What is the top-heaviest country?

This post is based on an interesting Twitter thread about country populations! In particular, this pair of tweets from Josh Fruhlinger:

It’s an interesting thing – how top-heavy is a country or federation? In other words, how much of the population is concentrated in its largest constituents?

If you look at the population breakdown of the US and the EU, you can see a difference. In the US, the largest state, California, is nearly 50% larger than the second largest, Texas, and it’s 68 times larger than the smallest, Wyoming. However, California only makes up 12% of the US population. Germany, the largest EU member state, is only 22% larger than the second largest, France, but it’s 186 times larger than Malta, the smallest EU member state, and makes up 16% of the EU.

The average EU member state would be 18 million people, while the average US state would be 6.5 million people. The EU has lots of big countries at the top and small countries at the bottom, but relatively few average sized countries – only Netherlands and Romania are within 10% of the mean. The US has far more states around the mean, even accounting for the greater number of states total – there are seven within 10%.

Instinctively, it looks like Josh is right – the EU is more top-heavy than the US. But is there a way to quantify this? Thanks to economics, yes!

The Gini coefficient is a popular measure of inequality, normally used in economics to assess income inequality across countries. I’ll put a slightly more detailed statistical explanation at the bottom of this post, but in short, all you need to know is this: a score of 0 means perfect equality – each person in the country has the same wealth, or in this case, each constituent part of the federation has the same population – and a score of 1 means perfect inequality – one person/constituent has everything, the others all have next to nothing. To be clear, in this post I’m using it to calculate population inequality, not wealth inequality.

I calculated the population Gini coefficients for the EU and US. They are:

EU: 0.61

US: 0.50

The EU’s population really is more unevenly distributed and top heavy!

But why stop there? There are plenty of other countries and international organisations to have a look at.

First, the world population Gini coefficient. How unevenly distributed is the world population, from 1.4 billion person China to 800 person Vatican City?

World: 0.80

Ouch. That’s our baseline. You can’t do worse than that, right?

Let’s have a few European countries:

UK: 0.61

France: 0.46

Germany: 0.46

Netherlands: 0.74

Poland: 0.32

After WWII, Germany’s borders were deliberately redrawn to ensure that no one state could become almighty, as Prussia did in the old German Empire (population Gini 0.85 in 1900!), but surprisingly it’s no more equal than France.

The UK’s population Gini coefficient is surprisingly low actually, given that fully 85% of its population lives in England. I think this might be partly because of a shortcoming of the Gini coefficient – it’s meant to be used for almost continuous data with lots of data points. For the UK, there are just four subdivisions – England, Scotland, Wales and Northern Ireland. This seems to break the maths a bit. The Netherlands is even more top-heavy, with 98% of its population in one part (European Netherlands), but again, there are just 4 constituents – Netherlands, Curacao, Aruba, Sint Maarten – which seems to limit the Gini coefficient a bit.

Also, I just want to say that Polish provinces are called “Voivodeships”, and that’s one of my favourite words ever.

We can also try using the statistical subdivisions of England. These were created to make England a bit easier to manage – but they were also designed to have roughly equal population. This is cheating a bit, but lets try it out, and compare it to French departments (also meant to have roughly equal population) and Dutch provinces.

UK (regions): 0.21

France (departments): 0.39

Netherlands (provinces): 0.39

So the UK regions really do make the population stats much fairer, but they do have the disadvantage of requiring you to always say “Yorkshire and the Humber”.

Let’s turn to Asia:

Russia: 0.46

Japan: 0.46

China: 0.39

India: 0.62

Wow, 0.46 really seems to be a magic number, huh? India’s huge Gini isn’t surprising – Uttar Pradesh, with 200 million people, is larger than most countries, while Lakshadweep, with 65,000, is smaller than Andorra. China’s seems low to me, but it’s true that away from its mountainous desert west, it’s quite evenly populated – a sea development across the flat east.

We can go lower though:

Nigeria: 0.23

Nigeria regularly redraws its state borders, so it’s no surprise that they are also very even. The largest state, Kano, is just seven times the smallest, the Federal Capital Territory.

Can we go higher?

Some island chains have ludicrously high population Ginis, since almost the entire population lives on one island:

Marshall Islands: 0.72

Bahamas: 0.86

70% of the population of the Bahamas live on the island of New Providence, the rest are scattered across 30 tiny islands, each with its own local government. The Bahamas population distribution is actually more unequal than the world population distribution as a whole! But… it’s a bit of an odd case. It’s a quirk of geography that the country is broken into these islands, nothing more.

Let’s have a look at some international organisations:

USSR (in 1979): 0.70

African Union: 0.62

Commonwealth of Independent States (the ex-Soviet one): 0.64

Commonwealth of Nations (the ex-British Empire one): 0.88

The AU and the CIS are quite close to the EU in terms of population spread. The USSR was very Russia-centric, as its Gini shows, but just look at the Commonwealth!

The population inequality in the Commonwealth is actually greater than in the world as a whole! How is this possible? I think this is a quirk of colonialism.

There are two main types of country in the Commonwealth: gigantic continental colonies like India (with 1.3 billion people, it dominates the Commonwealth), Pakistan and Nigeria, and tiny islands like the West Indies. Middle sized countries, with a population between 1 and 10 million, are actually underrepresented, making up just 11 of the 52 Commonwealth states. Countries over 10 million make up 19, those under, 22. In colonial terms, it made sense to agglomerate states on land, regardless of whether they crossed ethnic/tribal borders. So, the Commonwealth ended up hugely lopsided.

Here are some Lorenz curves, a way of showing inequality graphically. In a perfectly equal country, the population distribution will follow the straight diagonal line. The more its line curves away, the more unequal it is. You can select lines from the legend to highlight a particular country. Enjoy!

(You may have to turn your phone sideways to see this graph)

* Still here? Want to know about Gini? So, first you need to know how a Lorenz curve works. Imagine if everyone in the country was asked to deposit their wealth in a giant piggy bank, starting with the poorest and working up to the richest. If everyone had the same amount of money, the level in the piggy bank would rise steadily. Plotted on a graph, it would be a straight line. If a few people controlled all the money, the level would rise slowly right until the end, when suddenly it would shoot up, and you’d have a very sharp curve. The Gini coefficient is equal to the area between the Lorenz curve and the “perfect” line, divided by the total area under the total line. I am extremely grateful to the Excel and UDF Performance blog for the incredibly easy Fast Gini formula used here.

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