Introduction
We have many beliefs that aren’t true. Common examples:
Why do they believe these things if they aren’t true?
Today, more people believe in ESP than in evolution. In the US, there are 20 times more astrologers than astronomers.
It is not simply lack of exposure to evidence: what is particularly interesting is that they hold the beliefs in spite of evidence. Nor is it stupidity. Probably the opposite: evolution has given us brains that can process huge amounts of information using a variety of simple cognitive and perceptual processes. These processes are a great strength, but they are also the cause of some of our biggest follies. Many of these follies fall into 3 classes of cognitive problems:
Some of the motivational and social determinants of false beliefs:
In a way, you can trace all of these to egotism/self-involvement.
Why do we care about erroneous beliefs? They are the reason behind some of humanity’s most egregious and senseless acts, such as
Within organizations, erroneous beliefs and perceptual distortions cause all kinds of problems:
Misperception of Random Data (the clustering illusion)
People often see patterns that are not really there.
The ability to spot real patterns is the key to human success. We can exploit regularities we observe in nature to build technology. So the tendency to see pattern is evolutionarily adaptive.
A folk theory: in basketball, success leads to success. Getting a basket gives you confidence, and this helps you get the next basket. And so on. The result is hot streaks. Virtually everyone believes this, including coaches and the players themselves. But the data contradict this. (see page 13 of Gilovich).
Of course, it could be that some other process is masking the effects of "hot hand". Like that a person who is hot gets extra coverage by the defense. But even if you examine controlled situations like free throws, you see that the probability of getting a basket for a given individual is the same regardless of the success or failure of the previous shot (at least within a reasonable period of time: over the period of a year, a person can work on their shooting skills and improve significantly).
Or it could be that the essence of hot hand is not success but predictability: they know whether the next shot will hit or not. So this was tested experimentally. But players’ predictions were not correlated with the outcomes of their shots at all.
So why do we believe in hot streaks when they don’t really happen? One reason is that people have faulty images of what chance sequences look like. People expect that a coin tossed many times will more or less alternate heads and tails. If there are sequences of 4 or 5 heads in a row, they think there is something non-random going on. But in fact those are quite common. For example, a sequence like OXXXOXXXOXXOOOXOOXXOO looks non-random, but it is.
The clustering illusion. The sequence looks non-random because there are so many clusters, and we don’t expect clusters in random data. Why not? Because of the representativeness axiom that people seem to use to think with. We evaluate whether an outcome is likely or not based on similar on a few simple features to what we would expect given the cause. For example, we will believe that someone is a librarian if they look bookish – they are representative of the category. The salient feature of independent events like coin tosses is that, in the long run, we expect the two outcomes to occur an equal number of times: 50-50. But this is in the long run. Yet we expect the same result in the short run as well, so if a given sequence has 9 heads and 1 tail, we think there is something wrong with it.
There are lots of phenomena that are like this:
Both areas are filled with folk theories governing the outcomes. In births, there are theories involving the phases of the moon. In stocks, there are dozens of strange theories, like the hemline theory and the Super Bowl theory.
Even statistical analysis does not always help dispel the illusion. With hindsight, we can always pick the most unusual features of the data and build an analysis around them. An example is shown in pg 20 – pattern of bombs dropped on London. By choosing the right quadrants, we can make it look non-random.
After-the-Fact, Ad Hoc Explanations
It is easy to create a story that justifies an outcome. Experiments with split brains show this easily. The right brain is made to choose something based on something presented to the right brain only. The left brain is then asked why they chose that. There is never any hesitation: they make it up instantly.
Regression
Whenever two variables are imperfectly correlated, extreme values of one variable are always matched by less extreme values of the other variable. We have trouble internalizing this. So in life, we tend to assume that extraordinary performance in one year will be matched the extraordinary performance the next year, but this is rarely the case. We assume that extraordinary performance in one venue will translate to extraordinary performance in another venue -- again more rare than we think. This affects how we buy mutual funds and other stocks, how we hire people, lend money to businesses, etc.
If I tell you that someone who is in 90th percentile of sense of humor, you tend to predict that their gpa will be in the 90th percentile. Yet, if the correlation between sense of humor and gpa is near zero, your best guess for their gpa would the 50th percentile.
