Judgement Under Uncertainty: Heuristics and Biases by Amos Tversky and Daniel Kahneman

This article first appeared in Science, volume 185, in 1974. Tversky and Kahneman had been working for some time on unconscious biases in cognitive thinking and this paper summarises the findings of a number of their experiments. The paper was reprinted as an appendix in Kahneman’s 2011 book, Thinking, Fast and Slow. It is overflowing with ideas and insights about key aspects of how humans think, to be precise:

This article shows that people rely on a limited number of heuristic principles which reduce the complex tasks of assessing probabilities and predicting values to simpler judgmental operations.

The article focuses on three ‘heuristics’ which people use to assess probabilities and predict values and highlights their flaws and limitations. What is a heuristic? An intellectual short cut, a rule of thumb, a quick practical way of solving a problem.

The three heuristics discussed by the article are:

  1. Representativeness
  2. Availability
  3. Adjustment and anchoring

1. Representativeness

People make estimates and judgments of things and other people, based on their similarity to existing stereotypes, to representative types. This is the representativeness heuristic or, as it’s come to be known, the representative bias. In doing, people tend to completely ignore statistical and probabilistic factors which ought, in more rational thinking, to carry more weight.

T&K gave experimental subjects a description of ‘Steve’, describing him as shy and timid, meek and helpful and interested in order. The subjects were then asked to guess Steve’s profession from a list which included librarian and farmer. Most subjects guessed he was a librarian on the basis of his closeness to a pre-existing stereotype. But, given that there are ten times as many farmers in the U.S. as librarians and in the absence of any definitive evidence, in terms of pure probability, subjects should have realised that Steve is much more likely to be a farmer than a librarian.

In making this mistake, the subjects let the representativeness heuristic overshadow considerations of basic probability theory.

Insensitivity to prior probability of outcomes The prior probability or base rate frequency describes the likely occurrence of the event being assessed, the likelihood of an event occurring without any other intervention, its basic probability.

T&K told experimental subjects there were ten people in a room, nine men and one woman. Then T&K told the subjects that one of these ten people is caring and sharing, kind and nurturing, and asked the subjects who the description was of. Without any concrete evidence, the chance of it being the woman is the same as it being any of the men i.e. 1 in 10. But the representativeness heuristic overrode an understanding of base rate probability, and most of the subjects confidently said this description must be of the woman. They were overwhelmingly swayed by the description’s conformity to stereotype.

Insensitivity to sample size People don’t understand the significant difference which sample size makes to any calculation of probability.

Imagine a town has two hospitals, one large, one small. In the large one about 45 babies are born every day, in the small one about 15 babies. Now, the ratio of boys and girl babies born anywhere is usually around 50/50, but on particular days it can vary. Over a year, which hospital do you think had more days on which 60% or more of the babies born were boys?

When students were asked this question, 21 said the large hospital, 21 said the small hospital and 53 said it would be the same at both. The correct answer is the small hospital. Why? Because smaller samples are more likely to be unrepresentative, to have ‘freakish’ aberrations from the norm. T&K conclude that:

This fundamental notion of statistics is evidently not part of people’s repertoire of intuitions.

Imagine an urn filled with balls. Two thirds are one colour, a third are another. A subject draws five balls and finds 4 are red and one is white. Another subject draws 20 balls and finds that 12 are red and 8 are white. Which subject should feel more confident that 2/3 of the balls in the urn are red, and why?

Most people think it’s the first subject who should feel more confident. Four to one feels like – and is – a bigger ratio. Big is good. But they’re wrong. The second subject should feel more confident because, although his ratio is smaller – 4 to 3 – his sample size is larger. The larger the sample size, the closer you are likely to get to an accurate picture.

Misconception of chance Here are three sets of results from tossing a coin six times in a row, where T stands for tails and H stands for heads. Ask a selection of people which of the three sets is the random one.

  1. TTTTTT
  2. TTTHHH
  3. THHTTH

Most people will choose set 3 because it feels random. But, of course, all three are equally likely or unlikely. Tversky and Kahneman speculate that this is because people have in mind a representation of what randomness ought to look like, and let this override their statistical understanding (if they have any) that the total randomness of a system need not be exactly replicated at every level. In other words, a random series of tossing coins might well throw up sequences which appear to have order.

The gambler’s fallacy is the mistaken belief that, if you toss enough coins and get nothing but heads, the probability increases that the next result one will be tails, because you expect the series to ‘correct’ itself.

People who fall for this fallacy are using a representation of fairness (just as in the example above they use a representation of chaos) and letting it override what ought to be a basic knowledge of statistics, which is that each coin toss stands on its own and has its own probability i.e. 50/50 or 0.5. Just because someone tosses an increasing number of heads in a row is no reason at all for believing their next toss will be tails.

(In reality we all know that sooner or later a heads is likely to appear due to the law of large numbers, namely that if you perform probabilistic events enough times the total sum of events is likely to revert to the overall expected average. T&K shed light on the interaction of the gambler’s fallacy and the law of large numbers by clarifying that an unusual run of results is not ‘corrected’ by the coin (which obviously has no memory or intention) – such runs are diluted by a large number of occurrences, they are dissolved in the context of larger and larger samples.)

Insensitivity to predictability Subjects were given descriptions of two companies, one described in glowing terms, one in mediocre terms, and then asked about their future profitability. Although neither description mentioned anything about profitability, most subjects were swayed by the representativeness heuristic to predict that the positively described company would have higher profits.

Two groups of subjects were given descriptions of one practice lesson given by several student teachers. One group was asked to rate the teachers’ performances based on this one class, the other group was asked to predict the relative standing of the teachers five years in the future. The ratings of the groups agreed. Despite the wild improbability of being able to predict anything in five years time from one provisional piece of evidence, the subjects did just that.

