Anchoring and Numerical Estimation

Opening Hook

In 1974, Amos Tversky and Daniel Kahneman ran an experiment that should, by rights, have produced no result at all.

They brought participants into a room and had them watch a wheel of fortune spin. The wheel was marked with numbers from 0 to 100, but it was rigged: it stopped on either 10 or 65, nothing else. The participants watched this happen. They were told the number was random. They knew, consciously, that whatever came up had nothing to do with anything.

Then Tversky and Kahneman asked them a simple factual question: what percentage of countries in the United Nations are African?

First, participants had to answer a comparison question: is the true percentage higher or lower than the number on the wheel? Then they gave their actual estimate.

The wheel stopped on 10. The average estimate: 25 percent.

The wheel stopped on 65. The average estimate: 45 percent.

That is a twenty-percentage-point gap, produced by a number every participant knew was meaningless. They had watched the rigging happen. They understood the number on the wheel had been generated by a mechanism with no connection to the United Nations, to Africa, or to anything they were being asked about. It did not matter. The arbitrary number still pulled their estimates toward it.

This is anchoring. And once you know what it looks like, you will find it almost everywhere numbers are used.

---

The Concept

Anchoring is the tendency for an initial number, the anchor, to bias all subsequent estimates and judgements, even when that number is irrelevant, random, or obviously wrong.

The mechanism Tversky and Kahneman identified is called adjustment from anchor. When a person is given or generates an initial value and then asked to refine their estimate, they start from that value and adjust. The problem is that the adjustment is almost always insufficient. People stop adjusting too early, before they have moved far enough from the starting point. The anchor exerts a kind of gravitational pull on the final estimate.

This creates two distinct effects. First, when an anchor is provided from outside, people’s estimates cluster around it, even if it has been presented as arbitrary. Second, when people generate an anchor for themselves, by calculating from one direction rather than another, or by beginning with a specific number and working outward, their final answers remain contaminated by their starting point in a way that independent approaches from scratch would not produce.

Tversky and Kahneman illustrated the self-generated version with a multiplication problem. They asked one group to estimate the product of 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1. They asked another group to estimate the product of 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8. Both sequences contain the same numbers. The product is identical regardless of order: 40,320. But the first group, starting from the larger end, gave a median estimate of 2,250. The second group, starting from 1 and working up, gave a median estimate of 512. Both groups were wildly wrong, but they were wrong in the direction of their starting point. The anchor at the beginning of the sequence dragged the estimate toward itself.

The deliberate use of this effect is now well established in commercial and professional settings. A retailer who marks a coat as “was £200, now £99” is not simply providing information about the coat’s history. The £200 figure serves as an anchor that makes £99 feel like a bargain, regardless of whether £200 was ever a realistic market price for that coat. The reference price creates a frame within which the sale price is evaluated, and the frame does most of the persuasive work. Remove the “was” price, and the coat sits in a different context entirely. The numbers have not changed. The psychology has.

The courtroom is where the consequences become most serious. In 2006, psychologists Birte Englich, Thomas Mussweiler, and Fritz Strack published a study in which German judges with an average of more than fifteen years of experience read a case description involving a woman caught shoplifting. Before sentencing, each judge rolled a pair of dice. The dice were loaded to land on either three or nine. Judges were then asked whether they would sentence the woman to more or fewer months in prison than the number showing on the dice, and then to give their actual sentence.

Judges who rolled a nine sentenced the woman to an average of eight months. Judges who rolled a three sentenced her to an average of five months. The only difference between the two groups was the number on a die they had rolled themselves. The judges were experienced. They knew the dice were unrelated to the case. None of this reduced the anchoring effect by a meaningful amount.

This is the central unsettling fact about anchoring: it operates even when the anchor is known to be arbitrary. Awareness of the bias is not sufficient to eliminate it. Subjects in Tversky and Kahneman’s original experiments were sometimes told directly that the wheel was random, and the effect persisted. The knowledge that you should not be anchored does not, by itself, prevent anchoring from occurring.

---

Why It Matters

Anchoring is a Tier 2 concept in this curriculum rather than Tier 1, but it sits near the boundary. The domains where it operates consequentially are numerous.

In negotiation, the first number stated tends to set the range within which the conversation takes place. This is well established in research on salary negotiations, property transactions, and commercial deals. The person who names a figure first gains an advantage that is difficult for the other party to fully overcome, because every counter-offer is psychologically evaluated relative to the opening anchor rather than relative to an independent assessment of fair value. A buyer who hears an asking price of £500,000 for a property is evaluating all subsequent discussion in a frame anchored at £500,000, even if they know asking prices routinely exceed market value. Getting back to a genuinely independent estimate of value requires deliberate effort that most people do not make.

In retail pricing, anchored “original” prices shape consumer judgement about value at a scale affecting billions of purchase decisions every year. The mechanism is the same whether the anchor is a genuine previous price, a manufacturer’s suggested retail price that was never charged in practice, or a comparison price inserted to generate the appearance of a discount. The consumer’s job is to evaluate absolute value; anchoring consistently prevents them from doing it.

