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Mental Models

Transformative Learning Theory (Mezirow)

Summary: Transformative learning is a theory of adult learning that utilizes disorienting dilemmas to challenge students’ thinking. Students are then encouraged to use critical thinking and questioning to consider if their underlying assumptions and beliefs about the world are accurate.

Originator: Jack Mezirow (1923-2014)

Keywords: adult education, higher education, academic development, disorienting dilemmas, assumptions, beliefs, worldview, change, transformation, critical reflection

Transformative learning theory was developed by Jack Mezirow in the late 1900s. He used this theory to describe how people develop and use critical self-reflecting to consider their beliefs and experiences, and over time, change dysfunctional means of seeing the world. Mezirow was interested in peoples’ worldviews and what leads people to change their particular view of the world.[i]

Mezirow describes transformative learning as “learning that transforms problematic frames of reference to make them more inclusive, discriminating, reflective, open, and emotionally able to change."[ii]

So, what must happen for a person to change their view of the world? Mezirow believed that this occurs when people face a “disorienting dilemma." Disorienting dilemmas are experiences that don’t fit into a person’s current beliefs about the world. When faced with a disorienting dilemma, people are forced to reconsider their beliefs in a way that will fit this new experience into the rest of their worldview. This often happens through “critical reflection" in the context of dialogue with other people.[iii]

A Case Study

Researcher Michael Christie presents the following case study as a real life example of transformative learning theory in action. Christie describes his experience teaching adult woman in a Graduate Diploma course for Adult and Vocational Educators. Throughout the course, he asked his students to “keep a critical incident file of their experiences."

The content of the course provided many new ideas that functioned as disorienting dilemmas for these woman. The woman were forced to think through their assumptions in a number of areas, including beliefs about gender roles. Christie states, “For example, the belief that ‘a woman’s place is in the home’ was undermined, the assumptions underpinning it challenged, and a new perspective enacted."

Applications of Transformative Learning Theory

Disorienting dilemmas often occur in the context of academic learning environments, as teachers provide space to critically engage with new ideas. Teachers who want to utilize transformative learning in their classrooms can consider implementing the following opportunities for students.

  • Providing opportunities for critical thinking – Teachers can create opportunities for critical thinking through providing content that introduces new ideas. Students then need the opportunity to engage with new content through journaling, dialoguing with other students, and critically questioning their own assumptions and beliefs.
  • Providing opportunities to relate to others going through the same transformative process – Transformation often happens in community as students bounce ideas off one another and are inspired by the changes friends and acquaintances make.
  • Providing opportunities to act on new perspectives – Finally, research indicates that it is critical for teachers to provide the opportunity for students to act on their new found beliefs. There is some indication that true transformation cannot take place until students are able to actively take steps that acknowledge their new belief.



[i] Christie, M., Carey, M., Robertson, A., & Grainger, P. (2015). Putting transformative learning theory into practice. Australian Journal of Adult Learning, 55(1), 10-30

[ii] Mezirow, J. (2009). Transformative learning theory. In J. Mezirow, and E. W. Taylor (Eds), Transformative Learning in Practise: Insights from Community.

[iii] Howie, P. & Bagnall, R. (2013). A beautiful metaphor: Transformative learning theory. International Journal of Lifelong Education, 32(6), 816-836.

Stereotype Threat (Steele, Aronson)

Summary: Stereotype threat occurs when people are at risk for living up to a negative stereotype about their group. For example, a woman may fail to reach her career goal of being a scientist because of how she changes her behavior in response to perceptions about her own gender.

Originators: Claude Steele and Joshua Aronson

Keywords: stereotypes, vulnerability, self-defeating behavior, performance, gender, race, intelligence

Stereotype threat is a term that was created by social scientists Claude Steele and Joshua Aronson. They completed an important early study in 1995 which defined stereotype threat as “being at risk of confirming, as self-characteristic, a negative stereotype about one’s group."[i]

In this study, Steele and Aronson observed the performance of Black and White students on academic tests. Steele and Aronson created the study in response to a negative stereotype about Black students which pervades culture – Black students are portrayed as less intelligent and less competent than White students. Because of this stereotype, Steele and Aronson wondered if Black students would “protectively dis-identify with achievement in school and related intellectual domains." This desire to disengage from intellectual pursuits could possible lead Black students to live up to their negative stereotype.

