The First Number in the Room

In a small psychology lab at the Hebrew University of Jerusalem in the early 1970s, two men set up what looked like a carnival game. It was a wheel of fortune, the kind a child might spin at a county fair, marked with numbers from 0 to 100. Volunteers filed in one at a time, watched the wheel spin, and noted the number it landed on. Then the researchers asked a question that had nothing to do with the wheel: what percentage of countries in the United Nations are African?

The wheel was rigged. It only ever stopped on 10 or on 65. The volunteers did not know this. They believed they were watching chance unfold in front of them, the way chance is supposed to unfold, indifferent and unrelated to anything else in the room. And yet the number that came up on that wheel, a number generated by no process more meaningful than the friction of a pointer against pegs, reliably bent their answers.

Volunteers who saw the wheel land on 10 guessed, on average, that 25 percent of UN members were African. Volunteers who saw 65 guessed 45 percent. Same question. Same world. A twenty-point gap, carved into their reasoning by a number that meant nothing. ¹

The two men running the experiment were Daniel Kahneman and Amos Tversky. The paper they published in Science in 1974, titled Judgment under Uncertainty: Heuristics and Biases, would eventually rewire the foundations of psychology, economics, and the way modern institutions think about thinking. ² It would earn Kahneman the Nobel Prize in Economics in 2002, six years after Tversky’s early death made him ineligible. But the wheel of fortune experiment, almost a throwaway demonstration buried inside a longer paper, remains one of the most disturbing things either of them ever showed. It revealed that the mind does not begin its calculations from nothing. It begins from whatever happens to be nearby.

A Friendship at the Edge of a Discipline

Kahneman and Tversky met in the late 1960s as junior faculty in Jerusalem, and almost immediately began a collaboration so intense that colleagues described them as a single intellectual organism. They walked together for hours. They argued, refined, swapped sentences in shared drafts until neither could remember who had written what. Kahneman was anxious, given to dark moods, slow and excavating. Tversky was the showman, fast, brilliant, almost arrogantly precise. The combination was unusual. Their friendship would later be the subject of a book by Michael Lewis, The Undoing Project, which described it as the closest thing science has produced to a love story between two minds. ³

The field they entered, the psychology of decision-making, was dominated in the postwar decades by an assumption inherited from economics: that humans, when faced with choices involving probability, behave as approximate rational actors. They weigh evidence. They update beliefs in proportion to information. They calculate, more or less, the way a statistician would calculate. This idea, known as expected utility theory, was elegant. It was also, Kahneman and Tversky began to suspect, almost entirely wrong.

What they proposed instead was that the mind, faced with uncertainty, does not calculate. It reaches for shortcuts. They called these shortcuts heuristics, and they argued that while heuristics are usually serviceable, they fail in predictable ways. They produce biases. And one of the most persistent biases they identified was the pull of a number, any number, offered at the start of a judgment.

The Mechanics of Insufficient Adjustment

The formal name Kahneman and Tversky gave to the phenomenon was anchoring and adjustment. The mind, presented with a question it cannot answer precisely, latches on to a starting figure. It then adjusts away from that figure in the direction it suspects is correct. The adjustment, however, is almost always too small. The anchor holds.

In the original 1974 paper, the two men described a second experiment that made the mechanism unmistakable. They asked high school students to estimate, within five seconds, the product of a string of numbers. One group saw the string written as 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8. The other group saw exactly the same numbers in reverse: 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. The actual answer is 40,320. The first group, anchored by the small numbers at the start, gave a median estimate of 512. The second group, anchored by 8, gave 2,250. Both wildly wrong, but wrong in directions the anchor predicted. ²

What the experiment captured was not slowness, or innumeracy, or a lack of attention. It captured a structural feature of how the mind handles uncertainty. We begin with whatever is closest, and we move outward from there with caution that exceeds our judgment. The starting point matters more than almost anyone, before Kahneman and Tversky, had been willing to admit.

Later researchers refined the picture. Some suggested that anchoring is less about deliberate adjustment than about selective accessibility: the anchor activates memories and associations consistent with itself, and those associations crowd the mind when the answer is being assembled. A high anchor brings high-adjacent thoughts to the surface. A low one summons low-adjacent thoughts. The result is the same. The number arrives, and the mind builds its house around it.

A German Courtroom and a Pair of Loaded Dice

For years after the 1974 paper, anchoring lived mostly in the world of undergraduates and laboratory questionnaires. Skeptics could plausibly argue that the effect was a quirk of college students under fluorescent lights, not a feature of consequential adult decision-making. Surely a professional, trained for years in the careful weighing of evidence, would be immune.

In 2006, the social psychologist Birte Englich and her colleagues at the University of Cologne decided to test that assumption with subjects no one could dismiss as naive. They recruited experienced German trial judges, men and women with an average of more than fifteen years on the bench, and presented them with a detailed case file involving a shoplifting incident. The judges read the file. They considered the legal precedents. They prepared to render a sentencing judgment, as they had done countless times in their actual courtrooms.

