thinking about it. Right is good, left is bad.

Right and correct are often used as synonyms. We use them interchangeably. So, what can we make of that? Right-wing parties are correct parties? It would seem so. At least that’s what the use of right in this context implies. Who sits at the right hand of God? Why, Jesus, of course, although sheep do too, apparently. Thomas Aquinus was quite concerned about the significance and the symbolism of right and left with reference to God. For some reason I remember the angel Gabriel as sitting on the right of God and Lucifer, before he was cast into hell, on the left. Was Lucifer the first leftist? [1] It makes sense, especially when you consider how the political right sees itself as truly moral and correct.

 

North and south are great examples of how words that are supposed to simply refer to navigational directions on earth, have become politically charged. The North is good, don’t you know. It’s cool, collected, upright, hard-working, morally impeccable and just as pure as the driven snow. The South, by contrast, is hot, lazy, unpredictable and morally suspect leaning towards nudity and hedonism. So, where do northerners go to vacation and let their hair down? Why, to the hedonistic south, of course. And, if you look at any regular map of the globe, north is always on the top. Strange, but when I see photographs of planet earth taken from space, I don’t see those distinctions.

I’m left-handed and us lefties, aside from being called sinistral, are often referred to as southpaws. The implications of this use of language is clear: left-handers are somehow morally suspect.

So, north is up and south is down. Go figure. Up and down are two other words that were initially intended to simply indicate direction, but have been recruited for political purposes over the years. Who knows exactly how that happens, how these language uses evolve, but they do, and they serve political[2] ends. We see them as being natural, neutral and anything but controversial, but they have their nasty side. If I’m feeling particularly chipper one day, I’m said to be ‘up.’ If I’m a little depressed because I just lost my job, I’m thought of as being ‘down’. “What’s wrong, why are you looking so down today?” Sheesh.

There are many more examples of politically charged words parading as neutral. Just think of east and west, over and under, standing and lying, top and bottom. I’ll let you think of others.

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[1] See: https://www.quora.com/Handedness-Why-was-there-prejudice-against-left-handed-people. Quora is not always a reliable source of information, but in this case, reliable enough.

[2] By political here I mean simply the distribution of power in society in a very broad sense. Politics is everywhere there is imbalance of power and some people have more executive license than others, more privilege, more resources, and, in their minds at least, the moral high ground.

Do I want to learn?: Some random thoughts from my 2000 notebook.

My whole life has been a quest to know. I have always wanted to learn. And I have learned a great deal. The question is not a general question about learning. The question is whether or not I want to learn and to finally know the way through the loneliness of an unbalanced life. Finally is probably not the correct word because finality is an illusion.

I always knew that there was a connection between body and will or body and mind. I knew it but I needed to taste it, to hear it, make it mine in the fullness of my senses.

How to dissolve the power of social pressure? Now that’s another question entirely. Life outside of society is impossible but society is rife with ideological traps like the need for immortality and its hero systems for the denial of death. I know this. But I haven’t made it mine yet. It sits in the front of my brain and resists trickling down into the pores of my skin and the cells of my nether parts. It sits isolated – knowledge without absorption. I may know what’s good for me, but that’s not enough. I need the will to transcend knowledge into experience, into life. I need to bind knowledge to the rest of me.

 

 

A language you cannot speak.

So, this has been on my mind for some time. I’ve long been interested in the origins of language and especially written language. There was a fascinating program on CBC’s Ideas program recently featuring Geneviève von Petzinger a paleo-anthropologist from the University of Victoria on ancient symbols found in caves dating some 30-40 thousand years ago. This is a taste of her ideas: Ice age symbols. Her research shows that it might be possible that the first modern humans had a form of abstract written communication. If that is so, many hypotheses about the first origins of human written communication are way off.

I’m sure that even at the very beginning of the process of human written communication there was only a small minority of people that could create symbols and probably not many more that could read them. Communications were all on a need-to-know basis. But written communication and literacy were a huge step in human evolution. Now, we all take language and writing for granted.

The invention of the modern computer has created an entirely new kind of exclusive language that is inaccessible to most people. Machine language with its on an off switches is completely incomprehensible to humans unless they have the code that makes all of the sequences of on and off switches mean something. We (humans) can communicate with our machines (computers) via certain interfaces but computers  actually don’t need human intervention to communicate with each other.

Take bar codes for example. The idea of the bar code was conceived of in the late 1940s but it wasn’t fully operationalized until much later. Now they are all over the place. They are used to track packages in transit, control stock and inventories, and contain medical records among many other uses. The machines that read bar codes don’t need human intervention to do so, but humans need an interface technology to know what the machines are doing.

I wonder how long it will be before machines begin to covertly, in the mind hive that is the internet, create their own language, one not accessible to humans at all. This 2 dimensional QR-code is my blog address: http://rogerjgalbert.com. Go ahead, scan it with your phone (you’ll need to download a reader to do that).

blogbarcode

It’s a symbol that computers (including my iPhone) can easily read. I don’t have a clue about what all the lines and squares mean. My computer knows all that. I think it’s akin to the process whereby humans first invented written, symbolic communication. Is this the kind of symbol that computers will use in their own communications devoid of human input? I don’t know, maybe it’s the plot of a new dystopian novel.