The results of the study confirmed the researcher’s suspicion. When test instructors emphasized the role of race before the test, Black students performed worse than White students. When instructors did not emphasize race, Black and White students performed equally well.

In essence, stereotype threat occurs when people fear that they will live up to a negative stereotype about their group. In response to their fear, they participate in disengaging and self-defeating behaviors that ironically cause them to live up to the feared stereotype.

Stereotype Threat Impacts Peoples’ Behavior

Stereotype threat has been shown to impact peoples’ behavior in the following ways.[ii]

  • Reduced effort – People who fear they might live up to a stereotype sometimes reduce their effort so they can have an excuse if they fall into that stereotype. For example, people may not prepare for a test so they have an excuse when they do poorly.
  • Disengaging – People who are stereotypically not good at something (such as woman in mathematics) will often disengage from that field or area.
  • Changing aspirations and career goals – Some people go as far as to change their life aspirations and career goals in response to stereotype threat.

How to Reduce Stereotype Threat

Stereotype threat has been studied extensively, with a heavy emphasis on how to reduce this phenomenon in various populations. Research shows that the following strategies can be effective. Many of these are practical strategies that can be carried out in classrooms and other settings.

  • Providing role models. People who observe role models from their group engaging in certain fields and activities are more likely to think they can do the same thing. One study showed that woman who read about other woman who had succeeded in fields of architecture, law, medicine, and intervention performed better on a mathematics test than those who didn’t.[iii]
  • Encouraging self-affirmation – One study showed that having African students engage in a self-affirming journal exercise before the start of a semester closed the racial achievement gap by 40%.[iv]
  • Emphasizing motivation and effort – African American students who were taught that intelligence is “a malleable rather than fixed capacity" that can be increased through motivation and effort received better grades than those who were not taught this.[v]

Although stereotype threat is a significant concern for many vulnerable groups of people, research consistently shows that the effects of stereotype threat can be reduced through following strategies such as these.[v]

Over three hundred studies have investigated stereotype threat in a wide variety of areas.[vi]


[i] Steele, C. M., & Aronson, J. (1995). Stereotype threat and intellectual test performance of African Americans. Journal of Personality and Social Psychology, 69(5), 797-811.

[ii] Stroessner, S. & Good, C. (n.d.) Stereotype threat: An overview. Retrieved from

[iii] McIntyre, R. B., Paulson, R., & Lord, C. (2003). Alleviating women’s mathematics stereotype threat through salience of group achievements. Journal of Experimental Social Psychology, 39, 83-90.

[iv] Cohen, G. L., Garcia, J., Apfel, N. & Master, A. (2006). Reducing the racial achievement gap: A social-psychological intervention. Science, 313, 1307-1310.

[v] Aronson, J., Fried, C. B., & Good, C. (2002). Reducing the Effects of Stereotype Threat on African American College Students by Shaping Theories of Intelligence. Journal of Experimental Social Psychology, 38, 113-125.

[vi] Stroessner, Steve; Good, Catherine. “Stereotype Threat: An Overview”. Reducing Stereotype Retrieved 6 March 2011.

Chaos Theory

Summary: Chaos theory is a mathematical theory that can be used to explain complex systems such as weather, astronomy, politics, and economics. Although many complex systems appear to behave in a random manner, chaos theory shows that, in reality, there is an underlying order that is difficult to see.

Originators: Henri Poincaré (1854-1912), Edward Lorenz (1917-2008)

Keywords: order, chaos, complex systems, determinism, butterfly effect, sensitive dependence on initial conditions, nonlinear dynamics, chaos dynamics

Many complex systems can be better understood through the lens of Chaos Theory. Henri Poincaré, a mathematician, laid the groundwork for Chaos Theory.[i] He was the first to point out that many deterministic systems display a “sensitive dependence on initial conditions.” Poincaré described this concept in the following way: “It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible.”

For example, Poincaré pointed out that the apparent lack of order seen in many astronomical systems was actually not random or chaotic. Instead, astronomers were just not seeing the small changes in initial conditions that were leading to humongous differences in the final phenomena that were being observed.

