How close is Greenland to the United States?

Summary

More or Less (BBC Radio 4)

Episode: How close is Greenland to the United States?
Host: Tim Harford
Guests: Jay Foreman, Dr. Kat Phillips, Neil Hudson, Tom Coles
Date: January 21, 2026

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Episode Overview

This episode of More or Less dives into misleading statistics and persistent myths across news, politics, and everyday life. The main segment tackles the oft-repeated claim that Greenland is “just 300 miles from the US”—scrutinizing the numbers behind this assertion and how our conventional world maps can warp our perceptions. The episode then moves on to dissect inflated figures on the cost of reaching net zero in the UK, unspools myths about ever-rising house prices, and even applies mathematical reasoning to the strategies of TV game show The Traitors.

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Key Discussion Points and Insights

1. How Close is Greenland to the United States?

[02:27 – 06:52]

• The show parodies the “Map Man” theme to introduce Jay Foreman, co-creator of Map Men, for expert map-based fact-checking.

• Jay Foreman, referencing both physical globes and Google Earth, disputes the idea that “Greenland is 300 miles away” from the US.

  "Greenland is roughly 1,200 miles from the nearest US coast, which is Maine. And... it's 1,300 miles from Alaska."
  — Jay Foreman [03:23]

• Greenland is closer to the US than to Denmark (1,300 miles away), but the difference isn’t huge.

• The widespread misconception likely comes from the way Greenland is depicted on flat Mercator projection maps, which enlarge landmasses near the poles and skew distances.

  • On such maps, Greenland looks huge and close to North America.
  • In reality, maps distort both size and location at higher latitudes.

  "If you've ever looked at a flat rectangular map of the world. I have a hard hitting truth for you. That map was a lie."
  — Tim Harford [05:00]

• Africa, 14 times the size of Greenland, appears similarly large on the Mercator projection.

• The map myth might feed into political obsessions, such as Donald Trump’s interest in acquiring Greenland.

  "There is a popular theory that the reason Donald Trump is so keen on Greenland is because he's been looking at the Mercator projection. And it looks like by acquiring [Greenland] he would enormously increase the size of the USA."
  — Jay Foreman [06:13]

Key Segment Timestamps:

• [02:27] Jay Foreman gives initial source and methods
• [03:23] True distances revealed
• [05:00] The “map was a lie”—how Mercator projection misleads
• [05:38] Greenland vs. Africa, India comparisons
• [06:13] The “Trump globe” theory and strategic value

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2. Fact-Checking Net Zero Costs

[08:21 – 14:11]

• The press regularly cites a gross cost of £7.6 trillion for the UK's net zero transition by 2050—a figure that surfaces in multiple media outlets and a report by the Institute of Economic Affairs (IEA).

• Tom Coles investigates: Is this number as terrifying as it sounds?

• The £7.6 trillion is not the extra cost of decarbonizing, but rather the total cash outlay for running the entire energy system through 2050 in a scenario where net zero is achieved.

  "It's the cost of running the entire energy system for the next 25 years in one scenario where the net zero target is hit...If net zero policies were abandoned tomorrow, that would also be trillions of pounds."
  — Tom Coles [11:21]

• The more useful figure is the difference between the net zero scenario and a “do nothing” scenario. NISO (National Energy System Operator) finds the cost difference is only £400 bn (7.6 – 7.2 trillion) over 25 years (about 0.4% of GDP per year).

• No one seems to have modeled the true cost of running the system with all net zero policies abandoned.

  "It feels like that might be a useful exercise."
  — Tom Coles [14:04]

Key Segment Timestamps:

• [08:29] The £7.6 trillion figure explained
• [10:03] What the figure actually means versus media interpretation
• [12:05] The cost difference between net zero and “less ambitious” scenarios

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3. Can House Prices Defy Gravity?

[15:31 – 21:55]

• Tim Harford interviews housing analyst Neil Hudson about the trajectory of UK house prices.

• The conventional wisdom—house prices only go up—is undermined by recent history:

  • After the global financial crisis (2009), prices fell 20% in nominal terms.
  • The pandemic disrupted the market, but prices rebounded, hitting new highs until mid-2022.

