- [[ensemble method]], [[wisdom of crowds|wisdom of crowd]], [[crowdsourced fact-checking]] # Idea The diversity prediction theorem relates wisdom of individuals to wisdom of crowds. More accurate individuals, better crowd prediction. More diverse individuals, better crowd prediction. Diversity means variation in predictions. Thus, a crowd's accuracy depends on the individuals' accuracies and the diversity of the individuals (or of the crowd). The theorem says that a crowd's error ($CE$ or many-model error) is equals to the average error ($AE$ or average model error) minus diversity ($DIV$ or diversity of model predictions): $CE = AE - DIV$ $(c-\theta)^{2}=\frac{1}{n} \sum_{i=1}^{n}\left(s_{i}-\theta\right)^{2}-\frac{1}{n} \sum_{i=1}^{n}\left(s_{i}-c\right)^{2}$ - $c$: crowd's prediction - $\theta$: true value - $s_i$: individual $i$ prediction Thus for [[wisdom of crowds|wisdom of crowd]] to be true, the crowd's error has to be small (see [[Surowiecki 2004 wisdom of crowds]]). Diversity matters a lot. In [[machine learning]], an [[ensemble method|ensemble learning algorithm]] leverages multiple models to make better predictions. It is similar to the idea of the [[wisdom of crowds|wisdom of crowd]]. # References - https://www.coursera.org/learn/model-thinking/lecture/rVbCg/diversity-prediction-theorem - [[Surowiecki 2004 wisdom of crowds]]