Later, in the 1900s, Edward Lorenz officially coined the term Chaos Theory. Lorenz studied Chaos Theory in the context of weather systems. When making weather predictions, he noticed that his calculations were significantly impacted by the extent to which he rounded his numbers. The end result of the calculation was significantly different when he used a number rounded to three digits as compared to a number rounded to six digits.

His observations on Chaos Theory in weather systems led to his famous talk, which he entitled, “Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?" In reference to this talk, Chaos Theory has also been described as the “butterfly effect.”

Application of Chaos Theory

Chaos theory has a lot to teach people about decision making in complex environments. The mathematical concepts used to understand physical systems are now being applied to social environments such as politics, economics, business, and other social sciences.[ii]

Although applying Chaos Theory to business settings is still in its infancy, social scientists describe the following applications as useful when making business decisions.[iii]

  • Chaos theory suggests that spending a lot of time trying to predict the future of complex, non-linear systems may be better spent elsewhere. Instead of trying to predict long-term future outcomes, businesses should consider and plan for multiple possible outcomes.
  • Chaos theory reminds business owners that small changes in business practice can lead to huge changes in future outcomes based on the concept of sensitive dependence on initial conditions. Some business managers underestimate the possibility for large unexpected changes, and should reconsider their mindset on this matter.
  • Chaos theory assumes that there is order behind seemingly random events. Even though businesses may not be helped by making long-term future predictions, they can make short-term forecasts to help with business decisions.
  • Because of the complexity and unpredictability inherent in complex systems, businesses need clear guidelines for employees to follow. However, since sudden and drastic changes are bound to occur, business owners should be ready to adapt these guidelines as necessary.


[i] Oestreicher, C. (2007). A history of chaos theory. Dialogues in Clinical Neurosciene, 9(3), 279-289.

[ii] Richards, D. (1990). Is strategic decision making chaotic? Systems Research and Behavioral Science, 35(3), 219-232.

[iii] Chaos theory and strategy: Theory, application, and managerial implications. Strategic Management Journal, 15, 167-178.

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Social Proof

Summary: Social proof describes a psychological phenomenon in which people mirror the actions and opinions of others. In other words, people’s decisions are often impacted by the preferences and modeling of individuals or groups around them.

Keywords: informational social influence, marketing, group norms, standards of behavior, testimonials, crowds, social modeling, sales, business, conformity, group conformity, social media

Originator: Muzafer Sheraf (1906-1988)


Social proof was first described in scientific research by a psychologist named Muzafer Sheraf. Sheraf was interested in the impact of groups on individual decision making. In relation to this interest, he completed a famous experiment on group conformity in 1936.[i]

In this study, Sheraf asked participants to observe a blinking light. A blinking light in a dark room often appears to move, even when it remains still. Based on this common perception, Sheraf asked participants to indicate how many inches they thought the blinking light moved. Sheraf first asked participants to guess an answer when they were alone. Then, he asked them the same question again while they were surrounded by a group of other participants. Sheraf found that participants changed their initial answers once they moved to the group setting. Across the board, people changed their number to closer reflect what other group members had guessed.

The concept of social proof came out of studies such as this one. Researchers consistently observe a tendency for individuals to move towards group conformity. Individuals often change their behaviors, opinions, and decisions to match the people around them.


Using Social Proof to Influence People

Social proof is commonly used in marketing and social media to influence people to buy products. Listed below are a variety of different types of social proof that are used in the context of marketing.[ii]

Social proof uses the influence of social media friends. For example, a business might indicate how many of a person’s Facebook friends “liked" a particular product they sell. People are more influenced to buy something when they know that their friends like the product.

  • Social proof uses the influence of celebrities. Research shows that people are more likely to buy a product when it is endorsed by a familiar and well-liked celebrity.
  • Social proof uses the influence of professional certifications and testimonials. Experts in an area may be called upon to endorse a product or provide a testimonial of how they have enjoyed a product.
  • Social proof uses the influence of crowds. Sometimes businesses indicate the number of people who have bought a product. When people know that a product or service is popular, they are more likely to want to buy it.