The illusion of validity People make judgments or predictions based on the degree of representativeness (the quality of the match between the selected  outcome and the input) with no regard for probability or all the other factors which limit predictability. The illusion of validity is the profound mental conviction engendered when the ‘input information’ approaches representative models (stereotypes). I.e. if it matches a stereotype, people will believe it.

Misconceptions of regression Most people don’t understand a) where ‘regression to the mean’ applies b) recognise it when they see it, preferring to give all sorts of spurious explanations. For example, a sportsman has a great season – the commentators laud him, he wins sportsman of the year – but his next season is lousy. Critics and commentators come up with all kinds of reasons to explain this performance, but the good year might just have been a freak and now he has regressed closer to his average, mean ability.

2. Availability

Broadly speaking, this means going with the first thing that comes to mind. Like the two other heuristics, the availability heuristic has evolved because, in evolutionary terms, it is quick and useful. It does, however, in our complex industrial societies, lead to all kinds of biases and errors.

Biases due to the retrievability of incidences Experimenters read out a list of men and women to two groups without telling them that the list contained exactly 25 men and 25 women, then asked the groups to guess the ratio of the sexes. If the list included some famous men, the group was influenced to think there were more men, if the list included a sprinkling of famous women, the group thought there are more women than men. Why? Because the famous names carry more weight and literally influence people into thinking there are more of them.

Salience Seeing a house on fire makes people think about the danger of burning houses. Driving past a motorway accident makes people stop and think and drive more carefully (for a while). Then it wears off.

Biases due to the availability of a search set Imagine we sample words from a random text. Will there be more words starting with r or with r in the third position? For most people it is easier to call to mind words starting in r, so they think there are more of them, but there aren’t: there are more words in the English language with r in the third position than those with start with r.

Asked to estimate which are more common, abstract words like ‘love’ or concrete words like ‘door’, most subjects guess incorrectly that abstract words are more common. This is because they are more salient – love, fear, hate – and have more power in the mind. Are more available to conscious thought.

Biases of imaginability Say you’ve got a room of ten people. They have got to be formed into ‘committees. How many committees can be created which consist of between 2 and 8 people? Almost all people presented with this problem estimated there were many more possible committees of 2 than of 8, which is incorrect. There are 45 possible ways to create committees of 2 and of 8 (apparently). People prioritised 2 because it was easier to quickly begin working out permutations of 2, and then extrapolate this to the whole sample. This bias is very important when it comes to estimating the risk of any action, since we are programmed to call to mind big, striking, easy-to-imagine risks and often overlook hard-to-imagine risks (which is why risk factors should be written down and worked through as logically as possible).

Illusory correlation Subjects were given written profiles of several hypothetical mental patients along with drawings the patients were supposed to have made. When asked to associate the pictures with the diagnoses, subject came up with all kinds of spurious connections: for example, told that one patient was paranoid and suspicious, many of the subjects read ‘suspiciousness’ into one of the drawings and associated it with that patient, and so on.

But there were no connections. Both profiles and drawings were utterly spurious. But this didn’t stop all the subjects from making complex and plausible networks of connections and correlations.

Psychologists speculate that this tendency to attribute meaning is because we experience some strong correlations, especially early in life, and then project them onto every situation we encounter, regardless of factuality or probability.

It’s worth quoting T&K’s conclusion in full:

Lifelong experience has taught us that, in general, instances of large classes are recalled better and faster than instances of less frequent classes; that likely occurrences are easier to imagine than unlikely ones; and that the associative connections between events are strengthened when the events frequently co-occur. As a result, man has at his disposal a procedure (the availability heuristic) for estimating the numerosity of a class, the likelihood of an event, or the frequency of co-occurrences, by the ease with which the relevant mental operations of retrieval, construction, or association can be performed.

However, as the preceding examples have demonstrated, his valuable estimation procedure results in systematic errors.

3. Adjustment and Anchoring

In making estimates and calculations people tend to start from whatever initial value they have been given. All too often this value is not just wrong, but people are reluctant to move too far away from it. This is the anchor effect.

Insufficient adjustment Groups were given estimating tasks i.e. told to estimate various fairly easy values. Before each guess the group watched the invigilator spin a roulette wheel and pick a number entirely at random. Two groups were asked to estimate the number of African nations in the United Nations. The group which had watched the invigilator spin a roulette number of 10 guessed the number of nations at 25, the group which had watched him land a 65, guessed there were 45 nations.

Two groups of high school students were given these sums to calculate in 5 seconds: first group 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8, second group 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. Without time to complete the sum both groups extrapolated from the part-completed task: first group guessed 512, second group guessed 2,250. (Both were wrong: it’s 40,320).

Biases in the evaluation of conjunctive and disjunctive events People tend to overestimate the probability of conjunctive events and underestimate the probability of disjunctive events. I found their explanation a little hard to follow here, but it seems to mean that when several events all need to occur in order to result in a certain outcome, we overestimate the likelihood that all of them will happen. If only one of many events needs to occur, we underestimate that probability.

Thus: subjects were asked to take part in the following activities:

  • simple event: pull a red marble from a bag containing half red marbles and half white marbles
  • conjunctive event: pulling a red marble seven times in succession from a bag containing 90% red and 10% whites – the point is, that this is only an event if it happens seven times in succession
  • disjunctive event: pulling a red marble at least once in seven successive goes

So the simple event is a yes-no result, with 50/50 odds; the conjunctive event requires that seven things happen in succession (pretty low odds); and the disjunctive event is a one (or more) in seven chance. Almost everyone overestimated the chances of the seven times in succession event compared to the at-least-one-in-seven outcome.

