Some inequalities are more unequal than others

John Rentoul and others have been talking about economic inequality. John argues that the Gini coefficient is “the only statistical measure that captures the full extent of inequality in any population. Any other measure, such as 60 per cent of median income or the ratio between the 10th and 90th decile points, would fail to do this.”

 

In a sense that’s true, but for me the Gini coefficient’s strength is also its weakness. It gives you a single number for inequality in a population (from 0, meaning everyone is completely equal, to 1, meaning one person has everything) – but it can’t tell you whether that inequality is because the people at the bottom are a long way behind or the people at the top are a long way ahead.

 

For instance, these two sets of numbers both have a Gini of 0.13:

• 5, 21, 22, 23, 24, 25, 26, 27, 28, 29
• 21, 22, 23, 24, 25, 26, 27, 28, 29, 52

If we want to measure economic inequality meaningfully, we mustn’t treat it as a single phenomenon. If the very rich are racing ahead, then that’s quite a different thing from the very poor falling behind. These two phenomena have different causes and different consequences – and, if we want to do anything about them, different policies will be needed.

 

So I propose that rather than looking at a single Gini coefficient for everyone, we break the population down into, say, fifths. We look at the Gini among each group, from the poorest to the richest, and see how they compare.

What follows is a very crude attempt to do that (this post develops an idea I had a few years ago).

 

I start with this chart from the Institute for Fiscal Studies [PDF], showing household income for different percentiles of the population:

 

 

Unfortunately, the numbers that went into the chart aren’t given. So by measuring the size of the bars (I told you it was crude), I’ve reconstructed it:

 

 

It looks about right. Note that I’ve added a bar for the richest 1%, not shown in the original – perhaps because those people are hard to get data on. I’ve assumed that the gap between 99 and 100 is the same size as the gap between 98 and 99 (which I’m sure is a conservative assumption).

 

And, treating each percentage point as an individual, the Gini coefficient for these 100 numbers is 0.33. The IFS report gives the Gini for the whole population as 0.34, so again, I feel confident that my reconstruction of the numbers is about right.

 

Now I can break this down into five groups, from the poorest 20% to the richest, and calculate and compare the Gini coefficients across the spectrum:

 

  

The greatest inequalities are at the top and the bottom of the scale. To see the size of these, we can look at ratios: the Gini at the bottom is 3.6 times as high as the middle one; the Gini at the top is 4.9 times the middle one.

 

It would be good to see how these ratios have changed over time, and how they vary between countries. But here I really do run out of even approximate data. If better people than me agree that this approach is worthwhile, then I encourage them to give it a go.

 

One thing I feel confident in saying, though: John reproduces an IFS chart showing the distributional impact of government policies, and guesses that “overall inequality, as measured by the Gini coefficient, would be more or less unchanged”.

 

Maybe. But taking my approach, the government’s policies look like they’ll reduce the Gini at the top and increase it at the bottom and in the middle. The gap between the very rich and the fairly rich may fall, but all other gaps will grow.

The sense of unease: an open letter to David Davies MP

Dear David,

When I first saw your views on sexuality reported a few weeks ago, I took you to be a bog-standard old-fashioned Tory bigot who was worth no more of my attention than the time it took to write an angry tweet.

But in your interview today with Decca Aitkenhead – a cracking read – you come across differently. You seem more like someone who’s willing to engage on the subject, and to be engaged with. So, in a spirit of seasonal goodwill, I’ll give you the benefit of the doubt. And, even though ‘open letters’ are generally silly and pompous, and there’s a near-zero chance of you reading this, I’m writing anyway.

Because I think you do speak, in your own uncertain way, for quite a lot of people.

I personally don’t understand prejudice, of whatever kind, against homosexuality. From the thug wielding a baseball bat to the priest wielding Leviticus, I just don’t get the motivation. But I think most of the people who have a “sense of unease” (as you put it) about gay people aren’t near either of those ferocious extremes. You seem to be generally well-meaning, but you don’t like the thought of gay relationships and you find it very hard to say exactly why.

