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When we are studying the past, it is very difficult to be completely objective. Even if we don't produce fake histories, we cannot necessarily include everything in a history curriculum. So we include some things, while we exclude other things. The problem is that nations tend to favor historical events that make themselves appear more prestigious, while they tend to exclude historical events that make themselves appear less prestigious. This can perpetuate conflicts, such as for example the conflict between the Montagues and the Capulets in Romeo and Juliet by Shakespeare.
Selection bias in national histories
Figure 1: An example using the Montague and Capulet families from Romeo and Juliet by Shakespeare to show how selection bias in history curricula can perpetuate a conflict.
Most countries have some selection bias in their history curricula, and this might be one of the main reasons why the Israel-Palestine conflict and the Kashmir conflict never seem to end. It also seems to have been a prominent reason for the Cold War, the Yugoslav Wars, and presumably many other conflicts. You might assume however, that if we later in life are presented with historical facts which make our countries seem less prestigious, we tend to get a more unbiased and objective understanding of our histories. This is unfortunately not the case however, since we tend to ignore facts that oppose our beliefs, while we actively seek more facts to strengthen our beliefs. When people search for information on the Internet, they are likely to search for information that confirms their beliefs, rather than for information that might be opposed to their beliefs. Even when people are confronted with information that contradicts their beliefs, they are likely to ignore it. This causes different political and religious groups to grow further apart, which again creates more conflicts in the world.
Confirmation bias
Figure 2: How I am much more interested in finding information that confirms my beliefs
We are in general much better at seeing correlations that we are looking for, than seeing correlations we aren't looking for. If for example we want to figure out if a symptom is indicative of a disease, we might look upon if the infected are more likely to have the symptom or not. From just looking upon this, we might erroneously start to believe that the symptom is indicative of the being infected.
Commonality for the infected
Figure 3: The symptom is four times more common among the infected
It is however also possible to look upon if the people that aren't infected are more likely to have the symptom or not. From just looking upon this, we might start to erroneously believe that the symptom is indicative of not being infected.
Commonality for the noninfected
Figure 4: The symptom is four times more common among people that aren't infected
If we compare all of these things, we might see that there is absolutely no correlation between the symptom and the disease. The symptom is simply more prevalent among people in general; both people that are infected and people that aren't infected. The probability of being infected if you have the symptom, is the same as the probability to have the infection in general.
Equally common
This can also be related to political and religious convictions. We might selectively choose to look only upon the prevalence of favorable things in our own religions and/or political affiliations, without comparing it to the prevalence of these same favorable things in other religions and/or political affiliations. Similarly, we might look upon the absence of adverse things in our own religions and/or political affiliations, without comparing it to the absence of these same adverse things in other religions and/or political affiliations. People tend to associate perfection with one ethnicity, culture and/or personality type. Often their own ethnicity, culture and/or personality type. This way of thinking fails to recognize the benefits of diversity, as stated in the diversity prediction theorem.
Diversity theorem
Figure 5: The diversity prediction theorem, formulated by Scott E. Page at the University of Michigan[1]. A more detailed explanation of the theorem can be found here. The theorem has huge implications for how one might choose to put together a team.
We usually don't mind closed-minded people that adhere to the same ideologies as us, while we usually dislike closed-minded people that adhere to other ideologies[2]. On the other hand, if people adhering to different ideologies are open-minded, we tend to like them much more. So we should probably be a bit less tolerant of closed-minded people adhering to our own ideologies, since we dislike so much closed-minded people that are adhering to other ideologies.
Closed minded
Figure 6: How we usually don't mind closed-minded people adhering to our own ideologies, but dislike them when they are adhering to other ideologies.
According to the principle of least effort we tend to choose the alternative which requires least effort[3]. It is analogous to the path of least resistance in physics, which says that rivers over time usually will find the path with least resistance. When using search engines, we have a tendency to avoid complicated explanations in favor of more simplistic explanations, even when the complicated explanations are more accurate and/or more trustworthy.
Principle of least effort
Figure 7: Since it requires more effort to understand complicated explanations, we have a tendency to accept simplistic explanations, even if they are less accurate and/or less trustworthy.