  "For the last three years house prices have not continued to rise inexorably."
  — Tim Harford [15:31]

• The notorious "mini-budget" under Liz Truss in autumn 2022 caused a sharp spike in mortgage rates and a 6% nominal fall.

• Regional variation: Since late 2022,

  • London: Down ~4%
  • South of England: Down ~2.5%
  • Midlands: Up ~2%
  • North of England/Northern Ireland: Up ~4.5–5%

• Fluctuations are linked more to demand (affordability) than excess supply.

  "Where house prices are falling, that's not because of a glut of supply. Rather it's a dearth of demand. With mortgage rates and house prices where they are, people can't afford to buy houses, especially in London and the south."
  — Tim Harford [19:45]

• Annual growth rates differ for houses vs. flats, with flats lagging post-Grenfell safety concerns.

• Real, inflation-adjusted house prices are down 14% from the 2022 peak; relative to earnings, they are down 17%.

  "House prices have fallen by around about 17% relative to earnings over the period."
  — Neil Hudson [21:40]

Key Segment Timestamps:

• [16:38] House price trends over 20 years
• [17:46] Impact of the Liz Truss mini-budget
• [19:21] Regional house price variation
• [21:40] House prices vs. earnings

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4. The Maths Behind TV’s “The Traitors”

[23:59 – 29:10]

• Dr. Kat Phillips (University of Warwick; Instagram: @katdoesmaths) joins Tim to explore the mathematical strategies possible in The Traitors game show.

• The faithful have numbers, but traitors have critical information—knowing who they are while the faithful guess.

• Bayesian probability can theoretically be applied: players update their assessment of who is a traitor based on accumulating evidence.

  "Mathematically, you should be collecting evidence...and use that evidence to try and update probability of everyone being a faithful or being a traitor."
  — Dr. Kat Phillips [25:38]

• Shannon Entropy (information theory) discussed: faithfuls want to minimize uncertainty, traitors can thrive by maximizing uncertainty and sowing suspicion broadly.

  "For the traitor's perspective, you have this wonderful opportunity to sort of increase the uncertainty by throwing aspersions on people who otherwise would have been classed as, oh, they're definitely a faithful."
  — Dr. Kat Phillips [28:25]

• Human nature often foils mathematical logic; players act on hunches and emotions, making the game less predictable.

  "Adding in that human noise and human error, logical gameplay does tend to go out the window."
  — Dr. Kat Phillips [27:20]

Key Segment Timestamps:

• [23:59] Role descriptions and information asymmetry
• [25:38] Bayesian updating in gameplay
• [27:48] Entropy and maximizing confusion
• [29:08] Human error and emotion in decision-making

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Notable Quotes & Memorable Moments

• On Mercator Maps:
  “If you've ever looked at a flat rectangular map of the world. I have a hard hitting truth for you. That map was a lie.” – Tim Harford [05:00]

• On Africa vs. Greenland:
  “On the Mercator projection, Greenland and Africa look more or less the same size, but in real life, Africa is 14 times bigger than Greenland.” – Jay Foreman [05:38]

• On Net Zero Numbers:
  “The gross cash outlay is not the cost of the big change. It's the cost of running the entire energy system for the next 25 years in one scenario where the net zero target is hit.” – Tom Coles [11:21]

• On House Prices:
  “House prices can indeed go down, but it looks like it's just a blip. They may have dropped, but they're coming back up again. Right? Well, it depends where you live.” – Tim Harford [18:44]

• On Game Theory in The Traitors:
  “There is also a mathematical approach to the problem. So how does a mathematician think about this game?” – Tim Harford [25:08]

  “Bayesian probability, and this is actually a type of Bayesian coordination game, basically says that... you actually have the odds of someone being traitor given an amount of evidence.” – Dr. Kat Phillips [25:58]

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Episode Structure (Reference Timestamps)

• [02:27] Greenland–US distance: myth-busting with Jay Foreman
• [08:21] Net zero costs: examining headline statistics
• [15:31] House prices: historical perspective and current realities
• [23:59] The Traitors: applying probability and game theory

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Tone and Style

The episode is lively, wry, and educational, balancing serious statistical myth-busting with gentle humor. The host, Tim Harford, keeps things approachable with playful analogies (e.g., comparing house price analysts to Galileo) and whimsical asides (the “Map Man” theme, jokes about Trump and globes). The guests are factual but tongue-in-cheek, breaking down technical concepts for a broad audience.

