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The Census and what does 'rare' mean?
00:27:56
Why was the estimate, in 2003, for Eastern Europeans coming to the UK so wrong? Which...
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- [00:00]
Tim Harford
Thanks for downloading this edition of More or Less. This is the version from BBC Radio 4. Here's Tim Harford.
- [00:09]
Hello and welcome to More or Less opening the curtains and letting the light in on murky statistics and the lazy use of numbers. This week we commit an act of More or Less heresy by admitting that sometimes words are better than numbers. And we'll be wiping the smug smile off the faces of these laughing rats. But first, the census data released this week shows that the number of foreign born residents in England and Wales has risen by nearly three million since 2001 to seven and a half million people. A third of these new arrivals, that's one million, are from the European countries that have joined the EU since 2004. A few would have arrived before EU accession, but most came after. Compare this wave of immigration to the number the Labour government was expecting back in 2003. It said net migration from those countries would be between 5 and 13,000 each year. Even if the higher figure had been right, the total number would now only be 91,000, less than a tenth of the actual figure. So how did they get it so wrong? The estimate was based on work by researchers at University College London and the Centre for Research and Analysis on Migration. The problem was they had very little decent data to rely on. There were no migration figures for the 10 countries who were due to join in 2004. The team had to go on what migrants from other countries in different political and economic circumstances had done in the past. If you look at the original report, it's loaded with caveats, but alas, the politicians, the media and the chattarati don't do caveats. It's the number that people remember. The lead author was Christian Dustman. He says one of the difficulties was that migration would be heavily dependent on which other EU countries kept their borders open or closed to the new migrant workers. If others closed their borders, then the UK might well end up receiving extra migrants, which was, of course, what happened.
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Christian Dustman
We predicted net migrations to Germany to be in the magnitude of 200,000. We also pointed out in the report that in the case, migration to Germany would not take place because Germany would opt out of free movement of labor. And that is precisely what Germany did. A substantial part of that migration flow would be diverted to the uk. The estimates we gave, which again we pointed out, had to be taken with a lot of caution, was that possibly one third of the migration to Germany would have been diverted to the uk. Now for the largest scenario we had calculated for Germany, that would have been in the magnitude of about 70,000 net migration.
- [03:00]
Tim Harford
So that would nearly have doubled the estimate, which still wouldn't have taken this forecast close to the reality, as it turned out. Now, you might think it was obvious that a million people would show up when the UK opened its borders to migrants from much poorer countries in Central and Eastern Europe. But hindsight is a wonderful thing. Take Migration Watch, a pressure group concerned about excessive immigration. Migration Watch criticised the estimate of 5 to 13,000 a year and suggested that the true figure might be 40,000 a year. That's still less than half the eventual number. The census figures also give some context to a couple of stories pointed out by listeners from the last year. First, Greg Broadbent pointed us to this headline in the Daily Mail, Immigrant crime wave warning.
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Ruth Alexander
Foreign nationals were accused of a quarter of all crimes in London.
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Tim Harford
While Graeme Kendall also pointed out a similar headline in the London Evening Standard last month.
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Ruth Alexander
Foreigners make up more than a quarter of London's crime suspects.
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Tim Harford
A quarter sounds like a lot, but if you check the census figures, you can see that 24% of the population of London is made up of non UK nationals. So this would be pretty much what you would expect. You're listening to More or less on BBC Radio 4 in association with the Open University. Now, Nassim Taleb, author of Fooled by Randomness and the Black Swan, has a reputation for being violently allergic to economists. However, when I last interviewed him for More or less, both of us came away unscathed. We decided to extrapolate from this rather small sample and invite him back to tell us about his new book, Antifragile. Taleb is most famous for coining the phrase the Black Swan. So I began by asking him to explain what he means when he talks about black swans.
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Nassim Taleb
There are events that are very hard to predict, nearly impossible to predict and can carry massively large consequences. But after the fact, events are so explainable that you provide a narrative that gives you the illusion of the understanding of the world. And of course, we continue mispredicting. The mistake people made is to say, well, you know, let's try to predict them all right? You're not going to get there. And a lot of people who didn't see the crisis of 2008 coming keep thinking that sophisticated model was going to get somewhere.