This is why students often avoid topics that require a lot of work, in favor of topics that require less work. It can further be related to the appeal of populism in politics. Populistic politicians propose simplistic solutions to complicated problems, such as the war on drugs, the war on terror, or building a wall to stop immigration. Since such simplistic solutions are easy for people to comprehend, they tend to get widespread support, even if they aren't necessarily the best solutions to these complicated problems. We derive more pleasure from thinking about nice things that happened to us in the past, than from thinking about boring and distasteful things that happened to us in the past[4]. So we have a tendency to think more about nice things that happened to us in the past, and every time we remember something, we strengthen the memory. We also modify it a little, to make it appear even more agreeable, so that we can derive even more pleasure from thinking about it in the future.
Rosy retrospection
Figure 8: How we are inclined to remember the past as more colorful and beautiful than it really was, since we tend to focus more upon nice memories than upon boring and distasteful memories.
Over time this tends to make us get an overly positive image of the past. It also tends to make us think that things are getting worse, or that society as a whole is in a state of decline. This way of thinking also tends to lead civilizations to stagnation, since there is much more focus upon reestablishing the past, than upon incorporating new ideas. Sometimes when people are forced to explain their behavior or their choices, they might struggle a bit with coming up with an explanation. But after a while, most people manage to come up with some explanation. Research has however shown that these explanations tend to be fabrications, rather than true reasons[5,6]. We are often not aware of why we are behaving in a certain way, or why we made a choice, but if we are forced to come up with an explanation, we manage to fabricate something. We also tend to believe in these fabrications ourselves, even though they usually aren't based upon why we really behaved like that, or why we really made that choice. When we are starting to learn about a new topic or a new skill, we might overestimate our competence, simply because we haven't learned yet about all the things we don't know or haven't mastered[7]. As we learn more about what we don't know or haven't mastered, our confidence tends to go down. If however we continue to learn our confidence might start to increase again.
Dunning Kruger effect
Research has shown that the more people care about something, the more they tend think they know about it, regardless of if this is the case or not[8]. For example, people that are heavily involved in environmental organizations or care a lot about environmentalism, might erroneously think they know a lot about the scientific theories related to global warming even if this isn't necessarily the case.
People often feel like they know how an item works, if they know how to use it[9]. For example, people that drive a lot might think they have a better understanding of how their car works than what is actually the case. Similarly, people that use computers and cellphones a lot, might think they have a better understanding of how these devices work, than what is actually the case.
We often ascribe our own successes to our superior skills, rather than to external circumstances. When it comes to failures however, we tend to blame it on external circumstances. We are probably better off with taking more responsibility for our failures, since it gives us motivation to improve ourselves.
Self serving bias
Figure 9: How we tend to regard our successes as being related to our superior skills, while regarding our problems as being caused by external circumstances.
We are however good at blaming other people for their failures, without taking into consideration that external circumstances might also influence their failures. This can lead to hostilities in marriages and work environments.
Fundamental attribution error
Figure 10: How we tend to blame external circumstances for our own problems, while neglecting that other people might also fail due to external circumstances.
The brain is wired to find causal explanations. This also tends to make us believe in fallacious causes, especially in situations where things have a natural tendency to regress to the mean. If someone has an extremely bad performance, it is likely to be partially due to unfavorable randomness or bad luck. Similarly, if a person is performing extremely well, it is also likely to be partially due to randomness or luck.
How performance is determined by both talent and luck
Figure 11: How performance quality is determined by both talent and randomness.
However, the person performing extremely bad is likely to perform better the next time just due to less influence of bad luck or unfavorable randomness, while the person performing extremely well is likely to perform worse the next time just due to less influence of luck or favorable randomness.
Regression to the mean
Figure 12: Performance quality is partially determined by randomness. If the performance is exceptionally bad, it is likely that it will be better in the next case, just due to less unfavorable randomness. Similarly, if the performance is exceptionally good, it is likely that it will be worse in the next case, just due to less favorable randomness. This is regression to the mean. The tendency for expectational events to be followed by less expectational events closer to the mean.
In the past, it was commonly believed that punishment works better as an educational technique than reward. If exceptionally bad performance was punished, you might easily think that the punishment caused the performance improvement, even though it was just caused by less unfavorable randomness. If however exceptionally good performance is rewarded, we are likely to see a decrease in favorable randomness the next time, and then you probably wouldn't think of reward as a very useful educational technique. This has also caused a lot of superstition. For example, if you have the flue, you might start to drink some herbal tea, and after a few days you might feel better. In such a scenario, people are prone to believe that they got better because they were drinking herbal tea. It is however highly likely that you would have gotten better just as fast without drinking herbal tea, due to the normal functioning of your immune system. We usually believe too much in things that have very low probabilities of occurring, since there is a possibility for these things to occur. This is why people buy lottery tickets. They focus upon that it is possible, even though it is very unlikely. Similarly, people often do not believe sufficiently in very high probabilities, since they do not feel certain. This is why people often buy expensive insurances. So that they can feel safe, even for very unlikely occurrences.