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Bottom Line

If you’ve ever been misled by a map, a newspaper’s scary-sounding number, real estate cliché, or a reality TV strategy, this episode is your guide to seeing through the distortion, with a mix of sharp analysis and good-natured fun.

Transcript

[Tim Harford]

This BBC podcast is supported by ads outside the uk. When you give to a nonprofit, how do you measure success? Many focus on low overhead. But what about real impact on people's lives? For 18 years, GiveWell has researched the highest impact giving opportunities. Over 150,000 donors have confidently used GiveWell, saving 300,000 lives and improving millions more. Make a tax deductible [e-mail] first time donors can have their donation matched to up to $100 while funds last select podcast and more or less at checkout. The best B2B marketing gets wasted on the wrong people. So when you want to reach the right professionals, use LinkedIn ads. LinkedIn has grown to a network of over 1 billion professionals, including 130 million decision makers. And that's where it stands apart from other ad buys. You can target your buyers by job title, industry, company role, seniority, skills, company revenue. So you can stop wasting budget on the wrong AUD. It's why LinkedIn Ads generates the highest B2B return on ad spend of major ad networks. Spend $250 on your first campaign on LinkedIn Ads and get $250 credit for the next one. Just go to LinkedIn.com Broadcast that's LinkedIn.com Broadcast. Terms and conditions apply. Hello and welcome to More or Less. We're your faithful guide to the numbers behind the environment, the economy, the geopolitics of the Arctic Circle, and most importantly, the the mathematics of game shows. I'm Tim Harford. This week we try to put a price tag on net zero, or more precisely, we rip off a price tag we are sure has been misapplied. We ask whether house prices are defying the laws of physics. And we unleash some of the great mathematicians of history on the question of the hour. How to play the traitors? But first, the news has been dominated by a single story. You'd have to be living under a rock in the remote Arctic not to have heard. Wait, actually, that doesn't work. In fact, you're even more likely to have heard if you live in the remote Arctic, because this story is of course about Greenland and the designs upon it harboured by the US President Donald Trump. One piece of coverage came on Radio 4's from our own correspondent, where Europe editor Katja Adler filed this report for from Greenland's capital Nuuk.

[Jay Foreman]

As many Greenlanders have pointed out to me, trading with Denmark over 2,500 miles away makes far less business sense than working with the US 300 miles away.

[Tim Harford]

Loyal listeners got in Touch to ask if this was right. So is it? Well, for reliable map based fact checking, there was only one place to which we could turn. Map man, map man, map, map, map man. Jay Foreman is one half of the YouTube map and comedy sensation Map Men. So can Greenland really be just 300 miles from the U.S. that doesn't sound.

[Jay Foreman]

Quite right to me. And my source for these figures was looking at a globe and also looking at Google Earth where it actually allows you to draw a stick on the planet and change the angle to whatever looks best and actually measure for yourself.

[Tim Harford]

So how far is the US from Greenland, do you think?

[Jay Foreman]

Greenland is roughly 1,200 miles from the nearest US coast, which is Maine. And there are some people who say that it actually could be closer to Alaska. It's not, but it's very close. It's 1,300 miles from Alaska. And the strange thing is, most people, when they think about where Greenland is on a map, that doesn't sound intuitive at all.

[Tim Harford]

Yeah, it's way away from Alaska.

[Jay Foreman]

Yeah. But the thing is, one of the very few good things about this being in the news a lot lately is that it's a great opportunity to see unusual maps that, that show Greenland where it really is from a top down view. And what that shows is that Greenland, quite unintuitively, if you're used to the flat Mercator projection, is not that far from Alaska, but it is still further from Alaska than it is from Maine.

[Tim Harford]

And just to round off the fact check, the shortest distance from Greenland to Denmark is about 1,300 miles. So the US is closer, but only just. Not that you would know any of that from looking at typical maps of the world. They make it look like Greenland is just around the corner from the US east coast and absolutely ages away from both Alaska and Denmark. So what's going on?