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Wesley Stevenson
Let's predict the next PAX one.
- [05:15]
Nassim Taleb
Exactly. All right. So my point is about having systems that don't fall apart under these extreme circumstances, and that's much easier than predict anything.
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Wesley Stevenson
And this gets to the idea of the anti fragile System or the anti. So I love the idea that if I were to ask you an impertinent question and you took offence and you hit me, this would probably be very good for you. But if your publicist got upset with me, he's sitting very quietly in the corner of the studio. If he got upset with me and he hit me, this would be bad for him. And this is. I love this example from your book of anti fragile careers and. Fragile careers, exactly.
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Nassim Taleb
I was imagining that as an author, I hit someone and I beat him up, say physically, I'd be arrested probably. It'd be in the newspapers, my publisher would be thrilled. But if a minister, part of the government beats up a fragilista or something like that, he's gonna be in trouble.
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Wesley Stevenson
So the more trouble there is, the more disruption there is, the more you benefit. If you're a certain kind of person.
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Nassim Taleb
Exactly.
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Wesley Stevenson
You have a certain kind of career. And this of course is not just about people, it's not just about careers, it's about all kinds of systems.
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Nassim Taleb
Exactly. Let me define fragility. Basically, fragile is what doesn't like volatility. If you have a glass on a table, if the glass is fragile, if there's an earthquake, it's going to be harmed, it's not going to benefit from it. So it's like a package on which it's written, please handle the scare that's so fragile. Now the antifragile is a package on which you'd write, please mishandle.
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Christian Dustman
Yeah.
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Nassim Taleb
By definition, an antifragile system has to use errors as fuel. And unfortunately, when you have a system, the components of the system may suffer. So let's take air travel. Okay. A plane crashes, 70 persons die. Extremely sad. But now you know that air travel will save more lives in the future because we're never going to let that error go to waste, you see. So the probability of the next plane crashing has dropped.
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Wesley Stevenson
One of the challenges, I think, when I think about the black swan and I think about anti fragile systems, you think about a system that benefits from stresses, from errors, from disruption. But of course there are different kinds of disruption. You can look at a system that benefits from a 10% fall in sales or a 10% rise in sales, or 100%. But of course, as you know very well, you get these black swans. They may be a thousand percent, they may be 100,000%. Is there a way that we can develop systems that are antifragile or failing that, at least robust, if actually some of these unexpected events could never be predicted.
- [07:37]
Tim Harford
And there'll be extreme events.
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Nassim Taleb
So failures cannot be predicted. But you want to make sure that unlike the airline crashing, the probability of the next crash is not higher. And unfortunately, when a back fails, the next bank is more likely to fail. So you have to make sure that the system doesn't have contagion of failure.
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Wesley Stevenson
I want to ask you about predictions. We love predictions. We recently had the Chancellor's Autumn statement setting out the state of the nation's finances. And a lot of this was about predictions that an independent group of economists had made. They're called the Office of Budget Responsibility. They were projecting what the deficit would be in five years time, what the national debt would be in five years time.
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Tim Harford
And the debate completely revolved around these
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Wesley Stevenson
predictions, despite the fact that every year these predictions have to be changed radically.
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Tim Harford
But I mean, the truth is it's
- [08:28]
Wesley Stevenson
fun to blame economists for making these predictions that are always wrong. As an economist, I try to avoid making predictions, but people keep coming up to me, they keep asking me to predict the future.
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Tim Harford
So we have this huge demand to
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Wesley Stevenson
predict, even though it's very hard to do.
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Nassim Taleb
People should not predict. They should just only tell you what they've done. Because prediction is much more complicated than you think. There's a complication that sometimes, for example, you can say, well, I predict the stock market is going higher, but sold my stocks. Why? Well, it has a higher probability of going up, but if it goes down, it goes down a lot more. By doing that, I'm shifting from prediction to decision. You can only talk about something if you are harmed, if you're wrong, because the problem with the economic establishment is that they are never harmed by their bad models.
- [09:14]
Tim Harford
Nassim Taleb, author of Antifragile now loyal listener Les Halpin recently wrote to us with a question that brought us up short. Les has motor neurone disease, a condition which is both fatal and rare. But rare is a strange word. Here is Les's email, read by an actor.