Social Proof and Personal Decisions

Social proof is a great marketing strategy and an effective means of influencing people to make certain choices. However, individuals should consider if social proof is always the best way to make decisions.

Quite notably, Sharif’s original study indicated that people were not aware of the extent to which they were impacted by the group. When participants where asked if they thought they were influenced by the group, most of them believed they had not been influenced. However, it was clear from the results of the study that people were wrong to believe this.

Negative forms of social proof can lead to bad decision making and giving into peer pressure. A prime example of this is college students who abuse alcohol and drugs.[iii] Research has drawn connections between social proof and this common dangerous behavior in college students. On a college campus, so many people engage in substance abuse that this behavior is observed to be the norm. Incoming students are apt to conform with the group and begin abusing substances just like the older students around them.

It is not always wrong to make decisions based on social proof. However, Sharif’s study provides an important caution that people should develop self-awareness surrounding this topic, so they can know when their decisions are being influenced by the people around them.



[i] Sherif, M. (1936). The psychology of social norms. Oxford, England: Harper.

[ii] Talib, Y. Y. A. & Saat, R. M. (2017). Social proof in social media shopping: An experimental design research. SHS Web of Conferences, 34

[iii] Cullum, J., O’Grady, M., Armeli, S., & Tennen, H. (2012). Change and stability in active and passive social influence dynamics during natural drinking events: A longitudinal measurement-burst study. Journal of Social and Clinical Psychology, 31(1), 51-80.

Network Effects

Summary: Network Effects describes the phenomenon how the value of a good or service increases as more people start to use that good or service.

Originators: Theodore Vail (1845-1920), Robert Metcalfe (1946-Present)

Keywords: network externality, demand-side economies of scale, marketing, customer base, value, monopoly, social media, congestion, good, service

Certain products only have value if a large number of people are using them. A classic example is that of technology used for communication such as a phone or fax machine. Critical mass is needed — these devices are only valuable if lots of other people have phones that you can call and machines you can fax.

This phenomenon was first described by Theodore Vail in 1908. Vail used the concept of Network Effects to build AT&T into a monopoly of telephone communication in the early 1900s. Later, Robert Metcalfe described Network Effects related to the importance of more people engaging in use of the Internet for it to become beneficial to everyone.[i]

Both the Internet and the telephone are examples of Direct Network Effects, in which more customers directly increase the value of a product or service. There are also Indirect Network Effects, which occur when more customers indirectly increase the value of a product of service. For example, when more people use Uber, this does not directly make Uber more valuable. However, the more people who use Uber, the more Uber is motivated to improve the quality of their service, which ends up indirectly impacting the value of this service.[ii]

Another prime example of Network Effects can be found in various social media services, such as Facebook. The more people who use Facebook, the more valuable Facebook becomes. This in turn, attracts more people to Facebook, as people do not want to miss out on a service that so many other people are using. Thus, Facebook continues to increase in value and attract more people at the same time.

Using Network Effects to Improve Businesses

Businesses who succeed at utilizing Network Effects can gain a competitive advantage in their industry. Consider two ways in which this can happen:

  1. Businesses can harness the power of Network Effects through engaging with products that are already highly valuable. They can consider what products are being used by a large number of people and consider utilizing those products within their business.

For example, Visa is a type of credit card used by over 2.9 billion people. Businesses can make a point to accept Visa credit cards and gain more customers who might have gone elsewhere if the business only accepted cash.

Businesses can harness the power of social media through advertising via various media platforms that are already popular and attract large numbers of people.

  1. Businesses can create network effects within their own products and services through encouraging high engagement, interacting with customers, and providing high quality products.

The reason many social media platforms developed high network effects is because they are engaging and interactive. This is a means of drawing new customers in and building up a client base to build value within the business.

Once people engage with a product or service, businesses can focus on keeping products and services as high quality as possible. This keeps people engaged in the long run.


[i] Easley, D. & Kleinberg, J. (2010). Networks, crowds, and markets. Reasoning about a highly connected world. Cambridge University Press.

[ii] Clements, M. T. (2004). Direct and indirect network effects: Are they equivalent? International Journal of Industrial Organization, 22(5), 633-645.