[Jay Foreman]

Greenland is one of the hardest places in the world to show on a map where it really is. And there's two reasons for that. First of all, because it's very, very far north. And the map that we're mostly used to looking at is a flat map of the round world. And what that means is you have to distort the world and you have to do either squashing, stretching or slicing to make it work. And Greenland is a victim of this. Greenland being so far north means that it usually has to be massively stretched and it changes not only where it appears in relation to other places, it also changes the size.

[Tim Harford]

Yes, if you've ever looked at a flat rectangular map of the world. I have a hard hitting truth for you. That map was a lie. And that lying map's title, the Mercator projection, named after its author, everyone's favourite 16th century Flemish cartographer, Gerardus Mercator. As Jay explains, the further towards the poles you go, the more things get stretched and this produces some enormous distortions. For instance, look at how Greenland and the entire continent of Africa compare on a normal map.

[Jay Foreman]

On the Mercator projection, Greenland and Africa look more or less the same size, but in real Life, Africa is 14 times bigger than Greenland.

[Tim Harford]

Similar thing for India, Greenland looks much bigger on the map, but in reality.

[Jay Foreman]

Or on the globe, Greenland is about half the size of India. And they're a slightly similar shape as well. They're sort of triangles with a pointy bit at the bottom. So it's easy to compare the size when you look on a globe. But of course, when you look on the famous flat Mercator projection map, it looks far too big.

[Tim Harford]

So are you saying that we might be able to avoid a geopolitical crisis by just looking less at flat maps and looking a little bit more at globes?

[Jay Foreman]

There is a popular theory that the reason Donald Trump is so keen on Greenland is because he's been looking at the Mercator projection. And it looks like by acquiring GRE he would enormously increase the size of the usa. And I wonder if just showing him a globe might make him rethink just how valuable it is. Although the other problem is that by looking at a globe, you can see much more accurately than on a Mercator projection. Exactly why it's such a strategic position and because it's sort of in the center of the world in a way. By looking down, it's very close to Alaska and the north of Russia and Scandinavia and Iceland and the coast of Canada, which is something you don't really get to appreciate if you look at a traditional flat map.

[Tim Harford]

Yes, I can see why the Donald Trump needs to look at a globe theory has caught on on social media, but I strongly suspect that at some stage somebody has shown Donald Trump a globe and it doesn't necessarily change his views on things. Our thanks to Jay Foreman, one half of YouTube sensation and map men, and the co author of the book this Way Up When Maps Go Wrong. And we should say that from our own correspondent noticed and acknowledged their mistake before we got involved, which is the kind of honourable action we'd expect from our Radio 4 siblings. How much is it going to cost to transform our entire energy system to produce Net zero carbon emissions by 2050. According to a figure in the Telegraph, the gross cost to the UK economy of achieving the 2050 target could exceed even the highest official predictions of 7.6 trillion pounds. This figure of 7.6 trillion pounds as the gross cost of net zero was also repeated in the Mail, the Express and elsewhere. It's sourced to a report from pro market think tank the Institute of Economic affairs, written by energy policy substack writer David Turver. Indeed, the first sentence in the press release for that report is remarkably similar.

[Dr. Kat Phillips]

New analysis suggests gross costs of net zero could exceed even the highest official predictions of 7.6 trillion pounds.

[Tim Harford]

But is this 7.6 trillion pound number a good one? Sauna correspondent Tom Coles has been looking into it. Hello, Tom.

[Tom Coles]

Are we still keeping that one going?

[Tim Harford]

We are.

[Tom Coles]

Okay, so if I say to you that the gross cost of NET 0 is 7.6 trillion pounds, what would you think that meant?

[Tim Harford]

That if we didn't try to hit the net zero target by 2050, we'd save 7.6 trillion pounds.

[Tom Coles]

That is not what it's saying. So this figure was calculated for the Institute of Economic affairs report using figures from a report by niso. That's the National Energy System Operator. Their chief economist is Mike Thompson.

[Tim Harford]

We publish each year a set of scenarios for the future energy system. And this year we included costs for those. Those numbers include upfront costs, so the costs of building power stations, networks, costs of buying cars and boilers, and they include running costs, the costs of maintaining those things, taking a car for a service, but also the cost of fueling them. The petrol, the diesel, the gas that we're burning in our boilers and our power stations. And essentially what someone seems to have done is that they have added up all of that spending. Every power plant, every car, every heat pump, every gas boiler, whether petrol or electric or gas, they've added up all of the cost of the fuels that are being burnt in that system, and then they've repeated it as if it is the cost of net zero. So they basically said that the cost of the whole energy system added up over 25 years out to 2050 is the cost of net zero.

