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Way back in 1906, the English polymath Francis Galton visited a country fair in which 800 people took part in a contest to guess the weight of a slaughtered ox. After the fair, he collected the guesses and calculated their average which turned out to be 1,208 pounds. To Galton’s surprise, this was within 1 percent of the true weight of 1,198 pounds.

This is one of the earliest examples of a phenomenon that has come to be known as the wisdom of the crowd. The idea is that the collective opinion of a group of individuals can be better than a single expert opinion.

This phenomenon is commonplace today on websites such as Reddit in which users vote on the importance of particular stories and the most popular are given greater prominence.

However, anyone familiar with Reddit will know that the collective opinion isn’t always wise. In recent years, researchers have spent a significant amount of time and effort teasing apart the factors that make crowds stupid. One important factor turns out to be the way members of a crowd influence each other.

It turns out that if a crowd offers a wide range of independent estimates, then it is more likely to be wise. But if members of the crowd are influenced in the same way, for example by each other or by some external factor, then they tend to converge on a biased estimate. In this case, the crowd is likely to be stupid.

Today, Gabriel Madirolas and Gonzalo De Polavieja at the Cajal Institute in Madrid, Spain, say they found a way to analyze the answers from a crowd which allows them to remove this kind of bias and so settle on a wiser answer.

The theory behind their work is straightforward. Their idea is that some people are more strongly influenced by additional information than others who are confident in their own opinion. So identifying these more strongly influenced people and separating them from the independent thinkers creates two different groups. The group of independent thinkers is then more likely to give a wise estimate. Or put another way, ignore the wisdom of the crowd in favor of the wisdom of the confident.

So how to identify confident thinkers? Madirolas and De Polavieja began by studying the data from an earlier set of experiments in which groups of people were given tasks such as to estimate the length of the border between Switzerland and Italy, the correct answer being 734 kilometers.

After one task, some groups were shown the combined estimates of other groups before beginning their second task. These experiments clearly showed how this information biased the answers from these groups in their second tasks.

Madirolas and De Polavieja then set about creating a mathematical model of how individuals incorporate this extra information. They assume that each person comes to a final estimate based on two pieces of information: first, their own independent estimate of the length of the border and second, the earlier combined estimate revealed to the group. Each individual decides on a final estimate depending on the weighting they give to each piece of information.

Those people who are heavily biased give a strong weighting to the additional information whereas people who are confident in their own estimate give a small or zero weighting to the additional information.

Madirolas and De Polavieja then take each person’s behavior and fit it to this model to reveal how independent their thinking has been.

That allows them to divide the groups into independent thinkers and biased thinkers. Taking the collective opinion of the independent thinkers then gives a much more accurate estimate of the length of the border.

“Our results show that, while a simple operation like the mean, median, or geometric mean of a group may not allow groups to make good estimations, a more complex operation taking into account individuality in the social dynamics can lead to a better collective intelligence,” they say.

That is an interesting idea that highlights the way bias can destroy the wisdom of a crowd. What Madirolas and De Polavieja need to do now, of course, is to exploit the wisdom of the confident in some real-world situation.

Might it be possible to create a new generation of social news sites like Reddit which rely on the wisdom of the confident? That’s both possible and a little frightening. Either way, Dalton would be fascinated.

Ref: arxiv.org/abs/1406.7578 : Wisdom of the Confident: Using Social Interactions to Eliminate the Bias in Wisdom of the Crowds

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