Model: wisdom = aggregated local knowledge

Local knowledge contains bias and information.

Diversity means people are biased differently.

When aggregating local knowledge, with the right aggregation tool and a diverse group, diverse biases cancel each other out. This leaves information without much bias.

This is the formula for a diverse crowd

information == aggregate([
  new LocalKnowledge(information, bias_1),
  new LocalKnowledge(information, bias_2),
  new LocalKnowledge(information, bias_3),
  ...
])
where
bias_1 != bias_2 != bias_3 != ...

A diverse crowd averages out the bias and keeps the information

This is the formula for a non-diverse crowd

information + bias^3... == aggregate([
  new LocalKnowledge(information, bias),
  new LocalKnowledge(information, bias),
  new LocalKnowledge(information, bias),
  ...
])
where
bias == bias

A not-diverse crowd with the same bias, extrapolates the bias.

(src: Book: the Wisdom of Crowds)