[Tom Coles]

So this figure is not the additional cost of decarbonising our energy system. It's an attempt to work out the total cost of an energy system that is net zero by 2050.

[Tim Harford]

So the number seems to be being used in a very misleading way then.

[Tom Coles]

Right. And I put that to the report's author, David Turver, who accepts that there is some validity to that criticism. He said the figure as used in his report represents the gross costs of.

[Tim Harford]

Building and operating an energy system that will meet net 0 by 2050, and.

[Tom Coles]

Accepts that it shouldn't be used to suggest or imply that this figure is the additional cost of net zero policies.

[Tim Harford]

I think it probably ought not to be used in that way in isolation. But if you think of a scenario, say you're working for a business and you were putting forward a proposal to do some sort of big change, then you will put up what are the gross costs of doing this big change? And then you would have other scenarios to say, well, what if we do nothing? Or what if we do something else? And then you would compare the two. So the gross costs are important because, you know, essentially that's total cash outlay. The net costs are also important because that helps you identify the differences between different scenarios and different paths you may follow.

[Tom Coles]

Although I feel like I have to say this again, the gross cash outlay is not the cost of the big change. It's the cost of running the entire energy system for the next 25 years in one scenario where the net zero target is hit. And the cost of running the entire energy system for the next 25 years if the net zero policies were abandoned tomorrow that David accepts would also be trillions of pounds.

[Tim Harford]

Got it. But do we know how many trillions of pounds? It would be really nice to have these different scenarios that David mentioned. How much will it cost if we hit net zero? How much will it cost if we don't bother? Compare the two scenarios and we'd have a figure that might be worth putting in a newspaper headline. So do we have them?

[Tom Coles]

We do not. NISO do work out a scenario that produces a smaller cut in carbon emissions by 2050. The cost of the energy system in that scenario would be 7.2 trillion pounds instead of 7.6.

[Tim Harford]

So that suggests that scaling back net zero to some extent would save the difference between the two scenarios, which is 400 billion pounds.

[Tom Coles]

Yes, 380 billion over 25 years in these figures? While they don't give the numbers, NISO say the difference is about 0.4% of GDP per year.

[Tim Harford]

Has anyone tried to put a price tag on a world where we abandon all subsidies and regulations pushing towards net zero?

[Tom Coles]

The Committee on Climate Change do something a bit like that, but calculated in a different way, which we don't have time to get into. In their latest report, they put the cost of doing Net 0 at 0.2% of GDP annually versus a no policy baseline so similar ish ballpark but they confirmed that this number isn't one you can compare to the NISO number for the total cost of the energy system between now and 2050. David Turver accepts that he doesn't have a number for the overall cost of an energy system which immediately drops all net zero policies, but thinks net zero will cost trillions.

[Tim Harford]

And we can see the cost of what we're doing already in not just in our energy bills, but in deindustrialization. I mean, even Andrew Bailey warned last week that the cost of net zero policies are damaging the economy.

[Tom Coles]

Andrew Bailey is the Governor of the bank of England and he did mention climate related economic shocks and the policies aimed at tackling them as being among the headwinds facing the global economy. And it's certainly true that electricity in the UK is among the most expensive in the world.

[Tim Harford]

Okay, so David thinks net zero will cost trillions, but he hasn't done modelling to back up this claim. And to be fair, it seems that no one's really trying to compare the cost of a net zero energy system with one where the government ditches net zero and takes the brakes off fossil fuels.

[Tom Coles]

No they haven't. At least not that I can find. Which is a shame, because it feels like that might be a useful exercise.

[Tim Harford]

Thank you Tom. You're listening to More or Less and our email address is more or lessbc.co.uk. if you're the purchasing manager at a manufacturing plant, you know having a trusted partner makes all the difference.