Here’s some of your interview:

His big worry about gay marriage, he explains, is that it will necessitate a revision of sex education. … He looks down and shifts awkwardly. "But I suppose, at a certain level, I see heterosexual sex as being – and it's probably the wrong word to use – but the norm. I think it's reasonable to say that the vast majority of people are not gay." He hesitates, sighing. "I just worry if children are going to be taught that [heterosexuality] isn't necessarily the norm, and that you can carry on doing all sorts of other things, are we going to have a situation where the teacher's saying, 'Right, this is straight sex, this is gay sex, feel free to choose, it's perfectly normal to want to do both. And you know, why not try both out?' I mean, are we going to have that?
…
"I suppose what I'm trying to say, in a very clumsy way, which will again probably cause offence, is that some people might be going through a bit of a funny phase between the age of 15 and 20 when they're not sure. And I'm not absolutely convinced it's a good idea to be changing sex education in school to try and say to people, 'Feel free to go out and experiment and do this, that and the other.'"

Here’s a thought or two in response:

Talking about sex can be awkward and embarrassing. Talking about sex to children is even more so. I don’t have kids myself, but if I do someday then I’m sure that I’ll spend a long time mentally cringing in anticipation of The Talk.

One thing that might make that talk a little bit simpler would be if there were only one type of sexuality. Because where there’s variety, you have to explain the variations and how they differ. And then you have to start getting into orifices – so to speak – and talking about sex in perhaps more graphic detail than you’re comfortable with.

But the things you’re worried about would still exist even if there were only one type of sexuality.

Lots of young people have sexual partners who turn out not to be right for them. Some of these they go on to bitterly regret, others they look back on as learning experiences. It takes plenty of us a while to figure out what, or who, we really want. ‘Experimenting’ has become a euphemism for trying out a different sexuality, but in reality it covers so much more than that.

And sex education could in theory take any position on promiscuity, even if we took differences of sexuality off the table. As it is, the Department for Education guidance says:

Effective sex and relationship education does not encourage early sexual experimentation. It should teach young people to understand human sexuality and to respect themselves and others.
…
Teachers should be able to deal honestly and sensitively with sexual orientation, answer appropriate questions and offer support. There should be no direct promotion of sexual orientation.

That seems fair to me (although let’s not overestimate what effect teachers can have on teenagers here). Sex education shouldn’t encourage kids to try all sorts of different things with all sorts of different people, but it also shouldn’t tell them that they ought to be a certain way and that they’re abnormal if they aren’t.

This takes me on to what you said about heterosexuality being the “norm”.

You struggled with that word, and it’s understandable that you did. Sometimes people use “norm” and “normal” in a purely statistical way, about whether something is common or uncommon. And, at an estimated 5-7% of the population, people who are gay, lesbian or bisexual are definitely a small minority. But that’s hardly rare: one or two out of an average classroom.

But “norm” and “normal” also often carry a sense of moral judgement, implying that what’s different – or abnormal – is inferior or wrong. Do you believe that? I don’t think so. In the seven byelections this year, about 4% of people turned out to vote Conservative. The fact that they were in a small minority didn’t make them wrong to do so.

So when it comes to the question of what to teach children, my answer is: facts. Most people are heterosexual. Some aren’t. And as for what sorts of relationship are acceptable, we should teach children what the law says: gay and straight alike are OK.

There are lots of gay people. Even 5-7% works out as 3 or 4 million people in Britain. They have friends, families, neighbours, jobs, cars, mortgages, gas bills, votes and all the things in their lives that straight people have as well. They are part of society.

I think it would be best for all of us – especially any children or grandchildren you or I might have who might grow up to be gay – if our attitudes as well as our laws accepted gay people as full, equal members of society. I think that part of the way to master the “sense of unease” is to appreciate that we don’t need to share someone else’s tastes, or even understand them, in order to accept them.

I’m glad you’ve changed your mind on Section 28, on the age of consent and on civil partnerships. And I applaud your openness about your doubts – there should be a lot more of that in politics.

I hope that you’ll keep thinking, and that you have a merry Christmas.