In judicial sentencing, the Englich, Mussweiler and Strack findings have been replicated and extended. Subsequent work found that anchoring effects on sentencing were produced not only by dice rolls but by the presence of prosecutors’ sentencing recommendations, by arbitrary numbers introduced as part of case materials, and by a range of other irrelevant numerical cues. The implication is that the punishment handed down in a criminal case can be influenced by factors that have no relationship to the severity of the offence or the personal circumstances of the defendant. Two defendants convicted of the same crime, by judges who happened to encounter different numerical cues before sentencing, may receive materially different sentences for that reason alone.

---

How to Spot It

The tell for anchoring is a number that arrives early in a decision context and has no clear, independent justification.

One documented case from medical practice illustrates how anchoring operates outside the obvious commercial setting. Research on clinical decision-making has found that the first diagnosis a doctor considers for a presenting patient, often formed within seconds of reading the case summary, functions as an anchor that biases subsequent assessment of symptoms and test results. Findings consistent with the initial diagnosis are weighted more heavily than findings that suggest an alternative. This is anchoring operating as confirmation in a setting where it can directly affect patient outcomes. The anchor is not an externally imposed number but a hypothesis, and the mechanism is the same: adjustment from the initial position is insufficient.

In commercial settings, the anchor usually announces itself, because it needs to. A number that you are meant to compare against must be visible. Look for any situation in which you are given a “before” figure, a “list price,” a “recommended retail price,” a “market value,” or a “usual rate” before being shown the actual figure you are being asked to assess. The before figure is almost always functioning as an anchor, regardless of how accurately it describes reality. The question to ask is not “is this a good deal relative to the anchor?” but “what is this worth independently?” Those are different questions, and the answer to the second one will often be less flattering to the seller.

In negotiations, the equivalent question is: “Am I evaluating this counter-offer on its own merits, or am I evaluating it relative to the opening figure I heard?” If you find yourself thinking in terms of movement from the opening rather than in terms of the independent value of what is being offered, the anchor has done its work.

---

Your Challenge

You are about to begin salary negotiations for a new job. Before you have said anything, the employer opens with a number: £40,000 per year.

You had prepared your own research before the meeting. Based on comparable roles, advertised salaries for similar positions, and your assessment of what you bring to the role, you had settled on a range of £48,000 to £55,000 as a reasonable expectation.

The employer’s opening figure is £40,000. The conversation begins.

What do you know about the likely range of outcomes from this point, based purely on what anchoring research predicts? What would you need to do, and how would you need to structure your response, to prevent the anchor from distorting your negotiation? What is the risk in simply naming your target number in response, compared with the risk of engaging with the employer’s figure directly?

There is no answer key here.

---

References

1. Tversky A, Kahneman D. Judgment under uncertainty: Heuristics and biases. Science. 1974;185(4157):1124–1131. The foundational paper introducing the anchoring and adjustment heuristic, including the spinning wheel experiment and the multiplication sequences. Available at: https://www.science.org/doi/10.1126/science.185.4157.1124

2. Kahneman D. Thinking, Fast and Slow. New York: Farrar, Straus and Giroux; 2011. Chapter 11 (“Anchors”) contains the most accessible account of the wheel experiment, the multiplication sequences, and the retail and legal applications of anchoring. Kahneman also discusses why awareness of anchoring does not reliably reduce its effect.

3. Englich B, Mussweiler T, Strack F. Playing dice with criminal sentences: the influence of irrelevant anchors on experts’ judicial decision making. Personality and Social Psychology Bulletin. 2006;32(2):188–200. The study in which experienced German judges rolled loaded dice before sentencing and gave markedly different sentences depending on the number rolled. Available at: https://journals.sagepub.com/doi/10.1177/0146167205282152

4. Englich B, Mussweiler T. Sentencing under uncertainty: anchoring effects in the courtroom. Journal of Applied Social Psychology. 2001;31(7):1535–1551. An earlier study establishing that prosecutors’ sentencing recommendations anchor judicial decisions, even when judges are explicitly aware of this and advised to resist it. Available at: https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1559-1816.2001.tb02687.x

5. Strack F, Mussweiler T. Explaining the enigmatic anchoring effect: mechanisms of selective accessibility. Journal of Personality and Social Psychology. 1997;73(3):437–446. The theoretical paper proposing selective accessibility as the mechanism by which anchors bias estimates: the anchor activates information consistent with it, making anchor-consistent evidence more available for subsequent judgement.

6. Ariely D, Loewenstein G, Prelec D. Coherent arbitrariness: stable demand curves without stable preferences. Quarterly Journal of Economics. 2003;118(1):73–106. A study in which participants were asked whether they would buy products for an amount equal to the last two digits of their social security number, then bid for them in an auction. Higher social security digits produced systematically higher bids, demonstrating anchoring in a real-money consumer setting.

7. Chapman GB, Johnson EJ. Anchoring, activation, and the construction of values. Organizational Behavior and Human Decision Processes. 1999;79(2):115–153. A review of the mechanisms underlying anchoring across multiple domains, including the clinical setting. Contains a discussion of diagnostic anchoring in medical decision-making.