Was it one of the posters who also hasn’t watched the video?
If you haven’t watched it, that’s fine. But then I don’t think you are equipped to say either what the video presenter thinks or who in this thread has fairly explained what the video presenter thinks.
Having seen those hundred posts you should be fully aware that not everyone is understanding it or interpreting it in the same way. Whose word are you taking and why? I’d be fascinated to know if it is someone who’s views you already agree with because, as it happens, the latter part of the video (that you won’t watch) talks about exactly that sort of cognitive error as well.
The OP did leave some detail out of their text summary of the question (that’s what makes it a summary, after all), but I don’t think it’s missing anything essential. The summary starts out with
OK, so we’re judging junctions. I think it’s already pretty clear that junctions with fewer accidents (of whichever kind) are better than junctions with more accidents. That’s the basis on which we’re judging them. So if we want an “equivalent” intersection, it’s one we would judge the same way based on that criterion.
And then if you watch the video for more details, you find that an agency is trying to choose between two designs. Again, it should be clear that they’re trying to get the design with fewer accidents.
I’m not deflecting, I apologise if I was retreading old ground for you. I thought it was a relevant point to make, for others if not for you.
We can leave it there then?
Well–to some extent that’s exactly what I did, because I also immediately put the problem into that category of math word problems where the words are just labels to make it more memorable and don’t actually have any meaning. “Major accidents” and “minor accidents” could have just been gloops and glorps as far as I interpreted it.
Another aspect which makes the whole setup weird is how backwards it is. It’s presented as if the designers of layout B can somehow adjust the minor accident count to make the two equivalent, for some unknown end. I’d find the setup to be much clearer had the presenter said something like: “Suppose the DoT had found that the two layouts were equivalently safe for this location. Given that conclusion, what number would you have expected to show up in that box?”
Well that line of reasoning isn’t typical of the mindset that the question was designed to illuminate and it can be hard to put ourselves in the minds of others.
How can it be that what is blindingly obvious to us is not apparent to others?
I was imagining that the first three numbers had come back from the modelling and only the final one was still to be generated. The big question being then what would that need to be to make B as good/bad as A?
Everybody has a slightly different approach to the problem and sees it in a different light. For instance, I suspect one thing that led me down the path I did is this: as soon as he started drawing the 2x2 grid, with two different possibilities and two different measurements, I immediately thought of Simpson’s Paradox. I.e., the puzzle was about how road B could be safer even though it did worse on both metrics.
A few moments later I realized it wasn’t about that, but the impression was still set, which is to say that we’re looking at independent situations (Simpson’s Paradox kicks in when there is another confounding variable).
FWIW I rewatched now to see if there was some citation available, to see if the way it was presented to those college students was as garbled and unclear as his was. If it’s there I missed it on rewatch.
To my read this is very meta. He very much wants to see something that confirms the cognitive bias he knows exists. I know it exists too. He then sees in this “experiment” something that is not there, precisely because he is subject to the cognitive bias he wants to see, just like shared the graph on support for same sex marriage uncritically.
To some degree though he conflates two things. The point of the cognitive reflection test is how often we jump using broad heuristics and the degree we do or don’t stop to think if that answer makes any sense and rethink. But he conflates that with confirmation bias, accepting that which supports our existing beliefs as true fairly uncritically.
But that’s not how the actual video frames it. It’s clear enough from the opening minute of the video that it is not two separate cases of data from two separate sections of extant road, but a choice between proposed layout A and proposed layout B for the same section of road.
You can say that all you want, but I interpreted it a different way, and it was certainly not “clear enough” IMO. Looking at Brady’s animations again, I guess I can see they’re supposed to represent the same location, but I wasn’t looking at closely at them, and they aren’t part of Harford’s verbal description in any case.
There seems to me to be a thread of “this is important to understand because its not an abstract question, in the real world, you need to be able to understand how to judge these two cases”
Well in the real world, these two layouts are already equivalent. A thousand accidents resulting in hospitalization or death is completely unacceptable and neither layout should be considered for implementation without major changes. They are equivalent in suitability for implementation. (and just reading the description of how the problem is defined, this seems a perfectly cromulent interpretation of the term equivalent).
The words are enough. He describes it as a choice being evaluated by the DOT for the same spot of road. One of which will cause 2000 major and 16 minor accidents, the other of which will cause 1000 major and X minor accidents.
The will is important as it further emphasizes that this is not a comparison of historical data from two different sections of road, but two options for the same section of road which the DOT is evaluating. That’s not the only cue, but it helps to resolve the ambiguity.
As I said, clear enough.
ETA: And specifically he says “gonna” and “are predicted”
He never says they’re the same spot of road. He says:
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
Already the description is basically nonsense. Is there one road layout or two? And are they looking at “the fewest accidents” or some other metric like the financial or social cost of those accidents?
If he had actually said “the same spot of road” or “are proposing to build a road in a given location” or something equivalent, I’d have interpreted it differently. But nothing directly implies that they’re the same.
“…two different possibilities for the road layout…” seems clear enough to me. Note the use of the definite article “the.”
Ok, but he initially says a road layout. Since he clearly intended to say “two different possibilities for the [proposed] road layout,” a layout doesn’t make sense. He switches between an empty plot intended to contain a layout vs. the layouts themselves.
At any rate, having to narrowly parse the grammar of his question to interpret it the “correct” way should perhaps indicate that it was poorly phrased.
If, as Andy_L suggested, suppose the question had been “Person A has 2000 one-dollar bills and 16 nickels; person B has 1000 one-dollar bills and some number of nickels. How many nickels is that if A and B have an equivalent amount of money?” Do you think a similar number of people would get that wrong? If not, then the problem is with the phrasing of the question.
But the point of the video was that many people gave the answer eight.
Can you come up with a plausible use of the term equivalent that would say a location that has two thousand major accidents and sixteen minor accidents is equivalent to a location that has one thousand major accidents and eight minor accidents?
The point was that a lot of people were thinking “A is to B as C is to D, so what’s the value of D?” when they should have been thinking “A plus B is equal to C plus D, so what’s the value of D?”
And if the question had been instead “Person A has 2000 one-dollar bills and 16 nickels; person B has 1000 one-dollar bills and some number of nickels. How many nickels is that if A and B have an equivalent pattern of money?”, the right answer would be very different.
Once we admit / agree the two different questions give two different answers, it’s time to move on to the actual question posed:
“Person A has 2000 one-dollar bills and 16 nickels; person B has 1000 one-dollar bills and some number of nickels. How many nickels is that if A and B are equivalent?”
Equivalent in what way? Aye, there’s the rub.
Well, part of the rub. Even getting to the point where the definition of equivalence matters requires a specific parsing of the problem statement. But I agree that even with the right interpretation, you still have the problem of equivalence. Especially since Harford explicitly says they’re “trying to figure out which one is going to cause the fewest accidents”! By that metric, exactly 1016 is the right answer.
I feel like there’s an alternate universe where most people gave an answer of 100,000 or whatever, and the response was “Idiots! I defined equivalence such that it doesn’t distinguish between major and minor. The answer is 1016.”
We have already done that, numerous times. Why are you asking again?
I asked for a plausible use of the term equivalent. You didn’t produce one.
The problem was presented as an engineering question (albeit a hypothetical one).
I can see an engineer being asked to design a system on the basis of which one has fewer accidents. And I can see being asked to design a system based on which one has fewer serious accidents. Or maybe a design based on some other factor like cost or traffic flow or how quickly it could be constructed.
But an engineer being asked to design a system so it would have a specified ratio of major and minor accidents? With the specific ration being a 250:1 ratio favoring major accidents?
That is not even remotely plausible.