They then explain the real world significance of this finding. The development of a new product is a typically conjunctive event: a whole string of things must go right in order for the product to work. People’s tendency to overestimate conjunctive events leads to unwarranted optimism, which sometimes results in failure.

By contrast disjunctive structures are typically used in the calculation of risk. In a complex system, just one thing has to fail for the whole to fail. The chances of failure in each individual component might be low, but adding together the chances results in a high probability that something will go wrong, somewhere.

Yet people consistently underestimate the probability of disjunctive events, thus underestimating risk.

This explains why estimates for the completion of big, complex projects always tend to be over-optimistic – think Crossrail.

Anchoring in the assessment of subjective probability distributions This is an advanced statistical concept which they did not explain very well. I think it was to do with how you set a kind of basic value for a person’s guesses and estimates, and T&K then proceed to show that these kinds of calibrations are often wildly inaccurate.

Discussion

At the end of the summary of experiments, Tversky and Kahneman discuss their findings. This part was tricky to follow because they don’t discuss their findings’ impact on ordinary life, in terms you or I might understand, but instead assess the impact of their findings on what appears to have been (back in 1974) modern decision theory.

think the idea is that modern decision theory was based on a modern of human rationality which was itself based on an idealised notion of logical thinking calculated from an assessment or ‘calibration’ of subjective decision-making.

Modern decision theory regards subjective probability as the quantified opinion of an ideal person.

I found it impossible to grasp the detail of this idea, maybe because they don’t explain it very well, assuming that the audience for this kind of specialised research paper would be totally au fait with it. Anyway, Tversky and Kahneman say that their findings undermine the coherence of this model of ‘modern decision theory’, explaining why in technical detail which, again, I found hard to follow.

Obviously, for the lay reader like myself, the examples they’ve assembled, and the types of cognitive and logical and probabilistic errors they describe, give precision and detail enough to support one’s intuition that people (including oneself) are profoundly, alarmingly, irrational.

Summary

In their words:

This article described three heuristics that are employed in making judgements under uncertainty: (i) representativeness, which is usually employed when people are asked to judge the probability that an object or event A belongs to class or process B; (ii) availability of instances or scenarios, which is often employed when people are asked to assess the frequency of a class or the plausibility of a particular development; and (iii) adjustment from an anchor, which is usually employed in numerical prediction when a relevant value is available.

These heuristics are highly economical and usually effective, but they lead to systematic and predictable errors. A better understanding of these heuristics and of the biases to which they lead could improve judgments and decisions in situations of uncertainty.

My thoughts

1. The most obvious thing to me, fresh from reading John Allen Paulos’s two books about innumeracy and Stuart Sutherland’s book on irrationality, is how much the examples used by Tversky and Kahneman are repeated almost verbatim in those books, and thus what a rich source of data this article was for later writers.

2. The next thought is that this is because those books, especially the Sutherland, copy the way that Tversky and Kahneman use each heuristic as the basis for a section of their text, which they then sub-divide down into component parts, or variations on the basic idea.

Reading this paper made me realise this is exactly the approach that Sutherland uses in his book, taking one ‘error’ or bias at a time, and then working through all the sub-types and examples.

3. My next thought is the way Sutherland and Paulos only use some of the examples in this paper, the ones – reasonably enough – which are most comprehensible. Thus the final section in Tversky and Kahneman’s paper – about subjective probability distributions – is not picked up in the other books because it is couched in such dense mathematical terminology as to be almost impenetrable and because the idea they are critiquing – 1970s decision making theory – is too remote from most people’s everyday concerns.

So: having already read Paulos and Sutherland, not many of the examples Tversky and Kahneman use came as a surprise, nor did the basic idea of the availability error or representative error or the anchor effect.

But what did come over as new – what I found thought provoking – was the emphasis they put throughout on the fundamental usefulness of the heuristics.

Up till now – in Paulos and Sutherland – I had only heard negative things about these cognitive errors and prejudices and biases. It was a new experience to read Tversky and Kahneman explaining that these heuristics – these mental shortcuts – although they are often prone to error – nonetheless, have evolved deep in our minds because they are fundamentally useful.

That set off a new train of thought, and made me reflect that Paulos, Sutherland and Tversky and Kahneman are all dwelling on the drawbacks and limitations of these heuristics, leaving the many situations in which they are helpful, undescribed.

Now, as Sutherland repeats again and again – we should never let ourselves be dazzled by salient and striking results (such as coincidences and extreme results), we should always look at the full set of all the data, we should make sure we consider all the negative incidents where nothing dramatic or interesting happened, in order to make a correct calculation of probabilities.

So it struck me that you could argue that all these books and articles which focus on cognitive errors are, in their own way, rather unscientific, or lack a proper sample size – because they only focus on the times when the heuristics result in errors (and, also, that these errors are themselves measured in highly unrealistic conditions, in psychology labs, using highly unrepresentative samples of university students).

What I’m saying is that for a proper assessment of the real place of these heuristics in actual life, you would have to take into account all the numberless times when they have worked – when these short-cut, rule-of-thumb guesstimates, actually produce positive and beneficial results.

It may be that for every time a psychology professor conducts a highly restricted and unrealistic psychology experiment on high school students or undergraduates which results in them making howling errors in probability or misunderstanding the law of large numbers or whatever —  it may just be that on that day literally billions of ‘ordinary’ people are using the same heuristic in the kind of real world situations most of us encounter in our day-to-day lives, to make the right decisions for us, and to achieve positive outcomes.

The drawbacks of these heuristics are front-centre of Paulos and Sutherland and Tversky and Kahneman’s works – but who’s measuring the advantages?


