Amos Tversky

Traditional economics bases its models on the principle of humans as homo economicus: rational decision-makers who make choices in order to maximize what they value. While Tversky and Kanehman might concede that people follow logic when making decisions whose outcomes they already know, the pair developed a behavioral model known as prospect theory to show how, in reality, people make decisions that involve risk and uncertainty.²

Expected value theory, which opposes prospect theory, suggests that when faced with a risky proposition for a bet, like “If you correctly guess which face the coin will land on, you obtain $100, but if you guess incorrectly, you lose $50”, you will think in terms of absolute outcomes. Absolute outcomes suggest that since you have a 50/50 equal chance of winning or losing, but the amount to be won is larger than the amount to be lost, you would take the bet.³

However, Tversky and Kahneman realized that people did not actually think in absolute terms and when faced with a decision involving uncertainty, people thought of the amount to be gained (expected utility) relative to a reference point, such as their current wealth.² Moreover, these behavioral scientists found that both framing and loss aversion were cognitive biases that impacted people’s decision-making when it came to risky decisions.

Framing suggests that the way that a choice is presented to us impacts our decision and loss aversion suggests that because the psychological pain of losing something is more powerful than the pleasure of gaining something, we tend to avoid decisions that could lead to losses. That is because we think of the loss in terms of diminishing from the reference point of our current wealth and that has a greater weighting than absolute outcomes. We’d be more likely to take the aforementioned bet if we stood to only win $10 but wouldn’t lose anything if we were wrong, even though in absolute terms, the potential gain of $100 is a better deal than the potential gain of $10.

Tversky and Kahneman developed prospect theory and several associated cognitive biases in their 1979 paper “Prospect Theory: An Analysis of Decision Under Risk”.⁴ They outlined findings from their study, where they had given participants several variations of the well-known allais paradox. For example, in one scenario, participants were presented with the following pair of choice problems:

1. Option A: 50% chance to win a three-week tour of England, France and Italy
   Option B: 100% chance to go on a one-week tour of England
2. Option A: 5% chance to win a three-week tour of England, France and Italy
   Option B: 10% chance to win a one-week tour of England

Tversky and Kahneman found that for the first problem, 78% of participants chose option B. For the second problem, 67% of participants chose option A. Participants seemed to be using different reasons for selecting their choice in each problem, showing that they do not behave according to perfect rationality. The behavioral scientists instead concluded that people overweight certain outcomes relative to uncertain outcomes because when one reward becomes certain, the thought of losing it pushes them to play it safe, known as loss or risk aversion.⁴

Following his interest in studying decisions made under the context of uncertainty, Tversky work stressed the idea of reason-based choice, which refers to the fact that people tend to try and explain, justify and understand their decisions in terms that do not always follow homo economicus principles. Instead of treating people as objective agents, Tversky focused on individuals as problem-solvers who are active participants with nuanced ways of rationalizing their decisions.

In a 1993 paper “Reason-based choice” that he co-authored with Eldar Shafir and Itamar Simonson, Tversky examined the ways in which people frame their choices to ignore certain pieces of information.⁵ Prior to Tversky and his colleagues’ work, reason-based analysis had been limited to the fields of politics and business (non-experimental fields) because economics followed expected value theory, but as a pioneer of behavioral science, Tversky wanted to blend the two traditions. The value of this approach was outlined in the paper, with the researchers claiming that “a focus on reason seems closer to the way we normally think and talk about choices” (13).⁵

One aspect of framing that the paper examines is the different choices people make based on whether they are asked to accept one of two choices or reject one of two choices. If we were purely rational thinkers, the way a question was framed would not impact our decision. However, the researchers found that when individuals are asked to accept a choice, they tend to focus more heavily on the positive aspects of the options, whereas when they are asked to reject one of the options, the negative aspects of the options weighed more heavily in their minds, when the exact outcome of their decision is not known.⁵

Following his fascination with how humans behave under uncertainty, Tversky also examined the way that people’s judgment under uncertainty faltered from perfect rationality. He suggested that instead of adhering to the actual probability of particular outcomes, people often have their own preconceived perceptions of probability that were more likely to impact their decisions.

