The Mathematical Tourist
By Ivars Peterson
November 8, 2009
When you're making an estimate, extraneous factors or irrelevant information can strongly bias your judgment, especially when the situation involves a lot of uncertainty.
Physicist and writer Leonard Mlodinow provided a vivid illustration of such bias during his recent colloquium talk on randomness, which he presented at the National Institute of Standards and Technology in Gaithersburg, Md. Mlodinow is currently a professor at Caltech. He is the author of The Drunkard’s Walk: How Randomness Rules Our Lives.
Your powers of estimation are easily influenced by minor things, random things that happen around you, Mlodinow argued.
To demonstrate, Mlodinow divided his audience into two groups. Each member of each group independently wrote down on a slip of paper a numerical answer to the question: How many countries are there in Africa? The slips were collected and the results tallied.
Answers from the first group averaged about 47; answers from the second group, about 27. Why the difference?
Each group also answered an introductory yes-or-no question that the other group did not see. The first group was initially asked: Are there more than 180 countries in Africa? The second group was initially asked: Are there more than 5 countries in Africa?
Most members of the audience of scientists and engineers probably had no clear idea what the correct answer is. They had to make a guess and apparently were influenced by the number that they saw in the first question. The results would undoubtedly have been different with, say, an audience of Africa scholars, who would likely be much more familiar with the continent.
Africa actually has about 50 countries, depending on how you count disputed territories and whether you include offshore island nations.
At the NIST talk, I was in the first group, and I knew that Africa had a lot of countries. I also recalled that the United Nations had nearly 200 members, so I based my estimate on what fraction of the total would be in Africa. I came up with 70, which was too high and was probably influenced by my seeing 180 in the first question.
Mlodinow has tried the same experiment with a variety of audiences, always obtaining a striking difference between the two groups. When he presented the talk last year to an audience at Google, for example, the estimates averaged about 65 and 30. (At Microsoft, the estimates had been 50 and 24.)
Mlodinow called this effect "anchoring bias." When making estimates, "be careful before you trust them," he warned.
One practical lesson, however, is that in negotiations it pays to ask high, whether you're fishing for a higher allowance or suing someone for damages. In the face of uncertainty, this posited sum may very well influence the size of the final outcome.
We take in, filter, and interpret a lot of data every day, Mlodinow noted. When the situation involves uncertainty or randomness, we often make mistakes or draw improper conclusions.
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