WS MoreOrLess: What is "rare"?

Summary

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More or Less: "What is 'rare'?"

BBC Radio 4 • Host: Tim Harford • December 17, 2012

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Episode Overview

This episode of More or Less explores the ambiguity in how we use the word "rare" and other probabilistic language in everyday conversation, science, and public policy. Prompted by a listener with motor neurone disease, Tim Harford investigates how terms like "rare," "improbable," and "likely" correspond—or fail to correspond—with actual numerical probabilities. The episode features insights from psychologist Neil Stewart, linguist Linda Moxie, and a discussion with Nassim Nicholas Taleb about unpredictable events ("black swans") and systems that benefit from disorder ("antifragile").

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Key Discussion Points & Insights

1. The Listener's Challenge: What Does "Rare" Mean?

[00:13–01:02]

• Loyal listener Les Halpin, who suffers from motor neurone disease, writes in to question how words like "rare" are used:
  • Lightning strikes (12 per year, 3 fatal) and motor neurone disease (5,000 sufferers, 1,500 deaths per year) are both called rare—but what does that really mean?

"It struck me that the way we use words is clearly at odds with their precision as numbers... What does rarity really mean?"
— Les Halpin (via actor), [00:37]

• Definition from authorities:
  • In the context of rare diseases, both the UK and EU define "rare" as affecting fewer than 0.05% of the population (1 in 2,000 people).
  • There is no universally accepted definition of "rare" more broadly.

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2. How We Interpret Probability Words

[01:02–02:46]

• Psychologist Neil Stewart (University of Warwick):
  • Researchers study how people interpret words like "rarely," "good chance," or "improbable" by presenting scenarios (e.g., guessing 'balls in an urn').
  • Different people assign very different probabilities to the same word.

"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... some people said 0%, others as high as 20%..."
— Neil Stewart, [02:15]

• Stewart's Scale (selected):

  • Never = 0%,
  • Rarely = 8% (but variable: 0–20%),
  • Toss-up = 47%,
  • Always = 94%.

• Highlights the subjectivity and imprecision in translating words to numbers.

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3. Standardizing Risk Language: Lessons from Climate Science

[02:46–03:19]

• The Intergovernmental Panel on Climate Change (IPCC) Example:
  • The IPCC defines precise probability ranges for qualitative terms:
    • "Very high confidence" = ≥90% chance
    • "Medium confidence" = 50%
  • Goal: Map verbal expressions onto numerical probabilities for clarity.

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4. Words Do More Than Numbers Alone

[03:19–05:43]

• Limitations of Precise Numbers:
  • "Very unlikely" can feel reassuring but could actually mean a 10% chance in the IPCC lexicon—a high risk for catastrophic outcomes.

"Very unlikely could 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."
— Tim Harford, [03:19]

• Linda Moxie (University of Glasgow):
  • Words like "rare," "impossible," or "common" do more than give numbers—they help listeners infer significance.
  • The real meaning lies not just in the percentage, but in the implications and context.

"The usefulness of a number is determined by how much other quantity information you have already."
— Linda Moxie, [05:37]

• Example: Telling a traveler "20 seats left" is only meaningful if you know plane size, usual demand, etc. Sometimes "a few seats" or "plenty" is more practical than a number.

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5. Notable Quotes & Memorable Moments

• "Rarely comes in at an 8% chance, but it's quite variable..."
  — Neil Stewart, [02:15]
• "Always is twice the chance of a toss up."
  — Tim Harford, [02:46]
• "Very unlikely could mean a 1 in 10 chance."
  — Tim Harford, [03:19]
• "Although numbers can be very objective, they can be quite useless in a situation."
  — Linda Moxie, [04:46]
• "The usefulness of a number is determined by how much other quantity information you have already."
  — Linda Moxie, [05:37]

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Bonus Segment: Nassim Taleb on Black Swans & Antifragile Systems

[05:43–08:50]

• Tim Harford chats with Nassim Nicholas Taleb about "black swan" events and "antifragile" systems.
  • Black swans:
    • Hard-to-predict events with massive consequences.
    • Even after the fact, people try to explain them, but can't reliably predict them.
    • Focus should be on making systems resilient, not on unrealistic prediction.