Tom

The unspoken fallacies of the Second Amendment

The Second Amendment of the US Constitution is odd. It’s odd because, unlike all the others, it doesn’t just declare a right: it also gives a reason; it makes an argument.

A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.

Everything up to “State” is a preamble, a statement of fact (or apparent fact) that justifies the statement of the right that follows. (It’s probably best to ignore the first and third commas: people used a lot more of them back then.)

This needs a bit of unpacking. The argument implicit in the Second Amendment is this:

(a) We want the state to be secure.
(b) A well-regulated militia is necessary to the security of a free state.
(c) The right of the people to keep and bear arms is necessary for there to be a well-regulated militia.
Therefore:
(d) The right of the people to keep and bear arms shall not be infringed.

(a) is unstated, but as a general principle it’s completely uncontroversial. (b) is stated, albeit in the form of an absolute clause. (c) is unstated, but is the essential logical link that joins (a) and (b) to (d). And (d) is stated as the main clause of the sentence.

There are two obvious problems with this: (b) is not true and (c) is not true.

First, (b). There are plenty of free states that manage to be secure without having a militia (something distinct from the regular armed forces). It is also hard to argue that what remains of the US militia really makes that essential difference to national security.

Second, (c). It is perfectly possible to have a militia without the general population having the right to keep and bear arms. Local militia organisers could very easily look after the weapons and distribute them at the first sign of the invading English. Also, given that not all citizens would be in a militia, any right to arms need not extend beyond militia members.

Therefore (d) is not justified: the need for the people to have the right to keep and bear arms does not follow from a platitude and two historically short-sighted falsehoods.

And yet there it is, in the Constitution, in black and white.

And so I come back to the oddity of the Second Amendment: uniquely, it doesn’t just state a right but also gives a reason for that right. But it doesn’t therefore follow that the right legally depends on the stated reason.

My objections above are factual and logical. They are not legal objections. I don’t see that my argument justifies an interpretation of the Second Amendment that lets only members of well-regulated militias have access to guns.

What I do see is that this tragic piece of law, which seemed reasonable in 1789 but is now so drenched in the blood of innocents that its existence is an ongoing threat to the security of a free state, should be repealed.

Byelection results

Because turnout in byelections is usually so low, a handy way of looking at them is to see how much of a party’s previous vote it manages to hold onto.

For instance, in Rotherham last week, the Lib Dems got 2.1% of the vote on a 33.9% turnout – that’s 0.7% of the electorate. Back at the 2010 general election, they had managed 16% of the vote on a 59% turnout – that’s 9.4% of the electorate.

So they lost 92% of their previous support. On the same measure, the Conservatives dropped 81% and Labour – even though their vote share was up – dropped 53%.

The other defining feature of byelections is that they’re local elections for local people, and you shouldn’t generalise from any one result. But averaging across all the byelections that happen during a parliament is a bit more informative.

The chart below shows how much of their previous vote the parties lost (or, in some cases, how much they added to it) at byelections in the last eight parliaments:

The obvious points are that governing parties do particularly badly, and the Lib Dems (or their predecessor parties) have sometimes made impressive gains. Until now.

After only two years in government, the Conservatives are doing as badly as John Major did, and the Lib Dems are doing even worse. Labour are doing better than when they were in power, but not as well as during most of their last period of opposition.

Update: I've been asked if I could do a similar chart showing the conventional change in the share of the vote - so the Lib Dem fall in Rotherham from 16% to 2% would count as -14%. I think this is less significant, because the numbers are more easily distorted by the variability of the starting points of the constituencies that happen to have byelections.

For instance, across the 12 seats that have had byelections since 2010, the average starting point was Lab 46% Con 24% LD 19% - an unrepresentatively low start for the Tories, meaning that in these seats, there was a limit to how far they could fall. That's why I looked at how far the parties had fallen relative to their original positions.

But with that caveat, here's the chart:

And, while I'm here, below is a version of the first chart but disregarding changes in turnout. It shows the change in vote share as a percentage of the previous general election vote share. So the Lib Dem fall in Rotherham from 16% to 2% of the vote counts as -87%.