I remember well my amazement when I heard my first ever demonstration of Holmes's observational and deductional prowess in A Study in Scarlet. We had just settled in, as we did every Sunday night, to listen to the evening's reading entertainment. Earlier in the week, we had finished The Count of Monte Cristo--after a harrowing journey that took several months to complete--and the bar was set high indeed. And there, far from the castles, fortresses, and treasures of France was a man who could look at a new acquaintance for the first time and proclaim with utter certainty, “You have been in Afghanistan, I perceive.” And Watson's reply--“How on earth did you know that?”--was exactly how I immediately felt. How in the world did he know that? The matter, it was clear to me, went beyond simple observation of detail.

How, indeed? Again and again, Sherlock Holmes delights in displaying his prowess in identifying someone's past and present to the ever-appreciative Watson; and Watson, in turn, can never seem to quite master the art himself, only seeing the logical link once it has been explained. But Watson is not alone. Holmes's technique is so elusive not only because it relies on observational mastery that most of us do not possess but in that it also manages to both cast off and exploit one of the most common reasoning fallacies that we are prone to committing: the conjunction fallacy, whereby we give a conjunction a higher probability of occurring than we do either of its constituent parts, allowing one element to color our perception of the rest.

How do we form judgments?

When we form a judgment, we often compare something--in this particular case, a person--in the real world to a mental model of that thing in our heads. How closely that person corresponds with the model is called their representativeness. For instance, Holmes is likely close to exemplifying the model for “detective” in our heads--he is, after all, one of its original prototypes. Watson, on the other hand, may not always fit in with the mental model for “doctor” that one typically holds--few doctors (or so we'd hope) tag along on illicit criminal-catching adventures and leave their practice at a moment's notice to accompany a friend on a new quest.

In forming the original mental model--say, of a detective or a doctor--we normally focus on several salient factors. The more common and typical something is, the more representative it seems. If it were, for instance, brought to our attention that Watson always carries a stethoscope and has a certain type of bowler hat that we associate with our picture of the typical doctor, based on the frequency with which we've seen such elements tied to a doctor in the past, we may increase our confidence in his being representative of the profession, despite the original incongruities. If, however, we are given even more discordant information that we originally had--for instance, that he enjoys gambling and chasing women--we are even less likely to see him as fitting the mold. But it is in that process of assessing typicality that we often go wrong.

Typical and easy to recall does not mean likely or right

The fact that something comes to mind easily does not necessarily make it diagnostic or even particularly representative, even if we think it so. And when it comes to judging people, the distinction is an essential one. Consider the following classic example of Bill and Linda, taken verbatim from a 1983 paper by Amos Tversky and Daniel Kahneman. Each description is followed by a list of occupations and avocations, and the task is to rank the items in the list by the degree that Bill or Linda resembles the typical member of the class:

Bill is 34 years old. He is intelligent, but unimaginative, compulsive, and generally lifeless. In school he was strong in mathematics but weak in social studies and humanities.

Bill is a physician who plays poker for a hobby.

Bill is an architect.

Bill is an accountant.

Bill plays jazz for a hobby.

Bill is a reporter.

Bill is an accountant who plays jazz for a hobby.

Bill climbs mountains for a hobby.

Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Linda is a teacher in an elementary school.

Linda works in a bookstore and takes yoga classes.

Linda is active in the feminist movement.

Linda is a psychiatric social worker.

Linda is a member of the League of Woman voters.

Linda is a bank teller.

Linda is an insurance salesperson.

Linda is a bank teller and is active in the feminist movement.

When the researchers' subjects were presented with these lists, they repeatedly made the same judgment: that it was more likely that Bill was an accountant who plays jazz for a hobby than it was that he plays jazz for a hobby, and that it was more likely that Linda was a feminist bank teller than that she was a bank teller at all. Logically, neither idea makes sense: a conjunction cannot be more likely than either of its parts. If you didn't think it likely that Bill played jazz or that Linda was a bank teller to begin with, you should not have altered that judgment just because you did think it probable that Bill was an accountant and Linda, a feminist. An unlikely element, even when combined with a likely one, does not somehow magically become any more likely. And yet, 87% and 85% of participants, respectively, made that exact judgment. This, in essence, is the conjunction fallacy--and it is as difficult to get rid of as it is prevalent in our typical determinations of people. We allow one salient feature to override other determinations, and in so doing, we lose sight of logic.

Indeed, in a follow-up, where only the two relevant options (Linda is a bank teller or Linda is a feminist bank teller) were included, fully 85% of participants still ranked the conjunction as more likely than the single instance. And even when they were given the logic behind the statements, they sided with the incorrect resemblance logic (Linda seems more like a feminist, so I will say it's more likely that she's a feminist bank teller) over the correct extensional logic (feminist bank tellers are only a specific subset of bank tellers, so Linda must be a bank teller with a higher likelihood than she would be a feminist one in particular) in 65% of cases. We can all be presented with the same set of facts and features, but the conclusions we draw from them need not match accordingly.

The logic behind the conjunction fallacy

Why do we make this mistake? One of the reasons has to do with the number of details presented: the more details there are, the more confident we are--especially if one of those details makes sense. A longer list somehow seems more reasonable, even if we were to judge individual items on that list as less than probable given the information at hand. So, when we see one element in a conjunction that seems to fit, we are likely to accept the full conjunction, even if it makes little sense to do so.

