OP did take the trouble to transcribe the relevant parts - almost all of them, so far as I can tell from subsequent discussions.
Nope. Not given the ambiguity of “equivalent”.
And this is not just sophistry. Granted, I didn’t watch the video, I went only on the part that OP transcribed. But this was genuinely my first thought - that the ratio of major:minor incidents is so weird that the most important challenge is to explain it, which might mean finding “equivalent” junctions with a similar atypical ratio in order to see what they have in common with the first junction.
Combine that with a setup where if someone asks a question in a video… well it’s not an arrangement where you can usually interrogate the questioner further, is it? So if the right answer is “you should ask the questioner more questions”, that seems like it’s deliberately misleading.
Though an equally (or possibly more) valid reformulation would be:
Country A has 2000 murders a year and 16 other crimes.
Country B has 1000 murders.
To be “equivalent” how many other crimes would country B have a year.
In this case 8 is trivially the correct answer. And mathematically it’s the same question.
It’s a bit ambiguous, as they aren’t specific about what “equivalent” means but you would choose 8 every time if this was a test.
Without saying what you mean by equivalent (as in “to cause an equivalent amount of harm”) its absolutely not the case that 8 is obviously wrong.
I think if you watch to the end of the video you’ll learn more about what this tells us about human cognitive abilities, the errors we make and so further info about the person who orignally create this question and did research in this feild.
If you knew it all anyway and don’t think it is interesting then fine. You are one-up on a great many people and don’t need to go any further. I personally find it fascinating.
It’s not all that poorly framed. It tells you why you want to know the answer, which should be enough to understand which interpretation is needed. There are still gaps in the given, like @Bootb’s question of whether we want to measure “badness” by time lost, or money, or specifically taxpayer money, but what we do know is certainly enough to say at least something.
But even if the question is badly-posed, the proper response isn’t to give a snap answer. It’s to say that the question is badly-posed.
I read in my education classes about a study, where they asked a bunch of elementary school students “A captain is taking a bunch of animals on a ship. There are 24 sheep and 16 goats on the ship. How old is the captain?”. The answer, of course, is “There’s no way to know”. But that’s not the answer most students gave. They said things like “I think it’s 40. In questions like this, you’re supposed to add, subtract, multiply, or divide, and adding is the only one that gives an answer that makes sense”.
It’s mathematically the same question, and 8 is just as wrong an answer, for the same reason. If Country B has half as many murders as A and also has half as many other crimes as A, Country B is doing better than Country A.
I suppose it’s possible to understand the question as “equivalent in the ratio of major to minor incidents.” It doesn’t seem natural to me, but that could be just me.
I think that’s a function of how surprising you find the ratio to be. It stuck out immediately to me as a very prominent unexplained feature of the hypothetical.
No, I don’t think the verbal description of the problem given in the OP is at all a fair and complete statement of the problem as actually presented in the video. And that’s a big part of the problem you and others are having, I think.
I think carefully listening to the initial set-up would suggest some potential definitions of “equivalent” are far less sensible than others.
But, as has been proved in this thread, many people don’t listen carefully or are very easily knocked off course when presented with a superficially satisfactory answer that aligns with their preconceptions.
If someone listened carefully and understood that the authorities were trying to decide which junction type to build based on the outcome of the modelling (which was all info given in the first 45 seconds) then “equivalent” only really makes decent sense when interpreted as “how many minor accidents would there have to be on a type B to make it as bad as (the equivalent of) type A?”
I think many people weren’t listening at all, but rather relying on the (not really accurate) summary of the problem given by the OP.
Do we actually know that anyone, let alone a vast majority, responds with that wrong answer?
To me the set up clearly puts out there major means death and serious injury. Who doesn’t immediately go to well how many accidents of trivial or no injury is a death or serious injury worth? Then multiply by 1000 as the first rough approximation.
The error I make in doing that is assuming they have the same volume of traffic. That could be a false assumption. The first one could be a major interstate merge and the second a side street intersection rarely travelled. We need to know that these are on matching traffic volumes.
Of course I just read the OP and did not click the video.
Yup in the video they recorded responses and 8 was the popular answer.
Yes I think listening fully and carefully to the video and understanding exactly what was said would a good place to start.
It also gives some further background into the purpose of the question and what it is intended to show.
yes, when given to Yale students the vast majority gave the wrong answer and “8” was the most popular of the wrong answers.
who doesn’t? most people, that’s who.
right, but the video gives you information that speaks to that.
Honestly, I feel like a broken record here but how many people are actually listening to the video and taking note of the actual words used? I don’t anyone is in a position to offer a definitive opinion until they do.
I’ve watched the first part of the video several times now and I still fail to see how its implied that the two layouts are for the same location, and with the level of traffic held constant.
It’s possible to interpret it that way of course, but the way I interpreted it initially, the layouts were in different locations with different conditions, and the question of equivalence was about what would make the two situations have the same strange ratio.
Ok, I just watched the first 1:20, which is the entire setup.
He says the Department of Transport wants to work out (this is verbatim)
which one is going to cause the fewest accidents [1]
This makes no sense. If I take that question at face value, the Dept of Transport just wants the smallest total number of accidents, without regard for whether they are major or minor.
He then goes on to explain how “major” and “minor” are defined, in accord with common sense. Then he draws a 2 x 2 table of the two layouts, with the known numbers of major and minor accidents in 3 boxes and one empty box. But he completely glosses over the glaring fact that the ratio for the first layout is so strange, he just ignores it.
He then restates the question differently as (verbatim)
what goes here to make these two schemes equivalent [2]
So we have the question stated in two different ways. [1] makes no sense at all, because it implies that major and minor accidents carry equal weight. [2] is ambiguous, and posed just after giving us some strange data which are just left unexplained.
My opinion of the problem is, if anything, worse now that I have watched the setup.
Exactly the same as me, thanks.
Including the maker of the video, apparently, who first posed the question as “which one is going to cause the fewest accidents”, which implies the exchange rate is 1.
The question, as the questioner wants it answered, in unanswerable.
The obvious way would be by analyzing average cost of damage in a minor accident vs. a major one but even if you do that, I’d rather be in 1000 accidents where my bumper gets dented than 1 where my head goes one way and my torso goes another.
“The Department for transport is looking at a road layout and they’ve got two different possibilities for the road layout”
It seems fair to infer from that that it is one proposed road with two possible designs in question.
You can say it isn’t explicitly spelled out longhand but reads clearly enough to me.