Why Can a Random Number Change What You Think Something Is Worth?

A wheel of fortune that stops on 65 can lead someone to estimate that there are more African countries in the UN. It sounds like a carnival trick, but it’s one of the most robust findings in the psychology of decision-making. In Thinking, Fast and Slow (2011), Daniel Kahneman points out that most psychological phenomena can be demonstrated in an experiment, but very few can be measured with precision. The anchoring effect is one of them.

What the anchoring effect is

The anchoring effect happens when, before giving a numerical estimate about something we don’t know well, we’re exposed to some number, and that estimate ends up drifting toward that reference number, even though we know perfectly well it has no real connection to the question.

It isn’t that the number consciously convinces us: the mind simply adjusts its answer toward it without our fully realizing it.

The sequoia experiment

Kahneman describes an experiment conducted with visitors to San Francisco’s Exploratorium, who were asked two questions in a row:

1. Is the height of the tallest redwood more or less than 1,200 feet? (or, for another group, more or less than 180 feet)
2. What’s your best guess about the height of the tallest redwood?

The two groups, which differed only in the number in the first question (the “anchor”), gave very different average estimates: 844 feet for the high-anchor group, 282 feet for the low-anchor group.

The difference between the anchors was 1,020 feet; the difference between the final estimates, 562 feet.

Dividing one figure by the other gives the anchoring index: 55%, a value Kahneman describes as typical for this kind of experiment.

The anchor doesn’t need to seem credible

The most striking thing about the anchoring effect, according to the research the book cites, is that it doesn’t need to seem reasonable to work.

In one experiment, participants were asked to estimate what percentage of UN member countries are African, after watching a wheel of fortune spin which, without their knowing it, had been rigged to always stop on 10 or 65. The experiment is by Amos Tversky and Kahneman (1974).

The median estimates were 25% after a 10 and 45% after a 65.

Dan Ariely, George Loewenstein and Drazen Prelec (2003) took the idea into the realm of prices. They asked participants to write down the last two digits of their social security number and then say whether they would pay that amount in dollars for products such as wine or computer accessories. Their later valuations drifted toward those arbitrary figures, although the differences between products stayed consistent: the anchor set the absolute price, but the ranking of the products held. The authors called this coherent arbitrariness.

When the anchor affects decisions with real money

The anchoring effect doesn’t stay in the lab.

Kahneman describes an experiment with professional real estate agents, who were asked to appraise a real house after visiting it and reviewing a brochure that included an already-set asking price (high for half the agents, low for the other half). The result:

• The professional agents’ anchoring index was 41%.
• That of a group of business students with no real estate experience was 48%, practically the same range.
• The only real difference between the two groups: the students admitted the asking price had influenced their appraisal, while the agents denied any influence, convinced their experience made them immune.

The effect was also observed in donation decisions: visitors to the same museum, asked how much they’d pay to help save seabirds affected by oil spills, gave an average of $20 when the prior anchor was only $5, and $143 when the anchor was $400, compared with an average of $64 when no anchor was mentioned at all.

The most unsettling case: real judges and a pair of dice

The finding Kahneman describes as most disturbing involves German judges with more than fifteen years of courtroom experience on average.

They were asked to read the description of a woman caught shoplifting and, right after, to roll a pair of dice that had been loaded to always land on 3 or 9.

Only then were they asked to hand down a prison sentence for the case.

As Kahneman reports, those who rolled a 9 proposed about 8 months in prison on average, and those who rolled a 3, about 5. These were systematically longer sentences after the high number, even though the judges were professionals with years of experience deciding real cases and the dice had no connection whatsoever to the crime described. In the original paper, Birte Englich, Thomas Mussweiler and Fritz Strack (2006) also found that experience did not reduce the effect.

Why the anchor works even when you know it’s arbitrary

Kahneman explains this mechanism through associative memory: a high or low number selectively activates different memories and ideas related to that magnitude, and those ideas then bias the final estimate, without the person being aware of the process.

In an experiment by the German psychologists Thomas Mussweiler and Fritz Strack cited in the book, asking about the average annual temperature after showing the number “20 °C” (68 °F) activated words related to summer (sun, beach); showing “5 °C” (41 °F) activated words related to winter (ice, skiing), biasing the later estimate in each direction.

An effect that does hold up in replications

Unlike other famous experiments in the book, such as the one on old-age priming, anchoring has passed the replication test well. In the Many Labs project (Klein et al., 2014), 36 independent samples with 6,344 participants repeated thirteen classic effects in psychology; ten replicated consistently, and the anchoring questions were among them.

There are some nuances: not all variants work equally well, and at least one replication of Ariely and colleagues’ pricing experiments (Maniadis, Tufano and List, 2014) found a smaller, inconclusive effect. But the underlying phenomenon, that a prior number pulls the later estimate toward it, is one of the most solid in its field.

Where it shows up outside the lab

This mechanism has direct implications in any area where you have to estimate a value under uncertainty, from negotiating a price to assessing an investment’s risk, territory that connects to the conservative profile and the moderate profile when facing numerical uncertainty, and to any buying or selling decision where the first number mentioned in a conversation, however arbitrary, is rarely neutral.

Our investor profile quiz helps you identify how you tend to position yourself in decisions like these.

Sources

• Kahneman, D. (2011). Thinking, Fast and Slow. Farrar, Straus and Giroux.
• Tversky, A. and Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185(4157), 1124-1131.
• Northcraft, G. B. and Neale, M. A. (1987). Experts, amateurs, and real estate: An anchoring-and-adjustment perspective on property pricing decisions. Organizational Behavior and Human Decision Processes, 39(1), 84-97.
• Englich, B., Mussweiler, T. and Strack, F. (2006). Playing dice with criminal sentences: The influence of irrelevant anchors on experts’ judicial decision making. Personality and Social Psychology Bulletin, 32(2), 188-200. https://doi.org/10.1177/0146167205282152
• Ariely, D., Loewenstein, G. and Prelec, D. (2003). “Coherent arbitrariness”: Stable demand curves without stable preferences. The Quarterly Journal of Economics, 118(1), 73-106. https://doi.org/10.1162/00335530360535153
• Maniadis, Z., Tufano, F. and List, J. A. (2014). One swallow doesn’t make a summer: New evidence on anchoring effects. American Economic Review, 104(1), 277-290. https://doi.org/10.1257/aer.104.1.277
• Klein, R. A. et al. (2014). Investigating variation in replicability: A “many labs” replication project. Social Psychology, 45(3), 142-152. https://doi.org/10.1027/1864-9335/a000178