"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 understanding the world."
— Nassim Taleb, [06:15]

• Antifragile systems:
  • Systems that benefit from disorder and stress, not just withstand them.
  • E.g., plane crash leads to system reforms that decrease future crash likelihood.
  • Banking system often fails in the opposite way: failure increases system risk.

"By definition, an antifragile system has to use errors as fuel."
— Nassim Taleb, [07:34]

"When a bank fails, the next bank is more likely to fail. So you have to make sure the system doesn't have contagion of failure."
— Nassim Taleb, [08:33]

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Timestamps for Key Segments

• 00:13 – 01:02: Introduction & Les Halpin's question on "rare"
• 01:02 – 02:46: Neil Stewart on probability language & survey results
• 02:46 – 03:19: How the IPCC standardizes verbal risk descriptions
• 03:19 – 05:43: Linda Moxie on the functions of words vs numbers
• 05:43 – 08:50: Nassim Taleb on black swans and antifragile systems

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Summary

This episode demystifies how we use words like "rare" to convey probability and meaning. While institutions might define "rare" in numeric terms (less than 0.05% of the population), in practice, the public's interpretation of such terms is subjective and highly variable. Words do more than substitute for numbers; they trigger specific inferences and emotional responses, sometimes more helpful—or more misleading—than cold statistics. Philosophical reflections with Nassim Taleb on unpredictability and resilience highlight the limits of risk language and the importance of robust systems in an uncertain world.

Transcript

[BBC Announcer]

Thank you for downloading from the BBC. For details of our complete range of podcasts and our terms of use, go to bbcworldserveys.com podcasts

[Tim Harford]

hello and welcome to More or Less on the BBC World Service with me, Tim Harford, opening the curtains and letting the light in on the lazy use of numbers. 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.

[Actor reading Les Halpin's email]

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?

[Tim Harford]

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. 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.

[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, oh 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.

[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 Neal Stewart's list.

[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%. 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%.

[Interviewer]

Excellent.

[Tim Harford]

So always is twice the chance of a toss up. Back to Neil Stewart, the Intergovernmental Panel

[Neil Stewart]

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, 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.

[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.

[Linda Moxie]

These 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. Whereas the number that they tell you about is quite vague. The inferences that you make can be quite specific.

[Interviewer]

What about politicians using language or official reports using language? Should they be restricting themselves to quantum sensitive judgments of risk? Or do you think it's useful that they would also use everyday language?

[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.

[Tim Harford]

You're listening to more or less on the BBC World Service 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 and 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.

[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 understanding the world. And of course we continue mispredicting the. 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. So my point is about having systems that don't fall apart under these extreme circumstances. And that's much easier than predict anything.

[Interviewer]

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 offense and you hit me, this would probably be very good for you. But if your publicist, he got upset with me and he hit me, this would be bad for him. And I love this example from your book of anti fragile careers and fragile careers.

[Nassim Taleb]

Exactly. 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 going to be in trouble.

[Interviewer]

So the more trouble there is, the more disruption there is, the more you benefit. If you're a certain kind of person.

[Nassim Taleb]

Exactly.

[Interviewer]

You have a certain kind of career. And this of course is not just about people people, it's not just about careers, it's about all kinds of systems.

[Nassim Taleb]

Exactly. 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 air go to waste, you see. So the probability of the next plane crashing has dropped.

[Interviewer]

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. But of course, as you know very well, you get these black swans. They may be a thousand percent. Is there a way that we can develop systems that are anti fragile if actually some of these unexpected events could never be predicted?

[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 bank fails, the next bank is more likely to fail.

[Interviewer]

Yeah.

[Nassim Taleb]

So you have to make sure that the system doesn't have contagion of failure.

[Tim Harford]

Nassim Taleb AUTHOR OF antifragile if you want to find out more about the program or you have a question you want to ask, you can go to our website, bbcworldservice.com moreorless or you can email [e-mail] until next week. Goodbye.

[BBC Announcer]

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