The most famous example is height. If we look compare the average father's height with the average adult son's, we see that the son's are a little bit taller overall. That's because of changes in nutrition, elimination of childhood diseases etc. But now consider the relative height of a certain father compared to all other fathers, and consider the height of his son relative to all the other sons. If the father is extremely tall for a father -- say, top 1% -- it turns out that it is extremely unlikely that the son will be as unusually tall relative to other sons. He might be taller than his father (because most sons are), but he is probably not in the top 1% for sons. Maybe top 10% or 20%, but not top 1%. Similarly, a father who is unusually short even for fathers, say bottom 1%, is very likely to have a relatively short son, but not in the bottom 1% -- maybe bottom 20% or 30%.
Why is this? Because the correlation between father's height and son's height is not perfect. This is because there are many genetic and non-genetic factors that influence a person's height. For example the length of each bone in the leg could be controlled by a different gene, same with the pelvis, the spine, etc. Similarly, the genes for the attached muscles have to be compatible, etc., etc. Only if the person gets tall versions of all of these can they be truly extraordinarily tall. Suppose there are 500 little factors, each one of which can either add to or subtract from a person's height. Assume there is a certain amount of chance involved in which factors you get (for example, for each gene, you might get either mom's or dad's). If you happen to get a whole lot of the ones that add to your height, this gets added to your basic height. But that is like rolling sevens 500 times in a row using a pair of dice. It's unusual. More likely you'll get a blend of the adding and subtracting factors, and won't get too much added or subtracted from your height. So consider a father who is abnormally tall. That's because the 500 random factors happened to all line up to give him extraordinary height. Now consider his son. What are the chances that such a perfect line up happens twice? It's one thing to roll 10 sevens in a row, it's another to repeat that! Chances are, things won't line up quite so amazingly, so the son won't be quite as extraordinary as the father, relative to other sons.
In daily life, instead of recognizing regression effects for what they are, we tend to interpret them substantively. If someone who scored extremely high on a test before scores less high now, we think they got overconfident, or slacked off or were resting on laurels etc. If a person who scored extremely poorly before now scores much better, we think the low score motivated them to try harder. But even if they didn't try harder, it is likely that they would score better the second time simply because the chances of scoring that low again are small.
This may be why most people, like parents, use punishment more often than reward, even though psychological research suggests that reward works better. We give rewards when someone has done something extraordinarily well. Then, of course, they don’t do as well the next time, so you think the reward was not effective. In contrast, we give punishments when someone really screws up. And of course, the next time, they don’t screw up as much, so we think the punishment was effective. But it was just the regression effect: the lack of correlation between the events.
An experiment of this kind was done by having a teacher deal with a student’s lateness. A computer showed the teacher what time the kid arrived each day, and each day the teacher could either issue praise, punishment, or no comment. After several "days" of this, the teacher was asked which seemed to be most effective, punishment or reward. Most felt that punishment was more effective. What they didn’t know was that the student's arrival time was not only totally random, but pre-programmed into the computer and completely unrelated to anything the teacher did.
Coda
People combine the clustering illusion with the regression fallacy: seeing streaks or clumps of events, and then having their subsequent absence be interpreted causally.
An example is the trip to Israel described on pg 28. There was a flurry of deaths due to natural causes in the northern part of Israel. Statistically, this is to be expected: there is a certain probability of a death in a region every day, say 1 per 1000 residents. For a given region, this might work out to a longterm average of one every few days. But because its random, they are not going to be evenly spaced out. Some weeks you'll get 15 deaths. Other weeks you'll get none. It is chance!
But most people are not statisticians, and the flurry of deaths led to speculation of some new threat or health hazard. A group of rabbis attributed the problem to the sacrilege of allowing women to attend funerals, which was previously forbidden. So they decreed that women could not attend funerals anymore. Soon after this was enacted, the rash of deaths subsided, and this was taken as confirmation that the remedy was effective!
In other words, simple features of human cognition can account for major beliefs such as the proper role of women in society.