Two famous studies that Tversky and Kahneman conducted to show the influence of perceived probability are the “Feminist Bank-Teller experiment” and another based on a common misperception in basketball.⁶

The feminist bank-teller experiment was a study conducted by Tversky and Kahneman in 1972 that used the following story:

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice and also participated in antinuclear demonstrations.⁶

Participants were then asked to rank a number of statements based on how probable the participants thought they were. Within these statements were the two that Tversky and Kahneman were particularly interested in: “Linda is a bank teller” and “Linda is a bank teller and is active in the feminist movement”. Since the second statement has two different components, whereas the first statement only has one, and the first is guaranteed to be more probable than the second. However, they found that participants usually thought that the second statement was more likely to be true. Tversky and Kahneman coined this the conjunction fallacy.⁶

The second experiment that followed Tversky’s ideas about perceived probability had to do with basketball and was termed the hot-hand fallacy. In a paper with other leading figures in behavioral science, Tversky described the tendency for fans, players and coaches alike to believe in the idea that players can be on a hot streak when they are making a series of baskets and that they are therefore more likely to get another basket. People ignore the actual probability of a player making a shot, based on seasons of statistics, because of a common misconception of how random distribution works. The fact that a player makes a few successful baskets in a row is not taken to be ‘random’ but evidence that they are on a hot streak.

Both of these examples were but some of the heuristics that Tversky is responsible for identifying and coining that show that people are not always rational decision-makers.

Amos Tversky was born on March 16th, 1937 in Israel, into a half-Polish and half-Russian family who had immigrated to Israel.⁶ At a young age, Tversky became interested in literary criticism, already paving the way for his against-the-grain career. However, before beginning his higher education, Tversky had to serve in the military, as is obligatory in Israel, despite the fact that he had gotten involved with a youth movement that fought obligatory military service.⁷ Even if Tversky approached the military with apprehension, once a soldier, he exhibited exceptional bravery. At 19 he saved the life of another soldier by pushing him to safety right before an explosion, which earned him Israel’s highest military honor. He went on to become a captain and served in three wars.⁶

After his time in the military, Tversky began to pursue higher education. He obtained his bachelor’s degree from Hebrew University in 1961 before moving to the U.S. to complete his Ph.D. at the University of Michigan. He completed his doctorate in 1965, where he met his wife, Barbara, who was also a cognitive psychology student.⁶

Tversky began teaching at Michigan, before moving to Harvard and then returning to his roots in Israel to be a guest-speaker in Daniel Kahneman’s class, “Applications of Psychology''.⁸ Although they collaborated for most of their career, the first time the pair appeared to be working together came as quite a surprise - Tversky’s work was highly theoretical, whereas Kahneman’s focused on real-world problems. At the time, Tversky was thought of as a mathematical psychologist, detached from real-life and more focused on models and equations. He was in the midst of publishing a three-volume textbook Foundations of Measurement full of proofs and axioms. It was perhaps his complete contrast to Kahneman, in both their work and their personalities, that made the unlikely pair such a force to be reckoned with as they both took up full-time posts at the Hebrew University of Jerusalem. Tversky’s wife described their relationship as “more intense than a marriage” as they began to spend most of their time together, conducting ground-breaking studies that would forever change the face of economics and psychology.⁸ They were perhaps the strongest behavioral science duo to ever exist.

Tversky later moved to teach at Stanford in 1978 which would be his final post. Throughout his academic career, he received various awards and honors. One of the most notable was his election to the American Academy of Arts and Sciences in 1980, an academy dedicated to honoring the most brilliant minds across disciplines.⁶ Despite his math-focused start, Tversky’s insights were accessible and relevant to the layman. That might be why when he won a MacArthur Foundation Fellowship in 1984, he claimed that what he had studied was common knowledge for “advertisers and used car salesmen.” ⁹ 

Unfortunately, Tversky died at only the age of 59 in 1996 from skin cancer. This was six years before Kahneman received the Nobel Prize in economics. However, in his acceptance speech, Kahneman was sure to give his late friend the credit he deserved and informed the public that the work that had earned him the prestigious award was “done jointly with Amos Tversky during a long and unusually close collaboration. Together, we explored the psychology of intuitive beliefs and choices and examined their bounded rationality”.⁷ 

In elaborating on the way that people used perceived probability over actual probability to influence their beliefs, Tversky states that “chance is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. In fact, deviations are not ‘corrected’ as a chance process unfolds, they are merely diluted”.¹ This helps explain why people do not adequately comprehend random distribution.