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Irrationality: The Enemy Within by Stuart Sutherland (1992)

The only way to substantiate a belief is to try to disprove it. (p.48)

Sutherland was 65 when he wrote this book, nearing the end of a prestigious career in psychology research. His aim was to lay out, in 23 themed chapters, all the psychological and sociological research data  from hundreds of experiments, which show just how prey the human mind is to a plethora of unconscious biases, prejudices, errors, mistakes, misinterpretations and so on – the whole panoply of ways in which the supposedly rational human beings can end up making grotesque mistakes. By the end he claims to have defined and demonstrated over 100 distinct cognitive errors humans are prone to (p.309).

I first read it in 2000 and it made a big impact on me because I didn’t really know that this entire area of study existed, and had certainly never read such a compendium of sociology and psychology experiments before.

I found the naming of the various errors particularly powerful. They reminded me of the lists of weird and wonderful Christian heresies I was familiar with from years of reading medieval history. And, after all, the two have a lot in common, both being lists of ‘errors’ which the human mind can make as it falls short of a) orthodox theology and b) optimally rational thinking, the great shibboleths of the Middle Ages and of the Modern World, respectively.

 

Reading it now, 20 years later, having brought up a couple of children and worked for a while in big government departments, I am a lot less shocked and amazed. I have witnessed at first hand the utter irrationality of small and medium-sized children – and then so many examples of the corporate conformity, avoidance of embarrassment, unwillingness to speak up, deferral to authority, and general mismanagement to be found in the civil service that, upon rereading the book, hardly any of it came as a surprise, more a confirmation of what I’ve witnessed at first hand.

But to have the errors so carefully named and defined and worked through in a structured way, with so many experiments giving such vivid proof of how useless humans are at even basic logic was still very enjoyable.

What is rationality?

You can’t define irrationality without first defining what you mean by rationality:

Rational thinking is most likely to lead to the conclusion that is correct, given the information available at the time (with the obvious rider that, as new information comes to light, you should be prepared to change your mind).

Rational action is that which is most likely to achieve your goals. But in order to achieve this, you have to have clearly defined goals. Not only that but, since most people have multiple goals, you must clearly prioritise your goals.

Few people think hard about their goals and even fewer think hard about the many possible consequences of their actions. (p.129)

Cognitive biases contrasted with logical fallacies

Before proceeding it’s important to point out that there is a wholly separate subject of logical fallacies. As part of his Philosophy A-Level my son was given a useful handout with a list of about fifty of these. But logical fallacies are not the same as cognitive biases.

A logical fallacy stems from an error in a logical argument; it is specific and easy to identify and correct. Cognitive bias derives from deep-rooted, thought-processing errors which themselves stem from problems with memory, attention, self-awareness, mental strategy and other mental mistakes. Far harder to acknowledge, in many cases, very hard to correct.

Fundamentals of irrationality

1. Innumeracy One of the largest causes of all irrational behaviour is that people by and large don’t understand statistics or maths. Thus most people are not intellectually equipped to understand the most reliable type of information available to human beings – data in the form of numbers. Instead they tend to make decisions based on a wide range of faulty and irrational psychological biases.

2. Physiology People are often influenced by physiological factors. Apart from obvious ones like tiredness or hunger, which are universally known to affect people’s cognitive abilities, there are also a) drives (direct and primal) like hunger, thirst, sex, and b) emotions (powerful but sometimes controllable) like love, jealousy, fear and – especially relevant – embarrassment: acute reluctance to acknowledge limits to your own knowledge or that you’ve made a mistake.

More seriously people can be alcoholics, drug addicts, and prey to a wide range of other obsessive behaviours, not to mention suffering from a wide range of mental illnesses or conditions which undermine any attempt at rational decision-making, such as stress, anxiety or, at the other end of the spectrum, depression and loss of interest.

3. The functional limits of consciousness Numerous experiments have shown that human beings have a limited capacity to process information. Given that people rarely have a) a sufficient understanding of the relevant statistical data, and b) the RAM capacity to process all the data required to make the optimum decision, it is no surprise that most of us fall back on all manner of more limited, non-statistical biases and prejudices when it comes to making decisions.

The wish to feel good The world is threatening, dangerous and competitive. Humans want to feel safe, secure, calm, in control. This is fair enough, but it does mean that people have a way of blocking out any kind of information which threatens them. People irrationally believe they are cleverer than they in fact are, are qualified in areas of activity of knowledge where they aren’t, people stick to bad decisions for fear of being embarrassed or humiliated, and for the same reason reject new evidence which contradicts their position.

Named types of error and bias

Jumping to conclusions Sutherland tricks the reader no page one by asking a series of questions and then pointing out, that if you tried to answer about half of them, you are a fool since they don’t contain enough information to arrive at any sort of solution. Jumping to conclusions before we have enough evidence is a basic and universal error. One way round this is to habitually use a pen and paper to set out the pros and cons of any decision, which also helps highlight areas where you realise you don’t have enough information.

The availability error All the evidence is that the conscious mind can only hold a small number of data or impressions at any one time (near the end of the book, Sutherland claims the maximum is seven items, p.319). Many errors are due to people reaching for the most available explanation, using the first thing that comes to mind, and not taking the time to investigate further and make a proper, rational survey of the information.

Many experiments show that you can unconsciously bias people by planting ideas, words or images in their minds which then directly affect decisions they take hours later about supposedly unconnected issues.

Studies show that doctors who have seen a run of a certain condition among their patients become more likely to diagnose it in patients who don’t have it. The diagnosis is more ‘available’.

