The Basic Idea
If you saw the equation 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 and had to come up with a quick estimate of the product of this equation, what would your estimate be? Chances are you’d start with 8 x 7, and get the product 56. Knowing that this product would have to multiply by 6 and then by 5 and so on, your estimate would probably turn out to be a pretty big number, probably somewhere around 2000.
Now, imagine you’re given a new equation to solve: 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8. Once again, you must conjure up a quick estimate. When faced with this equation, you’re most likely multiplying 1 x 2 = 2, and then 2 x 3, and then realizing that you’re going to continue with a set of relatively small numbers. The weight your mind grants to the bigger numbers, 7 and 8, may not be as heavy as in the last equation since they don’t come first. This time, your final answer will end up reasonably-sized, but not huge: according to several studies, it is likely around 500.
As you’ve probably realized, the two equations given are equivalent, and their real product is actually closer to 40,000 than to either of the numbers projected as your estimates. However, studies show that when given these two equations, people use the first few numbers to estimate their final answer and pay less attention to the later numbers, resulting in hugely different estimates for the two identical equations. In other words, they fall prey to the anchoring bias: allowing the first number they see to cloud their decision-making process.
Theory, meet practice
TDL is an applied research consultancy. In our work, we leverage the insights of diverse fields—from psychology and economics to machine learning and behavioral data science—to sculpt targeted solutions to nuanced problems.
Anchoring was first introduced in a 1958 study on psychophysics by researchers Muzafer Sherif, Daniel Taub, and Carl Hovland. These researchers were trying to determine how the use of anchor numbers might influence their subjects’ estimates of different objects’ weights. Calling it the “assimilation effect,” the researchers concluded that placing anchoring numbers right next to an object could cause participants’ estimates of its weight to move in the direction of the anchor.
Psychologists Daniel Kahneman and Amos Tversky did not come up with the concept of anchoring but they were the first to demonstrate the absurd and irrational effects it can have on our everyday lives, even while we are aware of its existence. In their first study on anchoring, Kahneman and Tversky set up a wheel of fortune which was rigged to land only on numbers 10 and 65. After asking participants to spin this wheel of fortune—which would obviously have no bearing on future information—the researchers asked the subjects to estimate what percentages of countries in the United Nations are African. The average estimate of those who had spun a 10 was 25%; the average estimate of those who had spun a 65 was 45%. As a result of this study, Kahneman and Tversky eagerly published the finding that completely random and irrelevant numbers can have an undue influence on subsequent numeric decisions, even when participants know the irrelevance of these numbers.
Daniel Kahneman is widely considered the father of behavioral science. He and his research partner Amos Tversky first became well known for their famous article “Judgment Under Uncertainty: Heuristics and Biases.” This article, which later became a book, describes the mental tricks used daily by the human mind in its decision making process, many of which are described in detail on TDL’s website. Kahneman’s more recent book, Thinking Fast and Slow, delves into more detail on the two systems of our mind and the most recent applications of his heuristics and biases. Despite having never taken a single economics course, Kahneman earned the 2002 Nobel Memorial Prize in Economics for his application of psychological insights to economic theory, particularly within the realm of judgment and decision-making. Kahneman is currently a senior scholar at Princeton University. You can read more about him from TDL here.
Amos Tversky worked closely for over a decade with Daniel Kahneman on findings that have provided the foundation for modern and future behavioral science research. Aside from their many famous biases and heuristics, the pair is also well-known for developing prospect theory and loss aversion, a behavioral model that predicts how people will make decisions involving potential loss, risk, or uncertainty. Much of Tversky’s early research focused on cognitive science and the handling of risk, as well as the mathematical foundations of measurement. Upon teaming up with Kahneman, the pair worked for over a decade together, conducting creative and thoughtful behavioral science experiments in an effort to understand how the irrational human mind makes everyday choices. Tversky taught for many years at Stanford University, and was a recipient of the MacArthur Fellowship—known as a “genius grant”—in 1984. Tversky unfortunately died of melanoma in 1996.
