The Wisdom of Crowds: Can Collective Credences be Wise?

How many words are in this abstract? If you had to guess, without counting, you would probably get pretty close to the true number. However, if you and your friends all made guesses, the average of your guesses would likely be better than your typical guess. This is an example of the so-called Wisdom of Crowds effect.

The effect is surprisingly reliable â€” for example, the "Ask the Audience" lifeline on Who Wants to Be a Millionaire? has a 95% success rate. This seems to cry out for an explanation, especially given how irrational collectives can be â€” think: committee decisions, tulip prices, and rioting football fans. Scott Page (2008) has made some initial progress on this question with what he calls the Diversity Prediction Theorem. Roughly speaking, the theorem shows that if a collective is diverse, then its collective judgements are guaranteed to be better than the typical individual judgements. So it would seem that we have an explanation for the Wisdom of Crowds effect and its reliability: it's a mathematical necessity.

Not quite. For the theorem to have any explanatory power, it needs to be supplemented with bridge principles that connect the theorem to the explanandum. I will tease out these principles and show that they have some serious defects. An interesting consequence of these defects is that it appears to be impossible for there to be a Wisdom of Crowds effect for collective credences â€” i.e., averaged degrees of belief. However, after developing a Bayesian interpretation of Socrates' thoughts on wisdom (from the Apology), I will argue that collective credences are the only collective judgements that can be genuinely wise.

(In case you're still guessing: there are 286 words in this abstract, including these ones.)

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