Conjunction Fallacy, What’s Your Function?

August 25, 2012
Posted by Jay Livingston

The “conjunction fallacy.”  I've blogged about it before, but my beach reading yesterday was Thinking Fast and Slow by Daniel Kahneman, who discovered the concept – I nearly said, “who invented the concept”;  I'm still not sure which verb is more accurate – and the book has a chapter on this bit of twisted logic.

As Kahneman tells it, he and Amos Tversky were trying to show that heuristics, mental shortcuts, can replace logic even when logic is called for.  They went about this in the usual way of academic psychologists – they gave a quiz to undergraduates.  The quiz item that became famous was “the Linda problem.”  Students read or heard a brief description of Linda – “single, outspoken, concerned with social justice,” among other traits – and were then asked which conclusion about Linda was more likely

    a.  Linda is a bank teller
    b.  Linda is a bank teller and is active in the feminist movement [This was back in the 1980s.]

Nearly everyone chose “b.”

Wrong.  The conjunction of two events cannot be larger than either event.  “Feminist Bank Teller” cannot be larger (i.e., more likely) than “Bank Teller.”  Think of a Venn Diagram.

Hence, the conjunction fallacy.  Interesting that so many people can get it wrong, but I wonder whether it’s like some clever riddle or a joke – something with little relevance outside its own small universe. You’re never going to be having a real drink in a real bar and see, walking in through the door, an Irishman, a rabbi, and a panda.

Kahneman explains the fallacy as an instance of the more general problem of stereotyping or “representativeness.”  Linda in choice “b” fits with a plausible story, a stereotype.  She represents a more complete picture, and that picture overwhelms logical Venn-diagram reasoning.  Even when logic triumphs, it’s a struggle. Kahneman quotes Steven Jay Gould’s reaction to the problem.  Gould got the right answer, but

a little homunculus in my head continues to jump up and down shouting at me – “but she can’t just be a bank teller; read the description.”

I think Gould’s homunculus is miscommunication.  As I said in that earlier post about the conjunction fallacy (here), the question asked by researchers is sometimes not the question that people hear.  When I hear the question and the two choices, I don’t think of “a” and “b” as separate circles in a Venn diagram.  Instead, I picture a bank with its many tellers behind their counters.  One of them is wearing a large NOW button. Danny Kahneman taps me on the shoulder and whispers,”Which one is Linda?” I answer, “Most likely, she’s the feminist.”

Something else about this study bothers me.  Here’s Kahneman:

When I asked my large undergraduate class in some indignation, “Don’t you realize that you have violated an elementary logical rule?” someone in the back row shouted, “So what?”

I don’t usually have much sympathy for anti-intellectualism, especially at a university, but I have to admit that the backbencher has a point.  How might this fallacy ever come up in real life?  The scarcity of this fallacy may also be the reason it’s so difficult, even for Steven Jay Gould, to hear the literal question that the quizmaster is posing.  The other logical slips that Kahneman details in his book occur in many situations.  But what is the real-world function of the conjunction fallacy? 

Those other cognitive fallacies and shortcuts are often well-known, at least among cognitive psychologists, and Kahneman’s studies are attempts to specify the conditions under which they occur.  But the conjunction fallacy was new.  He had asked students the Linda question with something else in mind.  His assistant had gathered some of the questionnaires and left them lying in a tray

I casually glanced at them and found that all the subjects had ranked “feminist bank teller” as more probable than “bank teller.”  I was so surprised that I still retain a “flashbulb memory” of the gray color of the metal desk and of where everyone was when I made that discovery.

So the conjunction fallacy was a discovery.  But it was also an invention.  Kahneman created it, albeit unwittingly, with the Linda problem. 

At the end of each chapter of Thinking Fast and Slow, Kahneman offers short examples of how the ideas of the chapter might have real-world applications.  But the examples at the end of the Linda chapter are unrelated to the conjunction fallacy.  Linda seems to have no life outside of logic problems for psych students, much like the snee, the stoa, the edh, and other creatures whose existence, for most of us, is confined to crossword puzzles.