Overvalued and undervalued probabilities
Figure 13: How people often assign too much weight to very low probabilities, and too little weight to very high probabilities[10,11,12].
Even though we usually undervalue things that are highly probable, we also sometimes feel like we are completely certain about things, even if we cannot really be completely certain[13]. Most tests have false positives, since there usually is a bit of luck and/or randomness involved. For extremely rare conditions, these false positives can actually be far more common than the true positives. However, people often tend to neglect the background probabilities for rare conditions[14]. Such a rare condition might for example be to have more than 145 in IQ.
Normal distribution IQ
Figure 14: A normal distribution for IQ with associated percentages of the world population.
Let us imagine that someone developed an IQ-test which would predict if a person has an IQ of more than 145 with 99% accuracy. So you take the IQ-test, and you score positively for more than 145 in IQ. Should you believe that you have indeed more than 145 in IQ? After all, the IQ-test is supposed to be 99% accurate. However, since only 0.1% of the world population is supposed to have more than 145 in IQ, you need to take this into consideration and use Bayes' theorem to find the real likelihood you have such a high IQ.
Formula base rate
Figure 15: The likelihood that you have indeed more than 145 in IQ, when the base rate is taken into consideration. The likelihood is calculated using Bayes' theorem. A more detailed explanation of the theorem can be found here.
If you throw a fair coin, and assign the value 1 for heads, and the value 0 for tails, the average value gets closer to the expected value (0.5) with more trails[15]. For coin tosses, the average value doesn't seem to always get really close to the expected value before around 100 000 tosses. With medicinal, nutritional and behavioral studies, there is always a bit of randomness for each participant. This can be minimized by using a large number of participants.
Law of large numbers
Figure 16: How the average value of coin tosses gets closer to the expected value with more trials
Just like the average value of coin tosses gets closer to the expected value with more trails, it also gets more rare or extreme average values with less trails. This is known as the law of small numbers[16]. Rare or extreme cases are more common for smaller groups of people, or there is a higher variability between smaller groups of people than between larger groups of people. Smaller schools for example seem to be overrepresented among the best schools, but they also seem to be equally much overrepresented among the worst schools. Maybe just because there is a higher variability between smaller schools than between larger schools. Women have two X chromosomes, while males only have one X chromosome. Since males only get one copy of each gene on the X chromosome, they are much less likely than females of obtaining fully functional versions of all these genes. However, since females obtain twice as many X chromosomal genes, they are also twice as likely to obtain at least one dysfunctional version of each gene.
Probability distribution for x chromosomal genes in males and females
Figure 17: How the probability distribution for x chromosomal genes differ between males and females.
Statistically, this would mean that males have a higher variability of the genes expressed on the X chromosome. The X chromosome contains many genes related to neurological development[17]. Some feminists have argued that western democracies with equal rights for men and women still are discriminating women, since there tends to be more men in favorable highly paid societal positions. However, there also tends to be more men in prisons and in other unfavorable societal positions. This might simply be due to a greater variability in IQ for men than for women. Several studies have found males to be about 30% overrepresented among individuals with intellectual disability[18]. It is actually selection bias to only focus upon one side of the spectrum.
Gender and IQ
Figure 18: Graph showing that we might expect more men in both favorable and in unfavorable societal positions if men have a greater variability of IQ than women.
You might often hear people say something like this: "I know a guy that smoked and lived until he was 100, so smoking cannot possibly be that bad for you". This is a generalization based upon a single individual. As we have seen from the law of large numbers, the average value of coin tosses varies widely until around 1000 trials, and we don't get really good estimates of the expected value before between 10 000 and 100 000 trials. So we need a large amount of individuals (preferably around 100 000) to make reliable generalizations.
In order to make reliable generalizations, we also need to have a random selection of people, and your friends are not a random selection of people. You might for example work for a construction company, and most of your friends could be colleges from work. If you generalized based upon your friends, you might erroneously start to believe that people in general know a lot about construction.

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