- [09:33]
It struck me that the way we use words is clearly at odds with their precision as numbers. In particular, on TV the other day, a lightning strike on an individual was described as rare, probably 12 strikes per year, three fatal. At the same time, something like motor neurone disease is described as a rare disease with 5000 sufferers and 1500 deaths per year. What does rarity really mean?
- [09:58]
There's no precise, universally accepted definition of rare. But strangely enough, there is a widely accepted definition of a rare disease. It's a disease that affects fewer than 0.05% of the population, one in 2,000 people. Both the UK authorities and the European Union use that definition. Which raises the question, if rare diseases are diseases that affect 0.05% of the population, how come 6 to 8% of the population of Europe suffers from a rare disease? That's about 35 million people, roughly the population of Poland, assuming we have any
- [10:34]
Wesley Stevenson
idea what the population of Poland is these days.
- [10:36]
Tim Harford
But to come back to the question, rare diseases are those which affect 0.05% of people. Rare diseases affect 6 to 8% of people. How do these statements add up? It turns out that while any single rare disease is rare by definition, rare diseases themselves are unfortunately rather common. There are loads of them. And when you add up all the sufferers of all the rare diseases, you get many millions of people. Still, that doesn't quite answer Les Halpins question. What do we think we're saying when we use a word such as rare? And this isn't a question for a mathematician or a statistician, it's a question for a linguist or a psychologist such as Neil Stewart of the University of Warwick.
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Neil Stewart
What's been done is, I guess it's a first step. It's quite crude. People say questions like, if Tim looks into the urn and sees that there are 30 prize winning balls and he says there's a good chance of winning, how many balls do you think are in the urn? So if you said there's a good chance, maybe I'll think, well, Tim's an honest person, There are probably 25 balls in the urn. And so we'd interpret that to mean that I understand what you say when you say good chance as meaning 25% chance.
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Tim Harford
So that's how a psychologist goes about drawing up a list of words and deduces what we're trying to do when we use them. Here's a little sample from Professor Neil Stewart's list.
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Neil Stewart
If we start at the bottom, we've got never, which typically people think means zero percent chance. We've got the rarely that we're interested in here. That's coming in at an 8% chance, but it's quite variable. So some people who said rarely actually said they thought 0% and other people will have said numbers as high as 20%. And that's true for all of the phrases. There's quite a lot of variability between people in the number that they interpret the word to mean. So we've got never, rarely, seldom, improbable, uncommon toss up, which is coming in at 47%. Then we've got predictable, common, frequently, probable, often likely, usually and always is up there at 94%.
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Wesley Stevenson
Excellent. So always is twice the chance of
- [12:36]
Tim Harford
a toss up, which I suppose makes sense. And I did check whether the list includes the word inconceivable. Alas, not, perhaps we'll never know whether
- [12:45]
Wesley Stevenson
that word means what people think it means.
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Tim Harford
Back to Neil Stewart.
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Neil Stewart
The Intergovernmental Panel on Climate Change is one example where they've tried to legislate what words their researchers can use to describe certain events. So, for example, they've got a confidence terminology. So if something has, if you say very high confidence as a scientist, you have to mean at least a 9 out of 10 chance. Or if you say medium confidence, you mean a 5 out of 10 chance. And they've got a scale that maps the verbal phrases that we use to describe how confident we are onto sort of a numerical scale of probabilities.
- [13:21]
Tim Harford
But this is all a bit unsatisfactory, isn't it? I mean, let's say, and this is totally hypothetical, let's say the IPCC says that it's very unlikely that releases of methane from the seabed and from melting tundra will set off an uncontrolled planetary warming that ruins agriculture and condemns half the human race to starvation. In some ways, very unlikely is reassuring, and apparently very unlikely could mean that there is a 0% chance of this outcome. But according to the IPCC risk lexicon, very unlikely could also mean a 1 in 10 chance. So perhaps it's wiser for the boffins to stick to hard numbers, percentage probabilities, numbers affected. Then again, perhaps not. Linda Moxie is a senior lecturer in psychology at the University of Glasgow. She explained that when we say rare or common or impossible, these words are doing more than merely conveying numbers imprecisely.
