I just finished reading Wall Street iconoclast Nicholas Nassim Taleb’s Fooled By Randomness, which was basically a toned-down precursor to the inflammatory (yet highly accurate) Black Swan. A particularly interesting thing that Taleb mentions is that a lot of human irrationality comes from modularization, or using different parts of the brain for different situations. Some parts of the brain, especially those geared towards abstract reasoning, tend to be weaker for most. However, the part that we use to catch cheaters happens to be exceptionally strong.
I found this interesting enough that I made a mental note to research it some time. Fortunately, the next book I picked up, Malcolm Gladwell’s Tipping Point (I’m going through books pretty quickly at this point) referenced a study on this exact thing! So here goes:
Suppose that you are a tester in a playing card factory. The rule is that every card that is a red on one side must have an even number on the other side. Four cards lay in front of you:
1) A red card
2) A 6
3) A black card
4) A 3
It suffices to overturn only two cards to check whether the rules hold there. Which cards would you pick?
This seems to be quite a difficult question, as the majority of people get it wrong. They say 1) and 2), whereas the correct answer is actually 1) and 4). Here’s why:
From propositional logic, we know that if (if a then b), then it is not NECESSARILY true that (if b then a). Therefore, in this example, even though red cards must have even numbers, it is not true that even-numbered cards must be red. If you are in Atlanta, you are in Georgia. If you are in Georgia, you are not necessarily in Atlanta.
On the other hand, if (if a then b), then (if not b then not a). That means that if we have an odd-numbered card, it may not be red. If you are not in Georgia, you are not in Atlanta. This, the contrapositive, is well-known to anyone who has studied logic for at least 15 minutes. But most people don’t get this right.
Now let’s phrase it a little bit differently. How about a new scenario:
You are a bartender. You have been known to cater to underage drinkers before, and are at the moment under threat of heavy fines if any word gets out that you’ve served alcohol to minors, accidentally or inadvertently. You stand behind the counter, on the other side of which are four people:
1) A guy drinking Coke
2) A guy drinking beer
3) A guy facing away so you can’t see what they’re drinking. But their ID on the table says they’re 25.
4) A guy facing away, but their ID on the counter says they’re 18.
Who do you check this time? It should be fairly straightforward that it’s 2) and 4). In fact, it should be so easy that even poor Joe Bloggs, the Princeton Review’s imaginary friend who always “falls for it” on AP and SAT logical trap MC questions, would likely get this right. Yet it’s the exact same question. Just replace “if red then even” with “if over 21 then can drink beer” and you’re all set.
The reason for this is no doubt modularization – you use different parts of your brain to solve different setting-problems. This certainly sheds new light on the Kahneman/Tversky heuristics and biases experiments – although it certainly doesn’t negate their impact. Rather, the ease with which most people can solve the second question shows that we can be rational. Heuristics and biases experiments reveal we just aren’t, most of the time.
I was particularly taken aback by these results, for a personal reason. Last fall, I applied to study mathematics and computer science (Maths and Computing, as those Brits like to say) at Oxford University. I was granted an interview (I ended up having 5, actually). In one of those, I was asked the exact same question (the first one, of course). My abstract reasoning skills are quite developed so I answered it correctly, but it makes me wonder that my eventual acceptance into one of the most selective and prestigious universities in the world hinged, at least a little bit, on my ability to answer a question that people who had never opened a mathematics textbook in their life could easily answer, were it phrased differently. There were harder questions involved too, just to be clear. 😉
The Trouble With Science – Robin Dunbar (origin of the card puzzle)
The Tipping Point – Malcolm Gladwell
Fooled by Randomness – Nicholas Nassim Taleb