Okay, today's video is about annoying
puzzles. And I want to start with what I
think is possibly the most annoying puzzle
in the world. So it's a simple enough
question,
just imagine: the Department for
Transport is looking at a road layout
and they've got two different
possibilities for the road layout and
they're trying to figure out
which one is going to cause the fewest
accidents. So
let me just set out the possibilities;
okay this is road layout A,
this is road layout B okay?
Very easy. Now, both of them are predicted
to have a certain number of major
accidents, major accidents - this is going
to put people in hospital, we're talking
broken bones,
you know serious stuff. There's also a
certain number of
minor accidents, that might just be like
a bit of first aid, you might need to see a doctor,
cuts and scrapes, that sort of thing. Okay,
it's really simple.
Each of these different road layouts is
going to cause a certain number of major
and minor
road accidents, and I just want you to
fill in this gap here.
So, here we go. Two thousand,
one thousand,
sixteen. Now what goes here to make these
two schemes equivalent?
(Brady: It feels like 8.) - Doesn't it feel like 8?
Doesn't it feel like 8? So this
puzzle
comes from Shane Frederick, who's a
behavioural economist,
psychologist, at Yale University. Yale
University, they're smart at Yale
University.
And he asked a whole bunch of Yale
University students
what the answer was, and the most common number,
was a bit more than a quarter of them,
said 8.
The next most common answer was 32.
And the next most common answer was, if I
remember rightly, 1016.
Let's have a think about what's going on
here. Road layout A is going to cause
2000 major accidents, this is people in hospital;
oh and 16 people with bumps and bruises.
So why do we even care about this?
Rollout B
is going to cause only 1000 major
accidents, so
that's much better. So how many minor
accidents
would make it equivalent to to road
layout A?
And the reason this is an annoying question
is because there's no-
there is no right answer. But it's got to
be like a lot,
it's got to be many thousands, surely
many thousands. Because these are trivial accidents
and these are substantial. And a very
small number of people
in Shane Frederick's survey did say
10,000, 100,00, a million. And there's
no right answer but
it's gotta be something like that. But so
many just like you Brady,
the majority of people - or the
largest minority of people -
more than a quarter of people said, oh
we think
that the correct answer is 8.
And when you look at this you- your mind
is wanting you to say
8 right? Because it's like it just
puts everything in the same proportion, right?
Same. You've been asked, make these the
same, that's the same.
This is a- an example, it's quite a quite
a fascinating example, quite a
complicated example,
of something that Shane Frederick
studies which he calls
Cognitive Reflection Problems. And they
were made famous by the psychologist
Daniel Kahneman in his book 'Thinking
Fast and Slow' but
this one is not in 'Thinking Fast and
Slow'. So this one is-
this has barely seen the light of day
and I find it fascinating.
But um, another example, this one's
made very famous by 'Thinking Fast and
Slow' is a bat
and a ball together cost a dollar ten,
and the bat costs a dollar more than the ball.
So how much does the bat cost? You may
well have heard this before, a lot of
people have,
uh and instinctively you just think well
it's a dollar right? Because,
because the bat costs a dollar more than
the the ball, how much does- they cost a
dollar ten together so it's like a
dollar and ten-
but that's not right because that's 90
cents. And in fact the correct answer is
the ball costs five cents, the bat costs
a dollar and five cents.
But people leap to the wrong answer.
You want more? Oh yeah, this is a
classic; easier in the time of
coronavirus. Imagine a lake
that is filling with lily pads, has this
patch of
lily pads on the lake and the patch
doubles in size every day,
and after 48 days the lake is completely covered.
So the question is, on what day - out of
the 48 days - on what day
is the lake half covered? And people
often go oh well 48 divided by 2,
um it's 24. Or they'll they'll sort of
plot some kind of curve in their mind
and they'll say, oh maybe it's like
32 or something. But of course the actual
answer is
47 days, because the patch is doubling in size
every day. So it's half full the day
before you get to 48, that's what
exponential growth
uh looks like and we've kind of found
that the hard way. Now why do people get
these things wrong?
Why do people mess these cognitive
reflection tests
up? Why don't people look at this and go-
there is no right answer but it's got to
be something like
10,000 or 100,000 or a million.
The reason it's annoying is we don't
even have the information we need
to give the correct answer; but what we
do know is it can't possibly be 8.
(Why can't it be 8? Because,)
(because to look at that, if you look at)
(major accidents it looks like road A is)
(twice as dangerous as road B.) - Yeah.
So, remember what we've been asked, we're
being asked to make these two equivalent.
We're being asked
to to say, well, how many minor
accidents would it be
for for road layout B to be the
equivalent of road layout A?
So well the answer is, well it's the same
as how many minor accidents
are the equivalent of 16 minor accidents
plus a thousand extra major accidents?
And the answer is, well we don't
know but it's got to be
it's got to be at least a thousand and
sixteen. - (It's a bit apples and oranges)
(though isn't it? Because like)
(what's a- what's a major accident worth?)
Yeah, yeah, exactly,
there's there's no answer to the
question which is why I say it's the
most annoying question in the world.
But you don't look at it and go, oh
there's not enough- there's not enough
information. We need,
we need an exchange rate of major to
minor accidents. What you do is you look
at it you go - 8.