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Linda Moxie
If you say there are occasionally accidents on this stretch of road, then that's a terrible thing. You're saying that it's unfortunate because accidents happen. If you use rarely, which conveys roughly the same frequency as occasionally, and you say there are rarely accidents on this stretch of road, you have to say that's a good thing. It's a good thing that they're rare, because you're actually emphasizing the fact that accidents don't happen in this stretch of rain.
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Wesley Stevenson
Interesting. I had intuitively assumed that when people say that something is rare, that's a bit sloppy, it's a bit lazy. They would be conveying a lot more information if they were to say it's two In a thousand, it's one in a thousand.
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Tim Harford
But actually what you're saying is there are lots of other things that are
- [14:56]
Wesley Stevenson
being conveyed by rare not only, well, you're not conveying a particular number, but you are conveying good news or bad news, more or less than you would expect. This is a state of affairs that we should approve of or disapprove of all sorts of things that are not being conveyed. If I give you the number, these
- [15:11]
Linda Moxie
words perform other functions that have to do with inferences that you want to make on the basis of the number. If you like, they're telling you the significance of that number as well as giving you a number. And we ask. The number that they tell you about is quite vague. The inferences that you make can be quite specific.
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Wesley Stevenson
What about politicians using language or official reports using language? Should they be restricting themselves to quantitative judgments of risk? Or do you think it's useful that they would also use everyday language?
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Linda Moxie
Although numbers can be very objective, they can be quite useless in a situation. For example, imagine I wanted to fly to London at the end of the week, and I don't know whether I want to fly on Friday or Saturday, but I want to make sure that I'm going to be able to fly. And I phone up the travel agent and say, how many seats are left on the last flight on Friday? And the Travel agent says, 20. That's actually quite useless to me, that information, unless I know how many seats are on the plane, what's the normal rate of sales? Because what you really want to know is am I going to be able to wait and still get a ticket? So in that situation, it's more useful to be told that there's lots of seats or there's plenty, or that there's hardly any. There are lots of situations where you'd want to use a word and there's others where you would want to hear a number. And really the usefulness of a number is determined by how much other quantity information you have already.
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Tim Harford
That suggests quite a challenging communication problem,
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Wesley Stevenson
because very often when we ask an expert for information, the expert has all the numbers at her fingertips, and yet we're asking her to speak to an uninformed population who don't know all the background, don't know all the context, and
- [16:58]
Tim Harford
so the expert would naturally reach for the quantitative information. Whereas in fact, if you're speaking to someone who doesn't really know the context,
- [17:05]
Wesley Stevenson
it might be better just to use words. They're vague, but they convey all kinds of subtleties that the numbers don't.
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Linda Moxie
It's true they do, but I think quite often, especially if it was politicians talking, the public would think that they were just sort of being deliberately evasive if they used words. So perhaps, you know, there's a kind of white coat effect that you want to look more professional and sound more objective if you use the numbers.
- [17:29]
Tim Harford
Dr. Linda Moxie of the University of Glasgow. This is More or Less. I'm Tim Harford and if, like Les Halpin, you have a question, do please send your emails To More or lessbc.co.uk the BBC's Infinite Monkey Cage isn't normally a source of subject matter for More or less, because with their formidable brains and gorgeous hair, the Monkey Cage team is rarely wrong about anything. But our attention was drawn to this discussion about laughing rats.
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Johnny Ball
I've never heard of this. Laughing rats.
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Ruth Alexander
RATS LAUGH Rat laughter's basically.
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Wesley Stevenson
They love Jerry Lewis movies, that's their main thing. Nuts and professors.
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Tim Harford
Depressingly similar to us.
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Linda Moxie
They LAUGH at the tickle.
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Tim Harford
You know what?
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Johnny Ball
At any time time, we're only 7 foot from a human.
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Dave Cowan
That's hilarious.