Always placing an emphasis on studying real-life behavior, Tversky said that “my colleagues, they study artificial intelligence; me, I study natural stupidity.” However, he suggested that everyone falls victim to such stupidity when he said that “whenever there is a simple error that most laymen fall for, there is always a slightly more sophisticated version of the same problem that experts fall for”.¹⁰ 

Following his youthful interest in literary criticism, Tversky also had something to say about metaphors. He claimed that “metaphors replace genuine uncertainty about the world with semantic ambiguity. A metaphor is a cover-up”.¹

He believed that similarly, our reason-based choices were cover-ups for the uncertainty under which we made decisions. He said that “all too often, we find ourselves unable to predict what will happen; yet after the fact we explain what did happen with a great deal of confidence. This “ability” to explain that which we cannot predict, even in the absence of any additional information, represents an important, though subtle flaw in our reasoning. It leads us to believe that there is a less uncertain world than there actually is, and that we are less bright than we actually might be. For if we can explain tomorrow what we cannot predict today, without any added information except the knowledge of the actual outcome, then this outcome must have been determined in advance and we should have been able to predict it. The fact that we couldn’t is taken as an indication of our limited intelligence rather than of the uncertainty that is in the world. All too often, we feel like kicking ourselves for failing to foresee that which later appears inevitable. For all we know, the handwriting might have been on the wall all along. The question is: was the ink invisible?” ¹¹

A few of the heuristics and cognitive biases discovered and coined by Tversky and his colleagues are outlined in this article. For a full list of the heuristics that Tversky and Kahneman identified, you can take a look at their article “Judgment under Certainty: Heuristics and Biases”. There are also two different compilation texts of some of Tversky’s most influential publications: The Essential Tversky and Preference, Belief and Similarity. 

Tversky is also the co-author of a book titled Critical Thinking: Statistical Reasoning and Intuitive Judgment. Tversky and Varda Liberman, another scholar of judgment and decision-making, outline how people make decisions under uncertainty using every-day examples. This makes the book an easy, but deeply interesting, read.

Since there are a limited number of publications and books of Tversky’s, due to his untimely death, you might instead want to check out Michael Lewis’ The Undoing Project: The Friendship That Changed Our Minds. This book examines Tversky and Kahneman’s friendship and collaboration that helped pioneer the field of behavioral science.

1. Goodreads. (n.d.). Amos Tversky Quotes. Retrieved January 11, 2021, from https://www.goodreads.com/author/quotes/72452.Amos_Tversky
2. Behavioral Economics. (2020, September 9). Prospect theory. Retrieved January 11, 2021, from https://www.behavioraleconomics.com/resources/mini-encyclopedia-of-be/prospect-theory/
3. The Decision Lab. (2020, December 23). Daniel Kahneman. https://thedecisionlab.com/thinkers/thinkers-category-1/daniel-kahneman/
4. Kahneman, D., & Tversky, A. (1979). Prospect theory. An analysis of decision making under risk. Econometrica, 47(2), 263-292. https://www.jstor.org/stable/1914185
5. Shafir, E., & Tversky, A. (1993). Reason-based choice. Cognition, 49(1-2), 11-36. https://doi.org/10.1016/0010-0277(93)90034-s
6. New World Encyclopedia. (n.d.). Amos Tversky. Retrieved January 11, 2021, from https://www.newworldencyclopedia.org/entry/Amos_Tversky
7. Exploring Your Mind. (2019, November 12). Amos Tversky: Cognitive psychologist and mathematician Extraordinaire. https://exploringyourmind.com/amos-tversky-cognitive-psychologist-and-mathematician-extraordinaire/
8. Lewis, M. (2016, November 14). How two trailblazing psychologists turned the world of decision science upside down. Vanity Fair. https://www.vanityfair.com/news/2016/11/decision-science-daniel-kahneman-amos-tversky
9. Stanford News. (1996, June 5). Amos Tversky, leading decision researcher, dies at 59. https://news.stanford.edu/pr/96/960605tversky.html
10. A-Z Quotes. (n.d.). Quotes by Amos tversky. Retrieved January 11, 2021, from https://www.azquotes.com/author/41719-Amos_Tversky
11. Everton, S. F. (2017, March 28). For Those Condemned to Study the Past - Whenever Possible, Count! God, Politics, and Baseball. https://godpoliticsbaseball.blogspot.com/2017/03/for-those-condemned-to-study-past.html