Prisoner’s Dilemma

Summary: The Prisoner’s Dilemma is a hypothetical scenario which illustrates the difficulty of deciding whether to cooperate or compete with other people. Understanding the costs and benefits of cooperating and competing is applicable to various fields including business, economics, and politics.

Originators: Merrill Flood (1908-1991, Melvin Dresher (1911-1992), Albert William Tucker (1905-1995)

Keywords: game theory, cooperation, competition, problem-solving, strategy, consequences, cooperation level, individual behavior, evolutionary game theory, mutual cooperation

The Prisoner’s Dilemma is a scenario that was created to describe concepts behind game theory.[i] Game theory is the study of how and why people cooperate or compete with one another. The Prisoner’s Dilemma was originally created by two scientists named Merrill Flood and Melvin Dresher. In later years, professor Albert William Tucker developed the Prisoner’s Dilemma further, using it as a teaching tool for his graduate psychology students.

Here’s the scenario: Two friends – let’s call them Jim and Matt – have been convicted of a crime. The police bring Jim and Matt in for questioning and place them in separate rooms. Each of them has two options. They can confess to the crime, or remain silent regarding the crime. Matt and Jim are both told that the option they choose will affect them personally and affect their friend in the following ways.

  • If they both choose to remain silent, each will receive only 1 year in prison.
  • Another option is for both of them to confess. If this happens, they each get two years in prison.
  • The final option is for one of them to confess and the other to remain silent. If Matt confesses and Jim remains silent, Jim will get three years in prison and Matt will go free. And vice versa.

What should each of them do? Consider this scenario from Matt’s perspective.

Is it best for Matt to cooperate by remaining silent? In some ways, this is the riskier choice. There is no chance for him to go free. He will either serve one year with Jim or three years alone. But Matt may care about Jim and want to consider his well-being as well. Remaining silent could lead to the best case scenario for both of them together.

Or, is it best for Matt to compete by confessing to the crime. In some ways, this is the safest choice. Matt could go free. And he avoids any chance of the longest possible sentence of three years. But it would also be a decision made out of self-interest, and Matt may want to consider if only his interest is important to him.

Cooperating or Competing

Is it better to cooperate or compete? This is the main question behind The Prisoner’s Dilemma.

This question, as illustrated in the scenario, is highly applicable to a number of fields such as business, economics, and politics.

The Prisoner’s Dilemma is a reminder that cooperation is not always best.[ii] Immediately cooperating can lead to consequences if the other party is only thinking about personal self-interest. For example, when it comes to salary negotiations, it is not always in a person’s best interest to take the first salary offered. Sometimes it is better to push for a higher salary, even though this might not work out. Another example would be pricing a product. Often it is better for businesses to compete with one another by lowering prices. Lowering prices can lead to higher profit margins than if a business cooperated and priced similarly to other businesses in the area.

On the other hand, The Prisoner’s Dilemma also illustrates that it isn’t always best to look out for one’s self-interest only. When businesses show mutual cooperation, it can lead to increased profit for both of them. Businesses sometimes form mutually beneficial strategic partnerships, such as when Starbucks coffee is sold in Barnes and Noble bookstores. Mutual cooperation is also an important strategy in politics. For example, mutual cooperation between countries may be risky and require compromise; however, it can also be a means of keeping peace and enhancing trade.[iii]


[i] Dixit, A. “Prisoners’ Dilemma: The Concise Encyclopedia of Economics." Library of Economics and Liberty. Web.

[ii] Stucke, M. E. (2013). Is competition always good? Journal of Antitrust Enforcement, 1(1), 162-197.

[iii] Jervis, R. (1978). Cooperation under the security dilemma. World Politics, 30(2), 167-214.

Backup Systems (Redundancy)

Summary: The concept of backup systems, also known as redundancy, originated in the field of engineering. Many mechanical systems are created in such a way that if one part of the system fails, the system as a whole will still be able to function due to the presence of backup components. Redundancy and backup plans should play an important role in many decision-making processes for the purpose of risk reduction.

