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The paper, “A solution to the single-question crowd wisdom problem,” is being published today in Nature. The authors are Prelec; John McCoy, a doctoral student in the MIT Department of Brain and Cognitive Sciences; and H. Sebastian Seung, a professor of neuroscience and computer science at Princeton University and a former MIT faculty member. Prelec and McCoy are also researchers in the MIT Neuroeconomics Laboratory, where Prelec is the principal investigator.  

A capital idea

To see how the algorithm works in practice, consider a case the researchers tested. A group of people were asked a yes-or-no question: Is Philadelphia the capital of Pennsylvania? They were also asked to predict the prevalence of “yes” votes. 

Philadelphia is not the capital of Pennsylvania; the correct answer is Harrisburg. But most people believe Philadelphia is the capital because it is a “large, historically significant city.” Moreover, the people who mistakenly thought Philadelphia is the state capital largely thought other people would answer the same way. So they predicted that a very high percentage of people would answer “yes.”

Meanwhile, a certain number of respondents knew that Harrisburg is the correct answer. However, a large portion of those people also anticipated that many other people would incorrectly think the capital is Philadelphia. So the people who themselves answered “no” still expected a very high percentage of “yes” answers.

That means the answer to the two questions — Is Philadelphia the capital? Will other people think so? — diverged. Almost everyone expected other people to answer “yes.” But the actualpercentage of people who answered “yes” was significantly lower. For this reason, the “no” answer was the “surprisingly popular” one, since it deviated from expectations of what the answer would be.

And since the “surprisingly popular” answer differed in the “no” direction, that tells us the correct answer: No, Philadelphia is not the capital.

The same principle applies no matter which direction responses deviate from expectations. When people were asked if Columbia is the capital of South Carolina, the opposite happened: More people answered “yes,” compared to their expectations of how many people would say “yes.” So the surprisingly popular answer was, correctly: Yes, Columbia is the capital.

Source: MIT NEWS