HOW is it that people can believe something that they know is not true?

For example, Kansas City Royals fans, sitting in front of their television sets in Kansas City, surely know that there is no possible connection between their lucky hats (or socks, or jerseys) and the outcome of a World Series game at Citi Field in New York, 1,200 miles away. Yet it would be impossible to persuade many of them to watch the game without those lucky charms.

It’s not that people don’t understand that it’s scientifically impossible for their lucky hats to help their team hit a home run or turn a double play — all but the most superstitious would acknowledge that. It’s that they have a powerful intuition and, despite its utter implausibility, they just can’t shake it.

Consider a 1986 study conducted by the psychologist Paul Rozin and his colleagues at the University of Pennsylvania. The participants were asked to put labels on two identical bowls of sugar. The labels read “sucrose” and “sodium cyanide (poison).” Even though the participants were free to choose which label to affix to which bowl, they were nevertheless reluctant, after labeling the bowls, to use sugar from the one that they had just labeled poison. Their intuition was so powerful that it guided their behavior even when they recognized that it was irrational.

Psychologists who study decision making and its shortcomings often rely on the idea, popularized by the psychologist Daniel Kahneman in his book “Thinking, Fast and Slow,” that there are two modes of processing information. There is a “fast system” that is intuitive and quickly generates impressions and judgments, and a “slow system” that operates in a deliberate and effortful manner, and is responsible for overriding the output of the fast system when the slow system detects an error.