Before announcing their decision, each judge was asked to roll a pair of dice. The dice, unbeknownst to them, were loaded. They could only land on totals of 3 or 9. After rolling, the judges were asked whether the prison sentence they would impose would be higher or lower than the number of months shown on the dice, and then they specified the exact term.

Judges who rolled a 3 recommended an average sentence of 5 months. Judges who rolled a 9 recommended an average of 8 months. A pair of dice, rolled in plain view, with no possible bearing on the case, moved sentencing recommendations by roughly 50 percent. ⁴

The finding, published in the Personality and Social Psychology Bulletin, was greeted with a mixture of fascination and unease. It suggested that one of the most consequential institutions in modern society, the criminal court, was permeable to a kind of cognitive contamination its participants would have indignantly denied. And the judges had denied it. When asked afterward whether the dice had influenced them, they overwhelmingly said no.

This pattern, of the anchor working precisely while the anchored person insists it has not, has been replicated in domains ranging from real estate appraisal to medical diagnosis to legal damage awards. In a 1987 study, professional real-estate agents toured a property and were given a printed listing sheet that included, among other details, a suggested asking price. The price had been manipulated. Agents shown a high listing produced appraisals tens of thousands of dollars above those shown a low listing. When asked which factors had shaped their estimate, almost none mentioned the listing price. They cited square footage, neighborhood, condition. The anchor was invisible to them, and that invisibility was the source of its power. ⁵

Absurdity Does Not Help

A natural defense, when one first hears of anchoring, is to assume that the effect works only when the anchor is plausible. Surely a wildly impossible number, an obvious absurdity, would simply be discarded by the mind. Surely we are not so credulous.

The researchers tested this. In a now-classic series of studies, the German psychologists Fritz Strack and Thomas Mussweiler asked volunteers whether Mahatma Gandhi had died before or after the age of 9. Then they asked the same question to another group, substituting 140. After answering this preliminary question, both groups were asked to estimate Gandhi’s actual age at death. Those exposed to 9 guessed an average of about 50. Those exposed to 140 guessed an average of 67. Gandhi was 78 when he was assassinated in 1948. ⁶

No one in the second group believed Gandhi had lived to 140. They knew the anchor was nonsense. They had explicitly rejected it in the first question. And yet the second question pulled their estimates upward by nearly two decades. The mind, it appears, processes the number first and judges its plausibility second, and by the time judgment arrives, the number has already done its work.

In a particularly stark demonstration, researchers asked participants to write down the last two digits of their own social security number, then to estimate the wholesale value of various objects: a bottle of wine, a cordless trackball, a box of chocolates. The correlation between the social security digits and the estimated price was striking. Participants with high digits placed bids 60 to 120 percent higher than those with low digits. The number was their own, but it bore no relation to the question, and they would have laughed at the suggestion that it should. It anchored them anyway. ⁷

The Marketplace That Was Built on Anchors

Long before psychologists had a name for the effect, merchants had built entire industries on it. Walk through any department store, scan any e-commerce checkout, glance at any restaurant menu, and you will see anchoring operating in plain sight. The crossed-out original price, the suggested retail value, the bottle of wine at the top of the list priced at three times what anyone is expected to pay. These are not accidents of pricing. They are scaffolding.

The central trick is the same one Kahneman and Tversky identified. The price you pay is not compared, in the moment of decision, to your monthly income or to what the object is worth to you. It is compared to the first number presented. A jacket marked down from 280 dollars to 119 dollars feels like a small fortune saved. The same jacket presented at 119 dollars, with no anchor, feels merely expensive. The original price does not need to be true. It needs only to arrive first.

Restaurants exploit this with what menu engineers call decoy pricing. The 95-dollar steak at the top of the entrée list is not put there because anyone is expected to order it. It is put there so that the 38-dollar steak, which would have seemed extravagant in isolation, now reads as the sensible middle. Diners reliably move toward the middle. The high anchor does its quiet work, and the kitchen sells more of the dish it wanted to sell in the first place. ⁸

The same logic governs almost every consequential negotiation in adult life. Studies of salary negotiations and corporate deals have repeatedly shown that the first number put on the table predicts the final outcome more reliably than almost any other variable, including the strength of either party’s underlying position. Negotiation researchers Adam Galinsky and Thomas Mussweiler have shown that simply being the first to name a figure shifts agreements by tens of percentage points in the namer’s favor. ⁹ The conventional wisdom, that one should let the other side speak first, turns out in most cases to be precisely backward.

The Limits of Knowing

The most unsettling finding in the entire anchoring literature is not that the effect exists. It is that knowing about the effect does almost nothing to dispel it.