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Tim Harford
Now, that got us thinking about this old adage that in urban areas, we're no more than X feet from a rat. Sometimes it's 7ft, sometimes it's 6. Some reports have suggested it's as many as 20ft. But here on More Or Less, we like to know the real answer. So to work this out, first we need to know how many rats there are in the uk. We asked many experts about this, but most could only offer a wild guess that differed from 6 to 20 million. But where they all agreed was that the man who would know would be Dr. Dave Cowan, science leader in the wildlife program at the government's Food and Environment Agency.
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Dave Cowan
Rats are almost completely commensal in Britain, so they're associated with human activities. So that gives us a start. We only really need to think about how many rats there might be living in close proximity to ourselves.
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Wesley Stevenson
Let's start then with houses, because that's, I'm sure, what will concern a lot of people.
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Tim Harford
Are all our homes infested with rats and we just don't see them very
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Wesley Stevenson
often, or is it a rare thing?
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Dave Cowan
It's pretty rare, actually. Certainly in terms of rats being inside our dwellings, it's less than half, half a percent from the surveys that have been done. But the better figure to take is actually the number of dwellings that have rats outside. And there's around 3% of our dwellings have rats present immediately outside.
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Tim Harford
When we add all that up just
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Wesley Stevenson
in and around dwellings, then how many rats is that?
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Dave Cowan
We can come up with a figure of about 1.5 million in total in Britain, I think, is probably the best way of looking at that.
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Wesley Stevenson
Now, what about commercial environments? Warehouses, factories and so on, and shops. And we're always being told that broadcasting houses at any minute now is about to be infested with rats. So what's the story there?
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Dave Cowan
You need to start with how many commercial premises are there? And there's a figure of about 1.8 million commercial premises in Britain. And a survey that looked at that suggested around 5% of those commercial premises had rats present. But again, each presence was a relatively small number of animals. So actually, probably the total for, or total estimate for the number of rats in and around commercial premises is something like 200,000.
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Wesley Stevenson
Okay, now, are there any other urban environments?
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Dave Cowan
Well, the key one most people think about is rats in sewers. And this is a bit tricky, but there's an estimate of around 16,000 square kilometres of sewer in Britain. There's around 5% of the sewers that have rats present. And from work that was done actually in 1950s, we had an estimate of around 2,000 per hectare of sewer. Again, a bit difficult to work that, but if you multiply those together, you'd end up with a figure of about 1.6 million rats in British sewers.
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Wesley Stevenson
So my quick mental arithmetic says we're basically talking between three and three and a half million rats in urban environments where all the people are. Now, where else might we find rats?
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Dave Cowan
That's the kind of streetwise urban rat, 3 to 3.5 million usually, say, turning to their kind of country cousins in rural habitats. And that's mainly going to reflect rats in and around agricultural buildings on farms. Now, There are around 200,000 agricultural premises in Britain, and various surveys suggested around 40% of those premises will have rats present. And we actually have some pretty good census data for the average numbers of rats on each of those farms where rats are present. And that's around 90 rats per farm. Multiplying those together, we get a figure of around 7 million rural rats. So that's about twice as many as are found in our towns and cities.
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Wesley Stevenson
Dave, just for those of us who are not following all the details, can we just total everything up? Add them all up for us?
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Dave Cowan
Yeah, total everything. The number of rural rats, number of urban rats, we get a total of around 10 and a half million rats in Britain. And given the human population is around 60 million, we actually outnumber rats by about 6 to 1.
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Tim Harford
Dr. Dave Cowan Rat Whisperer so now we know how many rats there are in Britain, but how close are you to a rat right now? Well, I'm rather close to Ruth Alexander. Not so much a rat, Ruth, as a pied piper.
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Wesley Stevenson
You're going to sort all this out for us.
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Ruth Alexander
Yes, this is a bit rough and ready. We're going to work out how far you are from a rat in an urban area. So first of all, let's discount the rats on farms. That leaves us with around 3.1 million rats. Urban areas in Britain cover around 16,000 square kilometers, which means if we distribute the rats evenly across the urban areas, which is clearly unlikely, but necessary for the calculation, each rat has a rather spacious 5,000 square meters to roam around in.
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Tim Harford
So assuming you're standing at a given
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Wesley Stevenson
spot in an urban area, how close will you be to a rat?