The news media is hard-wired to publicise shocking and startling stories which leads to the permanent misleading of the reading public. One tourist eaten by a shark in Australia eclipses the fact that you are far more likely to die in a car crash than be eaten by a shark.

Thus ‘availability’ is also affected by impact or prominence. Experimenters read out a list of men and women to two groups without telling them that there are exactly 25 men and 25 women, and asked them to guess the ratio of the sexes. If the list included some famous men, the group was influenced to think there were more men, if the list included famous women, the group thought there are more women than men.

The entire advertising industry is based on the availability error in the way it invents straplines, catchphrases and jingles designed to pop to the front of your mind when you consider any type of product, to be – in other words – super available.

I liked the attribution of the well-known fact that retailers price goods at just under the nearest pound, to the availability error. Most of us find £5.95 much more attractive than £6. It’s because we only process the initial 5, the first digit, it is more available.

Numerous studies have shown that the effect is hugely increased under stress. Under stressful situations – in an accident – people fixate on the first solution that comes to mind and refuse to budge.

The primacy effect First impressions. Interviewers make up their minds in the first minute of an interview and then spend the rest of the time collecting data to confirm that first impression.

The anchor effect In picking a number people tend to choose one close to any number they were presented with. Two groups were asked to estimate whether the population of Turkey was a) bigger than 5 million b) less than 65 million, and what it was. The group who’d had 5 million planted in their mind hovered around 15 million, the group who’d had 65 million hovered around 35 million. They were both wrong. It is 80 million.

The halo effect People extrapolate the nature of the whole from just one quality e.g. in tests, people think attractive people must be above average in personality and intelligence although of course there is no reason why they should be. Hence this error’s alternative name, the ‘physical attractiveness stereotype’. The halo effect is fundamental to advertising which seeks to associate images of beautiful men, women, smiling children, sunlit countryside etc with the product.

The existence of the halo effect and primacy effect are both reasons why interviews are a poor way to assess candidates for jobs or places.

The devil effect Opposite of the above: extrapolating from negative appearances to the whole. This is why it’s important to dress smartly for an interview or court appearance, it really does influence. In an experiment examiners were given identical answers, but some in terrible handwriting, some in beautifully clear handwriting. Clear handwriting consistently scored higher marks despite identical factual content of the scripts.

Illusory correlation People find links between disparate phenomena which simply don’t exist, thus:

  • people exaggerate the qualities of people or things which stand out from their environments
  • people associate rare qualities with rare things

This explains a good deal of racial prejudice: a) immigrants stand out b) a handful of immigrants commit egregious behaviour – therefore it is a classic example of illusory correlation to associate the two. What is missing is taking into account all the negative examples i.e. the millions of immigrants who make no egregious behaviour and whose inclusion would give you a more accurate statistical picture. Pay attention to negative cases.

Stereotypes 1. People tend to notice anything which supports their existing opinions. 2. We notice the actions of ‘minorities’ much more than the actions of the invisible majority.

Projection People project onto neutral phenomena patterns and meanings they are familiar with or which bolster their beliefs. Compounded by –

Obstinacy Sticking to personal opinions (often made in haste / first impressions / despite all evidence to the contrary) aka The boomerang effect When someone’s opinions are challenged, they just become more obstinate about it. Aka Belief persistence. Aka pig-headedness. Exacerbated by –

Group think People associate with others like themselves, which makes them feel safe by a) confirming their beliefs and b) letting them hide in a crowd. Experiments have shown how people in self-supporting groups are liable to become more extreme in their views. Also – and I’ve seen this myself – groups will take decisions that almost everyone in the group, as individuals, know to be wrong – but no-one is prepared to risk the embarrassment or humiliation of pointing it out. The Emperor’s New Clothes. Groups are more likely to make irrational decisions than individuals are.

Confirmation bias The tendency to search for, interpret, favour, and recall information in a way that confirms one’s pre-existing beliefs or hypotheses. In an experiment people were read out a series of statements about a named person, who had a stated profession and then two adjectives describing them, one what you’d expect, the other less predictable. ‘Carol, a librarian, is attractive and serious’. When asked to do a quiz at the end of the session, participants showed a marked tendency to remember the expected adjective, and forget the unexpected one. Everyone remembered that the air stewardess was ‘attractive’ but remembered the librarian for being ‘serious’.

We remember what we expect to hear. (p.76)

Or: we remember what we remember in line with pre-existing habits of thought, values etc.

We marry people who share our opinions, we have friends with people who share our opinions, we agree with everyone in our circle on Facebook.

Self-serving biases When things go well, people take the credit, when things go badly, people blame external circumstances.

Avoiding embarrassment People obey, especially in a group situation, bad orders because they don’t want to stick out. People go along with bad decisions because they don’t want to stick out. People don’t want to admit they’ve made a mistake, in front of others, or even to themselves.

Avoiding humiliation People are reluctant to admit mistakes in front of others. And rather than make a mistake in front of others, people would rather keep quiet and say nothing (in a meeting situation) or do nothing, if everyone else is doing nothing (in an action situation). Both of these avoidances feed into –

Obedience The Milgram experiment proved that people will do any kind of atrocity for an authoritative man in a white coat. All of his students agreed to inflict life-threatening levels of electric shock on the victim, supposedly wired up in the next door room and emitting blood curdling (faked) screams of pain. 72% of Senior House Officers wouldn’t question the decision of a consultant, even if they thought he was wrong.

Conformity Everyone else is saying or doing it, so you say or do it so as not to stick out / risk ridicule.

Obedience is behaving in a way ordered by an authority figure. Conformity is behaving in a way dictated by your peers.

