The crowd only has wisdom when it's not really a crowd.
The central limit theorem states that the variables have to be *independent* (and identically distributed in the basic form, but not necessarily).
What makes crowds of humans strong is their direct feedback and interconnectedness. However this also takes away the otherwise magical discriminatory power you get from the law of large numbers; such crowds are actually stupid, not wise.
Modern society is now governed by crowds, on social media.

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