Moreover, the easier we can bring something to mind, the more we believe in it. If a mental image arises quickly and fits a description, we tend to think it is correct, even when it may be an exception in all cases. In fact, it's often easier to remember exceptions than rules--they stand out more, while rules are, generally, much more mundane and boring. In another Kahneman and Tversky example, for instance, Hollywood actresses who had been divorced more than four times were judged to be more representative than ones who voted Democratic - in keeping with a media-coverage stereotype, no doubt, that had little bearing on how actually representative any given piece of information would be. Is it newsworthy to report that most actresses are Democrats? Or that many have stable marriages and have not been divorced a single time--or perhaps never married at all?

The last example brings me to what is perhaps the most pervasive reason behind the conjunction fallacy: we tend to ignore base rates. To go back to the earlier judgment of either Holmes or Watson as representative or typical of his profession, it is essential to ask one additional question: How relatively frequent are detectives and doctors, respectively, in this particular society? Even were we to hear a precise description of Mr. Holmes--without, of course, knowing him to be Sherlock Holmes--we should not jump to the conclusion that such a man is likely to be a detective, as the prevalence of detectives in the general population is remarkably low (and of consulting detectives in particular, equal to precisely one individual). But we never think of that. We just grasp at a mental match and call it a day.

What Holmes does differently: sticking to logic, regardless of impressions

Holmes, however, manages to both cast off and exploit this tendency toward the conjunction fallacy in forming a judgment of a specific individual. He casts it off in the sense that he himself neither ignores base rates nor conflates ease of image or amount of information with actual representativeness and confidence. Consider his guesses of professions: rarely do they jump--unless with good reason--into the esoteric, sticking instead to more common elements - and ones that are firmly grounded in observation and fact, not based on overheard information (as in the media world) or conjecture. When he lists the elements that allowed him to pinpoint Watson's sojourn in Afghanistan, he points, to name one example of many, to a tan in London--something that is clearly not representative of that climate and so must have been acquired elsewhere; Holmes, we must remember, demonstrated his logic before the advent of the ubiquitous tanning salon and easy weekend travel--as illustrating his having arrived from a tropical location. One element, one conclusion. Step by logical step. The category “doctor,” you will see if you read Holmes's explanation, precedes “military doctor”--category before subcategory, never the other way around. Never would Holmes call Linda a feminist bank teller, unless he was first certain that she was a bank teller at all.

And Holmes exploits the tendency in others in the sense that he realizes that most people do make these mistakes, jumping around from point to point, letting irrelevant elements affect their judgment, allowing themselves to be influenced by easy representations and commonly reported facts. Hence his ability to impress, to stay a step ahead of not only Watson, but Scotland Yard - and, notably, to don such an array of successful disguises: he knows, for instance, how someone usually judges an old woman and so is safe in that getup many a time. (A side note: someone else who exploits these tendencies to the fullest is the typical fortuneteller.)

So how to avoid the conjunction fallacy and judge someone more accurately than you otherwise might? Kahneman and Tversky found it remarkably difficult--nearly impossible--to guide people in the right direction. No matter how they pried, Linda the feminist bank teller prevailed. My advice--apart from rereading Holmes's logical chains methodically and taking their structure and premise, if not their precise content, to heart--is to understand how the fallacy arises to begin with. Don't let highly salient and seemingly representative elements influence a judgment from the get-go. You would likely never judge Linda a likely bank teller from her description - though you very well might judge her a likely feminist. Don't let that latter judgment color what follows; instead, proceed with the same logic that you did before, evaluating each element separately and objectively as part of a consistent whole. A likely bank teller? Absolutely not. And so, a feminist one? Even less probable.

Or, to focus on another aspect, don't let the ease of thinking about Hollywood divorces lead you to believe that divorce is the norm, or even particularly representative of that group as opposed to any other group. Don't forget that even though a given political affiliation is not as sexy when it comes to news, it may be much more typical. And finally: don't forget that Hollywood actresses constitute only a tiny fraction of the general population - and even of the population of Hollywood. How likely is someone to belong to such a small group? It's from there that your conclusions should follow.

Photo credit: Sherlock Holmes sees Dr. Watson for the first time in A Study in Scarlet. By Richard Gutschmidt (1861-1926) [Public domain], via Wikimedia Commons

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Previously in this series:

Don’t Just See, Observe: What Sherlock Holmes Can Teach Us About Mindful Decisions

Lessons from Sherlock Holmes: Paying Attention to What Isn’t There

Lessons from Sherlock Holmes: Cultivate What You Know to Optimize How You Decide

Lessons from Sherlock Holmes: Perspective Is Everything, Details Alone Are Nothing

Lessons from Sherlock Holmes: Don’t Underestimate the Importance of Imagination

Lessons from Sherlock Holmes: Confidence Is good; Overconfidence, Not So Much

Lessons from Sherlock Holmes: The Situation Is in the Mindset of the Observer

Lessons from Sherlock Holmes: The Power of Public Opinion

Lessons from Sherlock Holmes: Don’t Tangle Two Lines of Thought

Lessons from Sherlock Holmes: Breadth of Knowledge Is Essential

Lessons from Sherlock Holmes: Don’t Decide Before You Decide

Lessons from Sherlock Holmes: Trust in The Facts, Not Your Version of Them

Lessons from Sherlock Holmes: Don’t Judge a Man by His Face

Lessons from Sherlock Holmes: The Importance of Perspective-Taking

Lessons from Sherlock Holmes: From Perspective-Taking to Empathy

Lessons from Sherlock Holmes: Why Most of Us Wouldn’t Be Able to Tell That Watson Fought in Afghanistan