When given four options, the consumers chose the most cost-effective plan only 42 percent of the time. When given eight options, the success rate plummeted to 21 percent—a rate indistinguishable from random assignments.

The researchers then repeated the study, but this time with added “cost calculators” on the mock website aimed at helping consumers. Even then, shoppers picked the most cost-effective option only 47 percent of the time, typically choosing plans that would cost them an extra $364.

In a final iteration, researchers offered the shopping choices to M.B.A. students enrolled in a consumer finance class. In this pool—where more than half of the subjects came from consulting or financial-services related fields—consumers made the most cost-effective choice 73 percent of the time, and the average mistake dropped to $126.