The wrong length lines experiment. You’re put in a room with half a dozen stooges, and shown a piece of card with a line on it and then another piece of card with three lines of different length on it, and asked which of the lines on card B is the same length as the line on card A. To your amazement, everyone else in the room chooses a line which is obviously wildly wrong. In experiments up to 75%! of people in this situation go along with the crowd and choose the line which they are sure, can see, know is wrong – because people are that easily swayed.

Sunk costs fallacy The belief that you have to continue wasting time and money on a project because you’ve invested x amount of time and money to date. Or ‘throwing good money after bad’.

Sutherland keeps cycling round the same nexus of issues, which is that people jump to conclusions – based on availability, stereotypes, the halo and anchor effects – and then refuse to change their minds, twisting existing evidence to suit them, ignoring contradictory evidence.

Misplaced consistency & distorting the evidence Nobody likes to admit (especially to themselves) that they are wrong. Nobody likes to admit (especially to themselves) that they are useless at taking decisions.

Our inability to acknowledge our own errors even to ourselves is one of the most fundamental causes of irrationality. (p.100)

And so:

  • people consistently avoid exposing themselves to evidence that might disprove their beliefs
  • on being faced with evidence that disproves their beliefs, they ignore it
  • or they twist new evidence so as to confirm their existing beliefs
  • people selectively remember their own experiences, or misremember the evidence they were using at the time, in order to validate their current decisions and beliefs
  • people will go to great lengths to protect their self-esteem

Sutherland says the best cleanser / solution / strategy to fixed and obstinate ideas is to make the time to gather as much evidence as possible and to try to disprove your own position. The best solution will be the one you have tried to demolish with all the evidence you have and still remains standing.

People tend to seek confirmation of their current hypothesis, whereas they should be trying to disconfirm it. (p.138)

Fundamental attribution error Ascribing other people’s behaviour to their character or disposition rather than to their situation. Subjects in an experiment watched two people holding an informal quiz: the first person made up questions (based on what he knew) and asked the second person who, naturally enough, hardly got any of them right. Observers consistently credited the quizzer with higher intelligence than the answerer, completely ignoring the in-built bias of the situation, and instead ascribing the difference to character.

We are quick to personalise and blame in a bid to turn others into monolithic entities which we can then define and control – this saves time and effort, and makes us feel safer and secure – whereas the evidence is that all people are capable of a wide range of behaviours depending on the context and situation.

Once you’ve pigeon-holed someone, you will tend to notice aspects of their behaviour which confirm your view – confirmation bias and/or illusory correlation and a version of the halo/devil effect. One attribute colours your view of a more complex whole.

Actor -Observer Bias Variation on the above: when we screw up we find all kinds of reasons in the situation to exonerate ourselves, we performed badly because we’re ill, jet-lagged, grandma died, reasons that are external to us. If someone else screws up, it is because they just are thick, lazy, useless. I.e. we think of ourselves as complex entities subject to multiple influences, and others as monolithic types.

False Consensus Effect Over-confidence that other people think and feel like us, that our beliefs and values are the norm – in my view one of the greatest errors of our time.

It is a variation of the ever-present Availability Error because when we stop to think about any value or belief we will tend to conjure up images of our family and friends, maybe workmates, the guys we went to college with, and so on: in other words, the people available to memory – simply ignoring the fact that these people are a drop in the ocean of the 65 million people in the UK. See Facebubble.

The False Consensus Effect reassures us that we are normal, our values are the values, we’re the normal ones: it’s everyone else who is wrong, deluded, racist, sexist, whatever we don’t approve of.

Not in Sutherland’s book, I’ve discovered some commentators naming this the Liberal fallacy:

For liberals, the correctness of their opinions – on universal health care, on Sarah Palin, on gay marriage – is self-evident. Anyone who has tried to argue the merits of such issues with liberals will surely recognize this attitude. Liberals are pleased with themselves for thinking the way they do. In their view, the way they think is the way all right-thinking people should think. Thus, “the liberal fallacy”: Liberals imagine that everyone should share their opinions, and if others do not, there is something wrong with them. On matters of books and movies, they may give an inch, but if people have contrary opinions on political and social matters, it follows that the fault is with the others. (Commentary magazine)

Self-Serving Bias People tend to give themselves credit for successes but lay the blame for failures on outside causes. If the project is a success, it was all due to my hard work and leadership. If it’s a failure, it’s due to circumstances beyond my control, other people not pulling their weight etc.

Preserving one’s self-esteem These three errors are all aspects of preserving our self-esteem. You can see why this has an important evolutionary and psychological purpose. In order to live, we must believe in ourselves, our purposes and capacities, believe our values are normal and correct, believe we make a difference, that our efforts bring results. No doubt it is a necessary belief and a collapse of confidence and self-belief can lead to depression and possibly despair. But that doesn’t make it true. People should learn the difference between having self-belief to motivate themselves, and developing the techniques to gather the full range of evidence – including the evidence against your own opinions and beliefs – which will enable them to make correct decisions.

Representative error People estimate the likelihood of an event by comparing it to an existing prototype / stereotype that already exists in our minds. Our prototype is what we think is the most relevant or typical example of a particular event or object. This often happens around notions of randomness: people have a notion of what randomness should look like i.e. utterly scrambled. But in fact plenty of random events or sequences arrange themselves into patterns we find meaningful. So we dismiss them as not really random.  I.e. we have judged them against our preconception of what random ought to look like.

Ask a selection of people which of these three sets of six coin tosses where H stands for heads, T for tails is random.

  1. TTTTTT
  2. TTTHHH
  3. THHTTH

Most people will choose 3 because it feels random. But of course all three are equally likely or unlikely.

Hindsight In numerous experiments people have been asked to predict the outcome of an event, then after the event questioned about their predictions. Most people forget their inaccurate predictions and misremember that they were accurate.