The consequences of anchoring may at first seem trivial, however their huge impact on the free market plays out everyday, as individuals and corporations make important choices about prices at which they will buy and sell goods and services. In any situation, anchoring typically provides positive consequences for one party and negative consequences for the other. In your lifetime, you will probably sit on both sides of the table.
One area in which anchoring has an enormous effect is the real estate market. When a seller decides to sell his home, he makes use of anchoring by proposing a starting sale price known as the ‘asking price.’ The seller will likely set his asking price high—this is because it is the frame of reference from which his buyers will decide what price they are willing to pay. Buyers will come in with their offers, which may be less than the asking price—especially if the house is not in high demand—but will still be reasonably close to it. Despite offers being under-asking, the seller in this scenario can still make money off the difference between his asking price and what the offers of buyers would have been if they came in with their own unanchored offers. The compounded influence of inflation or deflation that asking prices have on individual house sales can have rippling effects in a local real estate market.
On a smaller scale, anchoring rears its head in everyday purchases, as well as the livelihoods of business owners. In one study of anchoring, Kahneman and Tversky showed participants ads for fictional restaurants called Studio 17 and Studio 97. Afterwards, they asked the subjects how much they’d be willing to pay for a burger at this restaurant. Surely enough, subjects who were shown an ad with the number 97 forecasted they’d pay more for a burger than those who saw the number 17. Although the numbers are completely irrelevant to the worth of the burger, the last number they saw influenced how much they’d pay. At this point, you may be considering the ridiculousness of this scenario and imagining you’d never let a random number influence your decision to purchase. Now think back to the last time you bought something priced $99.99, or even $29.99. The effect of the “9.99” is to trick your brain into a downward anchor—while the real price is still virtually $100 or $30, the psychological price tag decreases to $90 or $20. At some point or another, you too have fallen prey to anchoring. Moreover, the businesses around you may have used it to make significant profits.
As you can see, there are both obvious and sneaky ways that anchoring presents itself in our society, and depending on whether you’re the restaurant owner or the loyal patron, you may be a hater or a lover of its effects. Anchoring can become useful to you as a negotiator, and you are encouraged to be aware of it by asking yourself if you’ve been around any anchors recently before making an important purchase or business deal. As it turns out, pricing is not a science or an art—often, it’s a sneaky psychological trick.
When Kahneman and Tversky began studying anchoring, they didn’t agree on the psychological mechanisms that informed it. They each came up with their own hypotheses but at the time, didn’t have the research methodologies to test them. Once these were later created, Kahneman and Tversky discovered they were both correct.
The anchor-and-adjust hypothesis
According to Tversky, anchoring occurred because people adjusted away from the anchor but simply failed to adjust enough. When asked, “Was Gandhi more or less than 144 when he died?” although you might correctly assume he was younger than 144—you know the correct direction—you will likely fail to adjust enough. The anchor of 144 has you assuming he was still extremely old when he died, perhaps 100 or 110. You only stop adjusting when you are no longer sure you should keep going, right near the edge of uncertainty.
When Tversky’s students Eldar Shafir, Tom Gilovich, and Robyn LeBoeuf looked for evidence of this hypothesis, they found it to be true that adjustment is an effortful operation. When their subjects were mentally depleted—either drunk or overwhelmed with information—their responses stayed closer to the anchor, meaning they therefore made less effort to adjust away from it. Evidently, adjusting was an intentional and effortful task that was not as easy to do without full mental resources. Tversky was correct.