Originator: Jon von Neumann (1903-1957)

Keywords: reliability, reliability engineering, redundancy, independent backup system, mechanical engineering, risk reduction, safety plan, disaster recovery, backup software

Backup systems were first described in the field of mechanical engineering by Jon von Neumann. In his well-known work, Probabilistic Logics and Synthesis of Reliable Organisms from Unreliable Components, Neumann described how computers can be built with redundant parts as a “technique [that] can be used to control error."[i] In the years to come, redundancy would become an essential concept in designing complex mechanical systems.

The engineering behind aircrafts is a prime example of how engineers use backup systems today. If an airplane experiences any form of mechanical failure while in the sky, this is clearly a major problem. Because of the inherent risk found in air travel, airplanes are built in a mechanically redundant way, with a number of backup systems in place. For example, most airplanes can run on only one engine, even though they have four engines in all. Up to three of these engines could fail, and the airplane would still be able to fly.

It has been argued that the redundancy of back-up systems should be used as a “design paradigm" for all modern technology. From airplanes to computers, from communication systems to emergency preparedness, backup systems should be an essential component of how society designs all important technology.

Backup Systems and Risk Reduction

When considered from the standpoint of making decisions, backup systems are a form of reducing risk in a variety of areas. The decision to include or not include backup systems can have a huge impact on communities, businesses, and individuals.

Backup systems are important to use in mechanical systems as described above, software systems, and for backing up data. Research shows that redundancy in software systems can reduce human error.[ii] And in terms of backup of data, many people know the importance of saving documents in multiple places to reduce the risk of losing information. For example, an important document might be saved on a computer hard drive, an external disc, and an online storage system. Some businesses have backup policies in place to ensure the safety of important documents.

Backup systems are especially important in decisions about emergency preparedness. In natural disasters, backup systems should be put into place to ensure that people have enough fuel, food, and shelter. When performing field work or travel in remote areas, redundancy in communication is important. A group should be able to communicate with the outside world through multiple means such as walkie talkies, cellphones, and flares to ensure help could find them should something go wrong.

Human backup systems are also important to consider.[iii] Are there enough operators to respond to 911 calls? Are there enough policeman to back up their coworkers and enough fireman for an area?

In situations where things could easily go wrong, redundancy is important to decrease the risk of negative outcomes.


[i] Downer, John. (2009). When failure is an option: Redundancy, reliability, and regulation in complex technical systems. Centre for Analysis of Risk and Regulation. Discussion paper No: 53.

[ii] Van den Brand, M. & Groote, J. F. (2015). Software engineering: Redundancy is key. Science of Computer Programming, 97(1), 75-81.

[iii] Hwang, S. L. & Li, Z. 2016). Human factors in digital systems. A study on human redundancy in execution of computerized emergency operating procedures. International Journal of Industrial Ergonomics, 51, 1-82.



Law of Large Numbers

Summary: The Law of Large Numbers is a statistical theory related to the probability of an event. This theory states that the greater number of times an event is carried out in real life, the closer the real-life results will compare to the statistical or mathematically proven results. In research studies, this means that large sample sizes average out to be more reflective of reality than small sample sizes.

Originators: Gerolama Cardano (1501-1576), Jacob Bernoulli (1654-1705)

Key Words: Probability, mathematics, sample size, anomalies, statistics, percentage, average, mean

The Law of Large Numbers was first observed by the mathematician Gerolama Cardano in the 16th century. Cardano noticed the theoretical presence of The Law of Large Numbers, but he never took the time to prove it mathematically. Another mathematician, Jacob Bernoulli, figured out the equations behind The Law of Large Numbers in 1713.[i]

A simple way to understand The Law of Large Numbers is to consider the probability of a coin toss. When a coin is tossed, there is a 50% chance that the coin will land on heads and a 50% chance that the coin will land on tails. This is a statistically proven fact. However, if a person tossed a coin in the air 5 times, there is a chance that the coin would land on heads every single time. This event would not seem to align with the mathematically proven probability of landing on tails 50% of the time.

How can we explain this? These real-life results don’t mean the math is wrong. They simply mean that the coin toss has to be carried out more times to accurately reflect what math says is true. If the same person tossed the coin in the air 500 times, by the end of all the tosses, the coin would have landed on heads an average of 250 times and on tails an average of 250 times. The real life coin toss is now more reflective of what math says to be true because it has been carried out a larger number of times.

