Sticking to Logic, Regardless of Impressions
Sherlock 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. 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.
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.
By Maria Konnikova