The priming hypothesis
While Tversky predicted that anchoring was a result of effortful adjustment, Kahneman thought anchoring to be an attack on the subconscious mind, an effect of priming. The priming effect occurs when exposure to a stimulus—image, word, or otherwise—influences later reactions or decisions without a person’s knowledge, and it happens all the time. Consider again the question, “Was Gandhi more or less than 144 when he died?” According to Kahneman, this question does not evoke conscious adjustment, but rather unconscious suggestion, similar to asking a child if their stomach hurts. (Don’t try this at home.) In this case, Kahneman thought, the suggestion of a 144-year-old-Gandhi would evoke in your mind the image of a very old person, and subconsciously lead you to answer with a higher number.
This hypothesis was proven true by Thomas Mussweiler and Fritz Strack who used the power of suggestion to ask participants about the annual average temperature in Germany. After this question, they showed participants a series of words and measured the speed with which the participants recognized them. Those who were probed with “Is the average temperature higher than 68 degrees?” were quicker to acknowledge words like ‘summer’ and ‘hot’ while those probed with the number of 40 degrees were quicker to recognize words like ‘winter’ and ‘snow.’ Evidently, Kahneman was also correct that associative memory and the power of suggestion is at work when anchoring does its best business. Both hypotheses were true.
Anchoring and the criminal justice system
In one anchoring experiment, German judges read a description of a thief and then rolled a dice. The dice were predetermined to land on either a 3 or 9, and after they did, judges were asked for the prison sentence they would give the shoplifter. On average, those who had rolled a 9 decided on a sentence of 8 months, while those who had rolled a 3 determined a sentence of 5 months, with an anchoring effect of 50%. Clearly, random numbers can have influence on even experienced professionals’ opinions on important matters. In other studies on the criminal justice system, researchers have found that setting a limit on the size of personal injury damages has had unfair effects for small firms and individuals. While setting a limit of $1 million on personal injury lawsuits ensures that damages cannot exceed that price, it can also pull claims that may be of lesser value closer to the $1 million limit.
Anchoring and personal goals
As we’ve already seen, setting high numbers for business or salary negotiations can increase your financial success. What if you’re negotiating with yourself, however, by trying to set a goal? Goals can sometimes act as limits, as reaching them can feel like cause for celebration but also an opportunity to stop. Using anchoring can help you motivate you to reach upward and keep climbing. If you set your goal as running 10 miles a day, you are likely to run more than if you set your goal at 5 miles a day, even if you don’t make it to the full 10. Allowing yourself the room to “fail” might allow you to actually do more than if you’d set a reasonable goal as a ceiling. In essence, the phrase “reach for the moon—even if you fail, you’ll land among the stars” can hold true in both your business and personal life.
Related TDL resources
If you’d like to learn more about the remarkable and potentially dangerous effects of anchoring, check out this article for more detail about how anchoring can influence a lawsuit or a prison sentence.
While anchoring’s effect is caused by numbers, priming can be caused by words, images, or other stimuli. Use this article to discover the similarities and differences and how priming may also have an undue effect on your daily decisions.
- Cook, K. (2020, July 27). How do “Anchors” affect damage awards for pain and suffering? Litigation Insights. https://www.litigationinsights.com/anchors-damage-awards-pain-suffering/
- Fink, S. (2021, January 19). Daniel Kahneman. The Decision Lab. https://thedecisionlab.com/thinkers/economics/daniel-kahneman/
- Kahneman, D. (2011). Thinking, Fast and Slow. Doubleday Canada.
- Pon Staff. (2020, May 21). The anchoring effect and how it can impact your negotiation. PON – Program on Negotiation at Harvard Law School. https://www.pon.harvard.edu/daily/negotiation-skills-daily/the-drawbacks-of-goals/
- Muzafer Sherif, Daniel Taub, and Carl I. Hovland, “Assimilation and contrast effects of anchoring stimuli on judgments.” Journal of Experimental Psychology, 1958, 55, 150-155.
- Wireless Philosophy. (2015, September 16). Critical Thinking – Cognitive Biases: Anchoring [Video]. YouTube. https://www.youtube.com/watch?v=NFiDdbquWJY&ab_channel=WirelessPhilosophy