Incomplete and Unrepresentative Data
How often have you heard things like this:
We tend to believe in things because we saw it happen once or twice. It doesn't really matter that in hundreds of other cases, it didn't happen. It happened once and this is enough to confirm our beliefs.
If something is true then there should be some evidence of it. That's sensible. But the existence of some instances do not prove the general case. If mixing a package of pop rocks with coke will kill you, then there should be some cases of people who did that and died immediately after. True. But just because somebody eats pop rocks with coke and dies immediately after doesn’t meant that there was any connection between the two, especially if millions of other people eat pop rocks with coke and don't show any ill-effects!
This problem in thinking is caused by a mixture of two things: belief in small sample sizes (if it works for these 10 people, it must be an eternal truth), and the tendency to attend to confirming data and ignore disconfirming data.
Take the claim that "african-americans are really into volvos -- more than other people are". If you believe that, you tend to find supported evidence everywhere: every time you see an african american driving a volvo you say "see, I told you!". But you don’t really notice volvos driven by whites, or other cars (not volvos) driven by african-americans.
| Volvo | Other Car | |
| African American | a. you notice these caes the most! | b. |
| Other person | c. | d. |
Yet all the cases are needed to evaluate the claim. Compare this table (the quanitities are numbers of people that fit into each box):
| Volvo | Other Car | |
| African American | 100 | 10 |
| Other person | 10 | 100 |
With this one:
| Volvo | Other Car | |
| African American | 100 | 10 |
| Other person | 10 | 1 |
If you focus only on the (a), (b) and (c) cells, the two situations look the same. But only the first table shows an actual relationship between Race and Car Manufacturer. The second table provides clear evidence that there is NO relationship between Race and Car Manufacturer. (Just convert the data to percentages and you’ll see.) In the second table, it's true that african americans like volvos, but so do others.
Similarly, if you are trying to evaluate whether seeding clouds is effective in making rain, you tend to look at only the (a) (and maybe (b)) cases. These are unambiguously relevant. But the (c) cases tend to be ignored because they are ambiguous: they don’t clearly speak to the issue.
| Rains | Doesn’t Rain | |
| Seed clouds | (a) you are persuaded by many cases of this type |
|
| Don’t seed | (c) ambiguous – ignored |
Consider these data:
| Rains | Doesn’t Rain | |
| Seed clouds | 50 | 10 |
| Don’t seed | 10 | 10 |
This says that there were 50 cases where you seeded the clouds and it rained. Seems convincing, right? But consider this table instead:
| Rains | Doesn’t Rain | |
| Seed clouds | 50 | 10 |
| Don’t seed | 50 | 10 |
The top row is identical. The only difference is the (c) cell. Note that the probability of raining if you seed the clouds (50/60 = about 83%) is no better than the probability of raining if don't seed the clouds (50/60 again).
It is particularly difficult to deal with variables in which one category signifies the absence of the other, as in "rains" and "not rains". We have difficulty working with the "not rains" category. In contrast, we do better with "Male" and "female".
We generally favor the positive. John Holt played 20 questions with kids. He would say, I’m thinking of a number between 1 and 10,000. You have twenty yes/no questions to guess the answer. So someone would say ‘is the number less than 5,000?’ and if the answer was Yes, the kids would cheer. If it was NO, they would groan. But it’s just as useful no matter how it comes out!
Suppose your job is to figure out what questions to ask a respondent to determine whether they are an extrovert. Most people ask things like "what would you do to liven up party?" They are thinking about behaviors that extroverts do. They don’t think to ask "do you like to curl up in front of a fire and read a novel", even though a yes answer would help to determine that the person is not an extrovert.
If asked to determine whether the respondent is an introvert, they ask about introverted behaviors.
Censored Data
Suppose we evaluate whether students with high sat scores really do perform better in college. We can look at the sat scores of good and bad students in colleges, but notice an important point: students with really bad sat scores don’t get into college at all. So you really can’t examine disconfirming cases, like students with bad sat scores that do well in college: they are artificially removed from the game. Similarly, students with really bad gpa’s, who might have had good sat scores (contrary to hypothesis), are bounced out and again are not available in your sample. Also, students with different sat scores don’t go to the same schools, so it is hard to assess the effect of sat on gpa alone.