Bertrand Corollary...

Source: Technology Review

TECHNOLOGY REVIEW: 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 analyse 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 favour of the wisdom of the confident.

However...

"The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts." Bertrand Russell

Physics arXiv:
Wisdom of the Confident: Using Social Interactions to Eliminate the Bias in the Wisdom of the Crowds