[Tom Coles]

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[Tim Harford]

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[Tom Coles]

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[Tim Harford]

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[Dr. Kat Phillips]

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[Tim Harford]

There are certain truths that we've come to accept as AXIOMS immutable laws that cannot be violated. Energy can't be created or destroyed, only conserved. The Earth orbits the sun. UK house prices always go up. Well, dear listeners, prepare to rewrite your very understanding of the world around us, because for the last three years house prices have not continued to rise inexorably. Neil Hudson is an independent housing analyst and founder of the housing research website Built Place. And he is the heretical Galileo to the estate agent industries, Pope Urban viii. And just like the pioneering astronomer, it's only right to put Neil's views on trial. Are the UK's house prices the centre of the universe for so many of us, really subject to the forces of gravity? Or have they slipped the surly bonds of Earth? I asked Neil to start by describing the long term trajectory of house prices in the UK over the last 20.

[Neil Hudson]

About 20 years ago was just before the global financial crisis hit. House prices were still rising and hitting what was then a record high peak. We then had a big downturn in 2009 when the global economy crashed and house prices in the UK fell by about 20% in nominal terms.

[Tim Harford]

Exhibit one, you, Holiness. It's happened before. Following the financial crisis, the market took.

[Neil Hudson]

A while to recover, but from about 2013, house prices began rising again. We then had the run up to the pandemic when a lot of commentators were probably thinking that the market had maybe sort of reached an upper limit and prices might start to slow down again. But we then had that very unique situation where the housing market actually shut for a period. And then we had a post pandemic race for space when house prices suddenly shot up again and hit new record highs.

[Tim Harford]

Right. So with order restored to the universe, house prices once again have been heading heavenwards, well up until 2022.

[Neil Hudson]

Then we had mortgage rates begin to increase quite slowly before we then had the events of the autumn of 2022 hit, when mortgage rates shot up quite substantially in a very short period of time.

[Tim Harford]

That was the famous mini budget. Liz Truss.

[Neil Hudson]

The famous Liz Truss mini budget. So we saw the impact of the budget in September 2022 hit mortgage rates and that led to a sharp fall in house prices by around about 6%.

[Tim Harford]

A 6% fall. Ouch. Of course, that wasn't just because of the mini budget. Interest rates were heading up anyway and they've risen in other countries too. Still not fun if you own a house.

[Neil Hudson]

They then held around that level as the market adjusted to these new higher rates. But since then they've actually increased slightly. So now we're looking at house prices back around where they were in September of 2022.

[Tim Harford]

Okay. So at this point, it is clear we do have to rethink our entire worldview. House prices can indeed go down, but it looks like it's just a blip. They may have dropped, but they're coming back up again. Right? Well, it depends where you live. Homeowners in London and the south of England. Cover your ears. Since the market peaked in September 2022, the average house price in London is down by about 4%. In the south of England, it's down by about 2.5%. But for the rest of the country, it's a different story.

[Neil Hudson]

So in the Midlands, we've seen house prices rise by around about 2%. Since then, in the north of England and across the rest of the UK, they're up around 4.5%, 5% in those markets. And Northern Ireland has actually been what nationwide would call the strongest performing market for the last couple of years, recording the highest levels of price growth. And that's specifically because those markets have been less affected by higher mortgage rates.

[Tim Harford]

And here lies the truth where house prices are falling, that's not because of a glut of supply. Rather it's a dearth of demand. With mortgage rates and house prices where they are, people can't afford to buy houses, especially in London and the south.

[Neil Hudson]

That has implications for activity in the market. If there's not enough people that can afford to buy new homes, then house builders won't build them.

[Tim Harford]

It's not just where you live that matters, it's what you may have bought for years. Buying a flat was a pretty good move. Between 1997 and 2007, flat prices rose by about 13% a year, which is a lot. And it's about the same as houses. But fast forward to the period between 2017 and 2022. While houses rose between 5 and 6% a year, flat prices only increased by about 2% annually, mainly due to the leasehold and building safety crises which affected flats after the Grenfell tower fire in 2017.

[Neil Hudson]

If you're looking in England at the moment, my strong recommendation would be try and buy a house rather than a flat.

[Tim Harford]

Well, more or less does not give investment advice, but we will pass on your comments to our listeners.

[Neil Hudson]

I tend not to either, but I feel quite strongly about that one in particular.