Sample Sizes

The Law of Large Numbers is most applicable to scientific research and sample sizes.[ii] When scientists complete research studies, they make decisions about how many people will be in the study. This is an important decision because small sample sizes can greatly skew results due to the presence of anomalies. The larger the sample size, the more the results will reflect the true nature of the population that is being studied.

Consumers trying to understand scientific research should take sample size into consideration when determining the validity of a study. Scientists should do everything within in their power to work with large sample sizes, as this makes their work more accurate and thus more beneficial to society.

Personal Decisions

The Law of Large Numbers is also an important reminder that individual instances don’t provide the whole story. There are times when people make decisions based on one event or instance they have experienced or heard about. This is often a bad way to make decisions.

For example, someone might hear a story about how their friend had a terrible reaction to a medication and refuse to take that medication based on that one example. However, this is a bad way to make a choice about medication, as one experience or story is often not reflective of the way things typically work. The medication may be extremely safe, and the one story simply reflects an anomaly. When making personal decisions it is important to gather a range of information. The Law of Large Numbers explains the theory and mathematics behind this important concept.


[i] Seneta, E. (2013). A tricentenary history of the law of large numbers. Bernoulli, 19(4), 1088-1121

[ii] Dinov, I. D., Christou, N., & Gould R. (2009). The law of large numbers: The theory, applications, and technology-based education. Journal of Statistics Education, 17(1), 1-19.



Summary: Scarcity is an economic term that describes the mindset people develop when they have many needs and not enough resources to meet those needs. When people operate out of a scarcity mindset, it can greatly impair their decision-making abilities.

Originators: Lionel Robbins (1898-1984), Sendhil Mullainathan (1972 to Present), Eldar Shafir (1959 to Present)

Keywords: paucity, poverty, scarcity mindset, resources, allocation of resources, cognitive load, goal-setting, short-term goals, long-term goals, finances, financial wellbeing, attention, effort, tunneling

Lionel Robbins was the first person to discuss the field of economics using the concept of scarcity of resources. In his article, An Essay on the Nature and Significance of Economic Science, Lionel stated, “Economics is the science which studies human behavior as a relationship between ends and scarce means which have alternative uses."[i]

The concept of scarcity has been further developed since then. Key research on the topic of scarcity has recently been completely by the behavioral scientists Sendhil Mullainathan and Eldar Shafir.

Perhaps the most pertinent example of scarcity is found in people who live in poverty. Research has found that living in a state of poverty impairs peoples’ decision-making abilities. This is because poverty leads to a scarcity mindset that negatively changes the way a person thinks, plans, and operates. Research has shown two main ways in which this happens.

First, living in a state of scarcity, “imposes a cognitive load that saps attention and reduces effort."[ii] Researchers studied low-income and high-income individuals who were faced with a large expense such as a car repair. They found that low-income individuals performed worse on an unrelated reasoning task when they were considering this repair than when they didn’t have additional expenses to consider. On the other hand, high-income individuals performed equally well on the task, whether they were considering an expense or not. The researchers hypothesized that this occurred because the high-income individuals did not have to worry about not being able to pay the expense, and therefore did not have to allocate any of their attention away from the reasoning task.

Second, living in a state of scarcity impairs peoples’ ability to make and carry out healthy long-term goals.[iii] The cognitive load described above leads to bad decision making. People become focused on present, short-term goals such as how to deal with immediate expenses. This is called tunneling – the brain becomes so focused on a particular short-term problem that it can’t focus on anything else.

People who engage in tunneling may make bad financial decisions such as playing the lottery or borrowing too much money. These bad decisions, that they hope will help them deal with the short-term problem of paying for a bill, can lead people into worse situations than they were in before.

From Scarcity to Abundance

Scarcity is also present in other situations such as when workers are not given enough resources to do their jobs or in the aftermath of a natural disaster when there aren’t enough goods to go around. Sometimes people even live out of a scarcity mindset when there are plenty resources to go around. When people make decisions from a scarcity mindset, they hoard resources, only think of themselves, and live with a lot of anxiety.

