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

Daniel Kahneman, psychologist and Nobel laureate in Economics, describes in Thinking, Fast and Slow (2011) one of the cognitive biases that, in his own words, is an exception within psychology: 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 shown 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 us 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 sequoia more or less than 1,200 feet? (or, for another group, more or less than 180 feet)
2. What’s your estimate of the tallest sequoia’s height?

The two groups, which only differed in the number in the first question (the “anchor”), gave very different average estimates: 844 feet from the high-anchor group, 282 feet from 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 countries are African, after spinning a (visibly rigged) wheel of fortune that always landed on 10 or 65. The anchoring index was 44%, a value on the same order as anchors that did seem informative. Similar effects have been observed using the last digits of each participant’s social security number as an anchor for completely unrelated questions, like the number of doctors practicing in their city.

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, when 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 over fifty years of average courtroom experience. They were asked to read the description of a woman caught shoplifting and, right after, roll a pair of dice that had been rigged to always land on 3 or 9. Only then were they asked to hand down a prison sentence for the case.

The judges who rolled the higher number handed down systematically longer sentences than those who rolled the low number, despite being professionals with decades of experience judging real cases, and despite the dice roll having absolutely no connection to the crime described.

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 another experiment cited in the book, asking about the average annual temperature after showing the number “68°F” activated words related to summer (sun, beach); showing “41°F” activated words related to winter (ice, skiing), biasing the later estimate in each direction.

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.