Yesterday was all about fallacies: the gambler’s fallacy, the conjunctive and disjunctive fallacy, the base rate fallacy, the framing effect (which, if you think about it, is a kind of fallacy) and one of my favorite stories from behavioral economics: the organ donation case from Europe. We’ll get to each one in turn.
The word fallacy comes from the Latin word fallere, which means to be decieved – also making me wonder if the phrase “to fall for” is related to the same word. The story with the three “fallacies” that we’re talking about in this post is the same: our brain falls prey to some errors that are in retrospect irritatingly obvious.
The Gambler’s Fallacy
Have you ever felt you were on a lucky streak while playing a game of cards – felt as if you were invincible while rolling a pair of die? That’s the hot hand fallacy. On the other hand, have you ever felt tempted to continue playing a game because you have been losing for a while, and feel like your luck is due to turn for the better? That’s the reverse of the hot hand fallacy – but both are really (excuse the pun) two sides of the same coin: you think the next outcome is a function of the previous ones, whereas basic probability teaches you that they are independent events.
The Conjunctive (and Disjunctive) Fallacy
Say a person is introduced to me at a party, and I learn that this person has done her education in finance and investing, and is very enthusiastic about Picasso’s paintings. Which of the two options I describe below is likelier?
One, that she is in banking. Two, that she is in banking and has some Picasso prints hanging on her wall at home.
Most people (myself included) would be tempted to go with the second option. But again, basic probability teaches us that this is wrong, because we are talking about the intersection of two things (the probability that she is a banker AND the probability that she has Picasso prints hanging at home) – and two things happening at the same time is unlikelier than either of these things happening individually.
The disjunctive fallacy is the same idea in reverse. Meet my friend Rahul. Rahul is six and a half feet tall, is built like a bull, and can demolish multiple plates of food at the same sitting. He spends a couple of hours a day (at least!) at the gym. What is likelier:
- Rahul is a wrestler
- Rahul is a wrestler or a classical singer
The point is that once should always choose the second option because it includes the first in any case.
The Base Rate Fallacy
I’ll not get into the math in this case, but just give you the short description of the idea: false positives are going to be overwhelmingly likely if the base rate is very low, and the human brain has trouble understanding this idea.
Here’s what this means:
Of the millions of people who transit through airports the world over, a vanishingly small minority will actually be terrorists. If the algorithms used to detect them are even slightly inaccurate, they are likely to err on the side of over-identifying potential terrorists. We would therefore be wrong to assume that every person who is flagged as a potential terrorist actually is a terrorist.
(Note that it is way more complicated than this, but that’s the shortest version I could manage).
This post is already a fairly dense one in terms of ideas, so I’ll split this one into two, and cover the rest tomorrow: the framing effect, and the European organ donation saga.