Overconfidence Most professionals have been shown to overvalue their expertise i.e. exaggerate their success rates.


Statistics

The trouble with this and Paulos’s books is that the entire area of statistics is separate and distinct from errors of thought and cognitive biases. I.e. you can imagine someone who avoids all of the cognitive and psychological errors named above, but still makes howlers when it comes to statistics simply because they’re not very good at it.

This is because the twin areas of Probability and Statistics are absolutely fraught with difficulty. Either you have been taught the correct techniques, and understand them, and practice them regularly (and both books demonstrate that even experts make howling mistakes in the handling of statistics and probability) or, like most of us, you have not.

As Sutherland points out, most people’s knowledge of statistics is non-existent. Since we live in a society whose public discourse i.e. politics, is ever more dominated by statistics…

Errors in estimating probability or misunderstanding samples, opinion polls and so on are probably a big part of irrationality, but I felt that they’re so distinct from the psychological biases discussed above, that they almost require a separate volume, or a separate ‘part’ of this volume. Briefly, common mistakes are:

  • too small a sample size
  • biased sample
  • not understanding that any combination of probabilities is less likely than either on their own, which requires an understanding of base rate or a priori probability
  • the law of large numbers – the more a probabilistic event takes place, the more likely the result will move towards the theoretical probability
  • be aware of the law of regression to the mean
  • be aware of the law of large numbers

Gambling

This is even more true of gambling. It is a highly specialised and advanced form of probability applied to games which have been pored over by very clever people for centuries. It’s not a question of a few general principles, this is a vast, book-length subject in its own right. Some points that emerge:

  • always work out the expected value of a bet i.e. the amount to be won times the probability of winning it

The two-by-two box

It’s taken me some time to understand this principle which is given in both Paulos and Sutherland.

When two elements with a yes/no result are combined, people tend to look at the most striking correlation and fixate on it. The only way to avoid the false conclusions that follow from that is to draw a 2 x 2 box and work through the figures.

Here is a table of 1,000 women who had a mammogram because their doctors thought they had symptoms of breast cancer.

Women with cancer Women with no cancer Total
Women with positive mammography 74 110 184
Women with negative mammography 6 810 816
80 920 1000

Bearing in mind that a conditional probability is saying that if X and Y are linked, then the chances of X, if Y, are so and so – i.e. the probability of X is conditional on the probability of Y – this table allows us to work out the following conditional probabilities:

1. The probability of getting a positive mammogram or test result, if you do actually have cancer, is 74 out of 80 = .92 (out of the 80 women with cancer, 74 were picked up by the test)

2. The probability of getting a negative mammogram or test result and not having cancer, is 810 out of 920 = .88

3. The probability of having cancer if you test positive, is 74 out of 184 = .40

4. The probability of having cancer if you test negative, is 6 out of 816 = .01

So 92% of women of women with cancer were picked up by the test. BUT Sutherland quotes a study which showed that a shocking 95% of doctors thought that this figure – 92% – was also the probability of a patient who tested positive having the disease. By far the majority of US doctors thought that, if you tested positive, you had a 92% chance of having cancer. They fixated on the 92% figure and transposed it from one outcome to the other, confusing the two. But this is wrong. The probability of a woman testing positive actually having cancer is given in conclusion 3 – 74 out of 184 = 40%. This is because 110 out of the total 184 women tested positive, but did not have cancer.

So if a woman tested positive for breast cancer, the chances of her actually having it are 40%, not 92%. Quite a big difference (and quite an indictment of the test, by the way). And yet 95% of doctors thought that if a woman tested positive she had a 92% likelihood of having cancer.

Sutherland goes on to quote a long list of other situations where doctors and others have comprehensively  misinterpreted the results of studies like this, with varied and sometimes very negative consequences.

The moral of the story is if you want to determine whether one event is associated with another, never attempt to keep the co-occurrence of events in your head. It’s just too complicated. Maintain a written tally of the four possible outcomes and refer to these.


Deep causes

Sutherland concludes the book by speculating that all the hundred or so types of irrationality he has documented can be attributed to five fundamental causes:

  1. Evolution We evolved to make snap decisions, we are brilliant at processing visual information and responding before we’re even aware of it. Conscious thought is slower, and the conscious application of statistics, probability, regression analysis and so on is very slow and laborious. Most people never acquire it.
  2. Brain structure As soon as we start perceiving, learning and remembering the world around us brain cells make connections. The more the experience is repeated, the stronger the connections become. Routines and ruts form, which are hard to budge.
  3. Heuristics Everyone develops mental short-cuts, techniques to help make quick decisions. Not many people bother with the laborious statistical techniques for assessing relative benefits which Sutherland describes.
  4. Failure to use elementary probability and elementary statistics Ignorance is another way of describing this, mass ignorance. Sutherland (being an academic) blames the education system. I, being a pessimist, attribute it to basic human nature. Lots of people just are lazy, lots of people just are stupid, lots of people just are incurious.
  5. Self-serving bias In countless ways people are self-centred, overvalue their judgement and intelligence, overvalue the beliefs of their in-group, refuse to accept it when they’re wrong, refuse to make a fool of themselves in front of others by confessing error or pointing out errors in others (especially the boss) and so on.

I would add two more:

Suggestibility. Humans are just tremendously suggestible.

Say a bunch of positive words to test subjects, then ask them questions on an unrelated topic: they’ll answer positively. Take a different representative sample of subjects and run a bunch of negative words past them, then ask them the same unrelated questions, and their answers will be measurably more negative.