[Tim Harford]

Now, so far we've just been talking about prices in nominal terms, the sticker price of a house. But economists can and do adjust these prices to take into account inflation, and this changes the picture Adjusted for consumer price inflation, average house prices are actually down substantially by 14% since the peak in September 2022. Another useful bit of context comes when we compare house prices to earnings.

[Neil Hudson]

So house prices have actually fallen quite sharply relative to earnings because although they haven't changed, earnings have actually grown quite significantly. So if we look at the latest data, house prices have fallen by around about 17% relative to earnings over the period.

[Tim Harford]

Bad news if you have a big house you want to sell, but not so bad if you're hoping to get on the so called housing ladder. Our thanks to housing analyst and fearless iconoclast Neil Hudson. You're listening to More or Less, and if you want to explore how language and numbers can be used to mislead and bamboozle us, check out the Open University's buzzword Bingo. To find it, have a look for BBC More or less on your search engine and follow the links to the Open University. Now for something completely different. Some of you may be familiar with this. Pit TV game show the Traitors. Now I have a confession to make. I've never watched the Traitors. We played the board game version during the weekly More or Less game night, but that didn't really work out. My editor, Richard and I are faithfuls, but it transpires that every other one of the More or Less team is a traitor, especially McNeil. My editor isn't just faithful to More or Less, he's also faithful to the Traitors TV show and he won't stop trying to get me to watch it. He even stooped so far as to try to tempt me by saying it's all to do with maths. Delicious, precious maths. But is it really? Or does human emotion ruin it all? I spoke to Dr. Cat Phillips, Innovation Research Associate at the University of Warwick, mathematician and traitor's aficionado to talk us through the sums behind the series. We started with probability the 19 faithfuls versus the 3 traitors. If you feel me touch your shoulder, that means you are a traitor. Players, I have selected my traitors.

[Dr. Kat Phillips]

So most of the players don't know all of the information and a small group of the players are the informed minority.

[Tim Harford]

Traitors you will meet and discover each other's identity is tonight. Your job is to remain undetected and.

[Dr. Kat Phillips]

Murder the faithful so they have all of the information. They know the entire game, who's who, which roles people are playing. Faithful.

[Tim Harford]

Your job is to stay alive, hunt the traitors and banish them before you become their next victim. Remember, if there are any Traitors left at the end, they take all the money. Right. So the faithfuls have the advantage of numbers.

[Dr. Kat Phillips]

Yes.

[Tim Harford]

And the traitors have the advantage that they know who the other traitors are. And the faithfuls have no idea. They're just guessing.

[Dr. Kat Phillips]

Yes, exactly. So you'd think there's power in number, but power in information is quite valuable in the game as well, because everyone's trying to figure out who's who. And if you know who's who, you're going to lie about it and try and shift people's opinions in the wrong direction.

[Tim Harford]

Do you know I'm suspicious of Jonathan? Did you see how he dug his grave? Claudia hasn't picked the traitor since. Oh, he hasn't picked the traitor yet. And so intuitively, because we are social creatures, people will try to play this game by just kind of looking other people in the eye and trying to figure out who's lying and who's kind of smiling in a funny way or who's being suspiciously silent. Which, you know, that might work. But there is also a mathematical approach to the problem. So how does a mathematician think about this game?

[Dr. Kat Phillips]

Mathematically, you should be collecting evidence, and that can be things people say, that can be how people vote, that can be how people perform in the game and who has been eliminated via murder or banishment and use that evidence to try and update probability of everyone being a faithful or being a traitor.

[Tim Harford]

You used the word update. That's a Bayesian word, right?

[Dr. Kat Phillips]

Yes. So Bayesian probability, and this is actually a type of Bayesian coordination game, basically says that you have, instead of having random probabilities, so just the odds of someone being a traitor, you actually have the odds of someone being traitor given an amount of evidence. So instead of just saying someone's 20% chance of being a traitor, it's trying to calculate or update given an amount of evidence. I once fell asleep in a wheelie bin.

[Tim Harford]

It's about.

[Jay Foreman]

It.

[Tim Harford]

So, yeah, at the beginning of the game, if there are, say four traitors and there are 20 players, the chance that any particular person is a traitor is four divided by 20 or one in five. 20%.

