Although these matters are tricky and frequently counter-intuitive, people are rarely short of confidence in confronting them. This leads us to another general lesson that cognitive psychology teaches: People are too often certain of their decisions because they fail to look for conflicting evidence, distort the facts and their memories of them, ignore alternative views, and let their own explanatory schemes seduce them.
Regarding the latter, consider an experiment in which subjects were told of two firemen — one successful, one not.
Half the subjects were told that the successful fireman was a risk-taker and that the unsuccessful one was not. The other half of the subjects were told that the successful one was not a risk-taker and that the unsuccessful one was. Afterward, they were informed that the firemen did not exist and that the experimenters had simply invented them.
Amazingly, they continued to be strongly influenced by whatever explanatory stories they had concocted for themselves. If they had been told that the risk-taking fireman was successful, they thought that prospective firemen should be chosen for their willingness to take risks; if not, then not. If asked to account for the connection between risk-taking or its absence and successful firefighting, the members of each group gave a cogent explanation consistent with the imaginary story originally told them. I leave it to the reader to judge the (ir)relevance of this to people's responses to the war in Iraq.
A famous study by psychologist Peter Wason neatly illustrates how we tend to look only for confirmation of our ideas, seldom for disconfirmation. Wason presented subjects with four cards having the symbols A, D, 3, and 7 on one side and told them that each card had a number on one side and a letter on the other. He then asked which of the four cards needed to be turned over in order to establish the rule: Any card with an A on one side has a 3 on the other. Which cards would you turn over? (The answer is below.)
These are just a few ways in which we systematically fall victim to psychological illusion.
Answer: Most subjects picked the A and 3 cards. The correct answer is the A and 7 cards.
Professor of mathematics at Temple University and adjunct professor of journalism at Columbia University, John Allen Paulos is the author of several best-selling books, including Innumeracy, and the just released A Mathematician Plays the Stock Market. His Who’s Counting? column on ABCNEWS.com appears the first weekend of every month.