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Tim Harford
A bit more than seven feet, I would imagine.
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Ruth Alexander
Yes, you could actually be up to 164ft away.
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Wesley Stevenson
I love the way we've segued here
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Tim Harford
between metric and imperial, but I guess
- [23:16]
Wesley Stevenson
this is the question, right?
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Ruth Alexander
Exactly. It's quite neat. But now, if the rats cluster together in the basements of Broadcasting House, for example, then you could be a lot further away than that. Unless you're us.
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Wesley Stevenson
Unless you're us. Thank you, Ruth, and sorry about the rat comment. Now, we have been faced with a few difficult questions in our time on
- [23:35]
Tim Harford
More or Less, but this one is a real humdinger.
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Ruth Alexander
Hello. My four year old daughter wishes to know what is a number before infinity? Can you advise on a mathematically reasonable answer that I could explain to a 4 year old? Thanks, Ellie.
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Tim Harford
Wow, where do you start? This calls for mathematical royalty. Who better to explain it than the man who inspired my childhood interest in mathematics, TV's Johnny Ball.
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Johnny Ball
What is the number before infinity? That would be the biggest number of all. And you can't have a biggest number of all because if you had the biggest number of all and added one to would be a bigger number still. So how can I explain it? I've got some sweets here and these sweets come in a bag and you could easily count the number of sweets in a bag, couldn't you? Right, so that's a finite number of sweets in the bag, and that's a strange word, finite. It means you can count it. If you wanted to count all the sweets in the world, do you think we could do it? No, it'd be difficult because people are eating them all the time, so the number changes and factories are making them all the time. So sometimes there's more, sometimes there's less. But if you stopped, everybody said stop, don't make anymore and don't eat anymore. It would be possible if everybody in
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Dave Cowan
the world agreed to help.
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Johnny Ball
It would be possible for us to count all the sweets in the world because there's a certain number. We don't know what the number is, but it's possible to count. But infinity is a number you can't count.
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Tim Harford
Okay, so what does Claudia think is the biggest number?
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Ruth Alexander
I think 100 or a million
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Dave Cowan
are
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Johnny Ball
big numbers, but they're nowhere near infinity. In fact, Claudia, I'm gonna give you some sweets. You've got some sweets.
- [25:38]
Nassim Taleb
I.
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Johnny Ball
And I've got more sweets because they're my sweets. But you've got some more now. No, they're not that many. All right, you start counting yours.
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Ruth Alexander
One, two.
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Johnny Ball
Right.
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Ruth Alexander
Three.
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Johnny Ball
That's very good.
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Ruth Alexander
Four, five, six, seven and eight.
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Johnny Ball
Have you got any more? No, but if I gave you another one that have been. How many is that?
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Ruth Alexander
Nine.
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Johnny Ball
Nine. You'd have nine sweets. Right. You asked what is the number before infinity? Well, as infinity goes on forever, you can't have the number before infinity because whatever that number is, however big it is, if you added one more, you'd have another number that's bigger. So you can't have the number before infinity. It goes on forever.
- [26:33]
Wesley Stevenson
Brilliant.
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Tim Harford
But it's not just children who struggle with the concept of infinity.
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Johnny Ball
Virtually everything we talk about is finite. The number of molecules of air in the atmosphere is finite. They could be counted. There's a number you can't go beyond, but infinity goes beyond that. You know, if you have a square, it's got four sides and it will fit into a circle. If you have a hexagon that fits into a circle, it's six sides and it still fits in the circle. If you have an octagon with eight sides that fits into a circle, all well and good, how far can you go? Many sides can you have to a figure that will still fit in a circle? Well, the definition of a circle is an infinite number of points, a set distance from a central point that together make up that circle.
- [27:23]
Tim Harford
Well, thank you to Johnny Ball, to Claudia and to her mum Ellie. If you've spotted any statistical connivances or you just have a number you want us to look at, please email more or lessbc.co.uk. and if you want to know more about the programme, please go to BBC.co.uk more or less until next week. Goodbye.
- [27:45]
More or less was presented by Tim Harford, the Financial Times undercover economist. The producer was Wesley Stevenson and the editor was Richard Varden. The program is made in association with the Open University.