[Dr. Kat Phillips]

One in five. Yeah.

[Tim Harford]

And then as an unsuspecting faithful. So I don't know. Well, probably a very suspecting faithful. I'm suspecting all kinds of people. I don't know who the traitors are. As more information comes in, I am up rating or down rating my assessment that each individual person is a traitor.

[Dr. Kat Phillips]

Yes.

[Tim Harford]

Who has the advantage then? You've got the faithful have the Advantage of numbers. The Traitors have the advantage of information. Looking back at previous series, who has.

[Dr. Kat Phillips]

Tended to win, I do think the Traitors do have an advantage over all of the different games and that sort of comes out from looking at who's won. But typically with this sort of game, an individual traitor versus an individual faithful, the Traitor does have a massive advantage if it was just one to one. But adding in that human noise and human error, logical gameplay does tend to go out the window. So the reasoning is a bit skewed.

[Tim Harford]

Flabbergasted, like, who uses that word? You can't just call someone a traitor because they have a better vocabulary than you. Now, in one of your Instagram videos, you started talking about Shannon Entropy and I love a bit of Shannon Entropy.

[Dr. Kat Phillips]

Yeah. So information entropy, or Shannon Entropy is basically how certain a bit of information is. So how surprised are you going to be when the outcome happens? I think the example that I used was a random fair coin is going to be 50% heads, 50% tails, so you're sort of half surprised either way. Whereas a weighted coin that I tell you is weighted, say it's weighted towards heads. If it flipped a tails, you'd be really, really surprised. So that has a much lower entropy. There's a lot less surprise across the options.

[Tim Harford]

So how would you use that, then?

[Dr. Kat Phillips]

In the Traitors, as a Faithful, you sort of want to find evidence that really cuts down your odds, so breaks down the beliefs that you have. But for the traitor's perspective, you have this wonderful opportunity to sort of increase the uncertainty by throwing aspersions on people who otherwise would have been classed as, oh, they're definitely a faithful. Like, you want to keep the doubt high across as many players as you can without then pulling a suspicion on yourself because you're just throwing shots into the air.

[Tim Harford]

Yes. How are the contestants doing? Are they playing a smart game at the moment or making a mess of it? Are they mathematical geniuses? What's going on?

[Dr. Kat Phillips]

There are some really interesting choices going on.

[Tim Harford]

Interesting as in rubbish.

[Dr. Kat Phillips]

I'm being polite.

[Tim Harford]

The sense I'm getting from Cat is that there's plenty of mathematics in the game if you know how to use it. Bayesian updating Shannon Entropy. And that's before we even discussed the Prisoner's Dilemma. And yet it's hard to use that maths, partly because none of the players are trained mathematicians, partly because human emotions overlay everything. I think my editor was leading me astray. Wait, wait, was he a secret traitor all along? I think I'll stick with being a Dungeon master. Thanks to Dr. Kat Phillips. She's on Instagram as katdoesmaths. That is all we have time for this week, but please send in your questions and comments to more or lessbc.co.uk. we'll be back for the last programme in this Radio 4 series next week. Until then, goodbye. More or Less was presented by me, Tim Harford. The producer was Tom Coles with Nathan Gower and Lizzie McNeil. The production coordinator was Brenda Brown. The programme was recorded and mixed by James Beard and our editor is Richard Varden. I'm Dr. Chris Van Tulleken. And I'm Dr. Zand Van Tulleken. Chris, it's that time of year when we set resolutions. It certainly is, Zand. And that is why In January, our four episodes of WhatsApp docs are going to be on the key themes that feature in resolutions alcohol, food, exercise and the whole notion of resolutions themselves. Can we change? Should we change? Well, a lot of us think we should. That's what we're doing the whole month, paying attention or thinking we should pay attention to our health and wellbeing. In addition, we will be dropping a daily dose of expert wisdom from previous episodes because Zahn and I have felt and found that we need. We need a reminder reminding about all the things that we've learned from difficult conversations to how to look after our knees, protein, the power of nature, snackable sized episodes every day. We've got you covered and these daily doses are going to be dropping into the medicine cabinet. That is the WhatsApp docs feed on BBC Sounds. If you're the purchasing manager at a manufacturing plant, you know having a trusted.

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