In experiment after experiment, researchers have warned participants explicitly. They have explained the wheel of fortune study, walked subjects through the mechanism of insufficient adjustment, even shown them video footage of other people being anchored. The bias shrinks under these conditions, but only modestly, and it does not disappear. Trained statisticians have been anchored on probability estimates. Experienced negotiators have been anchored on opening bids. The judges in the Cologne study had likely heard of anchoring effects, given that the term had been circulating in legal psychology for decades. They were anchored anyway. ⁴

This resistance to insight is one of the deepest themes of Kahneman’s later work, which he summarized in his 2011 book Thinking, Fast and Slow. The mind operates, he argued, on two parallel systems. System 1 is fast, automatic, associative, the system that grabs the first number it sees and builds outward. System 2 is slow, deliberate, capable of careful reasoning, but lazy and easily fatigued. Anchoring is a System 1 operation. By the time System 2 arrives on the scene, the work has already been done. The starting point has already been chosen. The slow, careful self can only marginally adjust what the fast self has already absorbed. ¹⁰

It is tempting to read this as a story of cognitive defeat, but Kahneman resisted that framing throughout his career. The point, he insisted, was not that humans are irrational fools. The point was that human reasoning is shaped by mechanisms it cannot easily observe in itself, and that institutions, not individuals, are the appropriate site of repair. A judge cannot simply will themselves to ignore an irrelevant number. But a court system can structure sentencing guidelines so that prosecutors do not name a recommended term in the judge’s presence. A consumer cannot reliably ignore a crossed-out price. But a regulator can require that advertised reference prices reflect actual recent sales. Anchoring is a feature of how minds work. The question is what to build around it.

What Remains

Daniel Kahneman died in March 2024, at the age of 90. Amos Tversky had died nearly three decades earlier, in 1996, of metastatic melanoma. The collaboration that produced the wheel of fortune experiment, and the larger framework of heuristics and biases, ended with Tversky’s illness, and Kahneman spent much of his subsequent career attempting to honor what they had built together. The Nobel speech he delivered in Stockholm in 2002 was as much a tribute to his dead friend as it was a scientific lecture.

What the two of them showed, and what fifty years of follow-up research has confirmed, is that the human mind, faced with a numerical question it cannot precisely answer, is not a clean instrument. It is a sponge with a memory. Whatever number was last in the room when the question arrived will leave a residue. The residue is small in some cases, vast in others, but it is almost always there. The wheel does not even need to be spinning. A price on a tag, a figure overheard in a conversation, the last two digits of one’s own identification number, a roll of dice on a desk: any of them can become the starting point from which the mind moves, too cautiously, toward an answer.

There is no clean exit from this. The practical advice that emerges from the literature is modest and worth following. Decide your own number before someone else names theirs. Pause before responding to any price, any offer, any opening figure, and ask where it came from and why it is being shown to you now. Ignore reference prices when assessing whether something is worth its cost, and consult instead what the item is worth to you. Make the first offer in negotiations where you can. These are useful habits, but they are partial defenses against a feature of cognition that does not yield to mere knowledge.

The deeper lesson is harder to act on, and was perhaps the one Kahneman cared about most. The decisions we believe we have arrived at through careful weighing of evidence are often, in significant part, decisions we absorbed. The starting point shapes the room. The first number heard is the room in which all subsequent negotiation takes place. To understand this is not to escape it. It is only to begin noticing the walls.

Sources

1. Tversky, A., and Kahneman, D., ‘Judgment under Uncertainty: Heuristics and Biases,’ Science, 1974. — https://www.science.org/doi/10.1126/science.185.4157.1124
2. Kahneman, D., Nobel Prize Lecture: ‘Maps of Bounded Rationality,’ 2002. — https://www.nobelprize.org/prizes/economic-sciences/2002/kahneman/lecture/
3. Lewis, M., The Undoing Project: A Friendship That Changed Our Minds, W. W. Norton, 2016. — https://wwnorton.com/books/the-undoing-project
4. Englich, B., Mussweiler, T., and Strack, F., ‘Playing Dice with Criminal Sentences: The Influence of Irrelevant Anchors on Experts’ Judicial Decision Making,’ Personality and Social Psychology Bulletin, 2006. — https://journals.sagepub.com/doi/10.1177/0146167205282152
5. Northcraft, G. B., and Neale, M. A., ‘Experts, Amateurs, and Real Estate: An Anchoring-and-Adjustment Perspective on Property Pricing Decisions,’ Organizational Behavior and Human Decision Processes, 1987. — https://doi.org/10.1016/0749-5978(87)90046-X
6. Strack, F., and Mussweiler, T., ‘Explaining the Enigmatic Anchoring Effect: Mechanisms of Selective Accessibility,’ Journal of Personality and Social Psychology, 1997. — https://psycnet.apa.org/doi/10.1037/0022-3514.73.3.437
7. Ariely, D., Loewenstein, G., and Prelec, D., ‘“Coherent Arbitrariness”: Stable Demand Curves Without Stable Preferences,’ Quarterly Journal of Economics, 2003. — https://doi.org/10.1162/00335530360535153
8. Poundstone, W., Priceless: The Myth of Fair Value (and How to Take Advantage of It), Hill and Wang, 2010. — https://us.macmillan.com/books/9780809078813/priceless
9. Galinsky, A. D., and Mussweiler, T., ‘First Offers as Anchors: The Role of Perspective-Taking and Negotiator Focus,’ Journal of Personality and Social Psychology, 2001. — https://psycnet.apa.org/doi/10.1037/0022-3514.81.4.657
10. Kahneman, D., Thinking, Fast and Slow, Farrar, Straus and Giroux, 2011. — https://us.macmillan.com/books/9780374533557/thinkingfastandslow