I mean you might not, but an awful lot of
very smart
students at Yale University immediately
said 8.
A whole other bunch, not quite as many,
said 32 and another bunch,
not quite as many, said a thousand and
sixteen.
A thousand and sixteen is maybe just
about right? If you say,
well we're just going to count accidents
and we can't compare them. But really
the answer's got to be, you know, a lot.
Way way more than 1016.
(You know what the problem with that question is?)
(You straight away forget what you're)
(trying to solve. You don't- you,)
(you forget the question.) - But that's it,
that's interesting though isn't it? Because it's-
you know, I told you I told you the story,
we're trying to compare these layouts,
we're trying to figure out, you know, which
which layout. We're trying to- what's the
equivalent of the two layouts?
And you- Daniel Kahneman often says, when
we're given a difficult question
we often substitute an easy question and
we don't notice that that's what we've-
(That's, that's exactly what I did. Because)
(I thought there was a solution)
(I contrived a question in my head that)
(had a solution.)
Yes absolutely. And 8 looks about
right. I mean you're absolutely right Brady,
8 is the- of course it's 8! Of
course it's 8. But of course it's not 8,
it's not even close to 8. So why do I
find these cognitive reflection
problems interesting? It's because my
own interest is in
how we think about statistical claims in
the news. Now when people see a claim on
social media; they see it on Twitter, on
Facebook, they see a newspaper headline,
they see a talking head on tv - how do we
think about
those claims? How do we process them? And
it's tempting, as a nerd, to go straight
to, you know, the technical details.
Have they confused correlation and
causation? You know, have they-
is it within the margin of error? All
the sort of statistical questions you
might ask.
But actually, very often
what's getting between us and the truth
is our own tendency
to leap to conclusions. Just as you saw
this and you thought '8, that sounds
about right',
very often we see somebody talking and
we very quickly go,
yeah that can't be right, that's just
fake news. What would you expect,
you know, from those guys. Or instead they
go, oh yeah yeah that sounds right; this
goes to prove I was I was right all
along. I always knew that this government was,
you know, was full of rogues and villains
and and they can't be trusted with
anything; I-
you know. I was having this argument with
my friends in the pub last night, ha!
In the pub - I remember the pub. I was
having this argument with my friends
last night and this proves I was right, and we
leap in with this emotional reaction. There
was a really interesting study published I think
about a year ago by Gordon Pennycook and
a bunch of other psychologists. And
Gordon Pennycook is interested in fake news
and why fake news spreads, and why people
spread misinformation. What they found
was you could take a bunch of people who
were, say, die hard Trump supporters
and show them a ridiculous claim
like '500 migrant caravans have been
intercepted
at the mexican border wearing suicide
vests'. You know, if you show them that claim
in the wild they might well click on it,
they might well
amplify it, like it, share it; and you ask
them and they'll say yeah yeah that
that is the kind of thing I might share.
If you instead go,
just wait a moment, how likely do you
think that claim is to be true? There's
no judgment, do you think that claim is
likely to be true?
About 90 of them will go actually yeah
that can't- like,
why would they be wearing suicide vests?
Why would- why would migrant-
it doesn't make any sense. None of this
makes any sense.
And so they're able to see, despite the
fact they have a strong
you know view of the world, we all have
strong views of the world, they're able
to see that that can't be true.
And yet at the same time, in a moment of
distraction a moment of inattention,
they would they admit that they would
retweet, it they would amplify it. And I think
I personally wouldn't be amplifying
stuff about migrant caravans in suicide
vests but we all
have stuff that we see, that we we
are tempted to retweet because it fits
our biases. I can give you an example,
a few years ago I saw a graph about
support for same-sex marriage.
Personally I think that's great news,
more Americans in favour of
equal rights for everybody - great. And I
retweeted this graph, which I think was from a-
The Washington Post or a perfectly
decent source.
And I tweeted it because of my emotional
reaction. Like, oh that looks right,
great, tweet. 150,000 followers.
The very first reply was 'Tim,
have you looked at the axes on that graph?'
And I hadn't. And actually it was a mess.
It was-
they'd done that thing where the, the,
opinion polls, the questions have been
asked
different distances apart. So maybe 10
years would pass and then they'd ask it twice
within one year. And they were all
equally spread- the whole thing was a mess;
I should have clipped it for my bad data
visualisation
file; but instead I was amplifying it to
all of my followers on Twitter,
because it just seemed like the kind of
thing that should be true and I wanted
it to be true and I wanted to
to share the news. Just like this seems
like it should be 8.
I love these puzzles because I- you know,
I love being
tricked and falling over my, you know, my
own feet
mentally. I love watching other people
get tricked by funny little puzzles;
but there's something deeper going on
here. When we're reading the newspapers,
looking at social media,
we shouldn't be just accepting or
rejecting things
because they feel right, because they fit
our view of the world.
You only need to notice your own
emotions, count to three,
have a little think, and that is a way to
stop yourself spreading misinformation.
If you enjoyed this, why not check out
Tim Harford's book,
How to Make the World Add Up. It's also
out in America under a different title,
the Data Detective or the Da-ta Detective
if that's how you like to say it.
There are links in the description.
And if you like puzzles,
why not check out today's episode
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[Preview] I had some delicious toast. One bit with
peanut butter, and a different bit with
cheese.
Because, you know, living the dream.