Ask subjects how they get a party started and they will talk and behave extrovert to the questioner. Ask them how they cope with feeling shy and ill at ease at parties, and they will tend to act shy and speak quieter. The initial terms or anchor defines the ensuing conversation.

In one experiment a set of subjects were shown one photo of a car crash. Half were asked to describe what they think happened when one car hit another; the other half were asked to describe what they thought happened when one car smashed into the other. The ones given the word ‘smashed’ gave much more melodramatic accounts. Followed up a week later, the subjects were asked to describe what they remembered of the photo. The subjects given the word ‘hit’ fairly accurately described it, whereas the subjects given the word ‘smashed’ invented all kinds of details like a sea of broken glass around the vehicles which simply wasn’t there, which their imaginations had invented, all at the prompting of one word.

Many of the experiments Sutherland quotes demonstrate what you might call higher-level biases: but underling many of them is this simple-or-garden observation, that people are tremendously easily swayed, by both external and internal causes, away from the line of cold logic.

Anthropomorphism Another big underlying cause is anthropomorphism, namely the attribution of human characteristics to objects, events, chances, odds and so on. In other words, people really struggle to accept the high incidence of random accidents. Almost everyone attributes a purpose or intention to almost everything that happens. This means our perceptions of almost everything in life are skewed from the start.

During the war Londoners devised innumerable theories about the pattern of German bombing. After the war, when Luftwaffe records were analysed, it showed the bombing was more or less at random.

The human desire to make sense of things – to see patterns where none exists or to concoct theories… can lead people badly astray. (p.267)

Suspending judgement is about the last thing people are capable of. People are extremely uneasy if things are left unexplained. Most people rush to judgement like water into a sinking ship.

Cures

  • keep an open mind
  • reach a conclusion only after reviewing all the possible evidence
  • it is a sign of strength to change one’s mind
  • seek out evidence which disproves your beliefs
  • do not ignore or distort evidence which disproves your beliefs
  • never make decisions in a hurry or under stress
  • where the evidence points to no obvious decision, don’t take one
  • learn basic statistics and probability
  • substitute mathematical methods (cost-benefit analysis, regression analysis, utility theory) for intuition and subjective judgement

Comments on the book

Out of date

Irrationality was first published in 1992 and this makes the book dated in several ways (maybe this is why the first paperback edition was published by upmarket mass publisher Penguin, whereas the most recent edition was published by the considerably more niche publisher, Pinter & Martin).

In the chapter about irrational business behaviour he quotes quite a few examples from the 1970s and the oil crisis of 1974. These and other examples – such as the long passage about how inefficient the civil service was in the early 1970s – feel incredibly dated now.

And the whole thing was conceived, researched and written before there was an internet or any of the digital technology we take for granted nowadays. Can’t help make wonder how the digital age has changed or added to the long list of biases, prejudices and faulty thinking he gives, and what errors of reason have emerged specific to our fabulous digital technology.

Grumpy

But it also has passages where Sutherland extrapolates out to draw general conclusions and some of these sound more like the grumblings of a grumpy old man than anything based on evidence.

Thus Sutherland whole-heartedly disapproves of ‘American’ health fads, dismisses health foods as masochistic fashion and is particularly scathing about jogging. He thinks ‘fashion’ in any sphere of life is ludicrously irrational. He is dismissive of doctors who he accuses of rejecting statistical evidence, refusing to share information with patients and wildly over-estimating their own diagnostic abilities.

He thinks the publishers of learned scientific journals are more interested in making money out of scientists than in ‘forwarding the progress of science’ (p.185). He thinks the higher average pay that university graduates tend to get is unrelated to their attendance at university and more to do with having well connected middle and upper middle class parents, and thus considers the efforts of successive Education Secretaries to introduce student loans to be unscientific and innumerate (p.186). He criticises Which consumer magazine for using too small samples in its testing (p.215). In an extended passage he summarises Leslie Chapman’s blistering (and very out of date) critique of the civil service, Your Disobedient Servant published in 1978 (pp.69-75).

He really has it in for psychoanalysis which he accuses of all sorts of irrational thinking such as projecting, false association, refusal to investigate negative instances, failing to take into account the likelihood that the patient would have improved anyway, and so on. Half way through the book he gives a thumbnail summary:

Self-deceit exists on a massive scale: Freud was right about that. Where he went wrong was in attributing it all to the libido, the underlying sex drive. (p.197)

In other words, the book is liberally sprinkled with Sutherland’s own personal opinions, which sometimes risk giving it a crankish feel.

On the other hand it’s surprising to see how some hot button issues haven’t changed at all. In the passage about the Prisoners’ Dilemma, Sutherland takes as a real life example the problem the nations of the world were having in 1992 in agreeing to cut back carbon dioxide emissions. Sound familiar?

He also states that the single biggest factor undermining international co-operation was America’s refusal to sign global treaties to limit global warming. In 1992! Plus ça change.

Against stupidity the gods themselves contend in vain

And finally, these are the mistakes made by the most intelligent and best educated among us, people trained to assess and act on evidence.

Neither this nor John Allen Paulos’s books take into account the obvious fact that lots of people are stupid. They begin with poor genetic material, are raised in families where no-one cares about education, are let down by poor schools, and are excluded or otherwise demotivated, with the result that :

  • the average reading age in the UK is 9
  • about one in five Britons (over ten million) are functionally illiterate, and probably about the same rate innumerate

which all adds to the general festival of idiocy.

Trying to keep those pesky cognitive errors at bay (in fact The Witch by Pieter Bruegel the Elder)

Trying to keep those pesky cognitive errors at bay (otherwise known as The Witch by Pieter Bruegel the Elder)


Related link

Reviews of other science books

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Environment / human impact

Genetics

  • The Double Helix by James Watson (1968)

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