Steven Covey is a businessman who wrote a book entitled The Seven Habits of Highly Effective People. In the context of business, Covey encourages people to embrace an abundance mentality over a scarcity mentality as they make decisions about their lives and careers.[iv] People with an abundance mentality make decisions out of a mindset that there is enough to go around. They are more generous with their resources, more gracious when other people succeed, and less anxious that they will miss out. They make decisions out of a belief that there is enough to go around.


[i] Robbins, L. (1932). An essay on the nature and significance of economic science. London: Macmillan, First Edition. Retrieved from

[ii] Mani, A., Mullainathan, S., Shafirt, E., Zhai, J. (2013). Poverty impedes cognitive function. Science, 351(6149), 976-980.

[iii] Shah, A. K., Mullainathan, S., & Shafir, E., (2012). Some consequences of having too little. Science, 338(6107), 682-685.

[iv] Covey, S. (2004). The seven habits of highly effective people: Powerful lessons in personal change. NY, New York: Free Press.

Pareto Principle

Summary: The Pareto Principle describes how in a variety of situations, 80% of a product or phenomenon’s output often comes from only 20% of the available input. For example, a business may receive 80% of its income from the sale of only 20% of the products available in their inventory.

Originators: Vilfredo Pareto (1848-1923), Dr. Joseph, M. Juran (1904-2008)

Keywords: 20/80 principle, 20/80 law, 20/80 rule, productivity, business, prioritizing, Pareto’s principle of unequal distribution, distribution, wealth distribution, input, output, products, profit

The concepts behind the Pareto Principle were described by Vilfredo Pareto in the late 19th century. Pareto observed the wealth distribution in his home country of Italy and noticed that 80% of all the wealth was held by 20% of Italy’s richest people.

In the 1940s, Dr. Joseph Juran was studying Pareto’s work and realized that this 80/20 rule could also be applied to the area of quality control. When looking at defects in products, he observed that most of these defects were being caused by a small number of problems in the production process. He called this principle Pareto’s Rule in honor of its founder.[i]

Over time, people have described how this 80/20 law can be applied to a variety of areas related to economics, productivity, marketing, cost estimating, and healthcare.

Real Life Examples

A number of real life examples describe how a smaller percent of a situation’s effects lead to a much greater percent of that situation’s results.

In 2002, Microsoft announced that 80% of errors that occur in their system are caused by 20% of all bugs found in their system.[ii]

The American distribution of wealth holds closely to the 80/20 rule. In 2012, 20% of Americans held 89% of all wealth in America.[iii]

Pareto’s principle has been noted in relation to healthcare, as a small percentage of patients use the majority of healthcare resources.[iv]

Prioritization and Increasing Productivity

Pareto’s principle continues to help people by showing best ways to prioritize resources. Noticing unequal patterns of distribution and acting on this knowledge is a great way to improve businesses and personal productivity. Those who observe this principle are able to prioritize in ways that lead to increased quality, productivity, and profit.

For example, in some businesses, 20% of employees complete 80% of the work. Employers may notice workers who are high producers and consider providing a raise or promotion. Contrarily, they might notice low producers and seek to determine what is leading to low levels of output.

In some businesses, 80% of sales come from a mere 20% of products. Some products are much more popular than others. Businesses may take notice of what qualities these popular products hold and seek to produce similar products that appeal in the same way.

If 80% of views on a blog come from 20% of the articles, this is a helpful way to determine best types of articles in the future. Or, if a person completes 80% of their best work in 20% of their working time, this is a great way to consider what conditions lead to greatest productivity.

Pareto’s principle helps people notice patterns and act on them to improve the ways they go about work and production. It helps people decide how to best use resources to make a profit.


[i] The Economist. (2009). Joseph Juran. Retrieved from

[ii] Rooney, P. (2002). Microsoft’s CEO: 80-20 rule applies to bugs, not just features.

[iii] Wolff, E. N. (2012). The Asset Price Meltdown and the Wealth of the Middle Class. New York: New York University.

[iv] The High Concentration of U.S. Health Care Expenditures: Research in Action, Issue 19. June 2006. Agency for Healthcare Research and Quality, Rockville, MD. Retrieved from

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