Tuesday, May 4, 2021

Condorcet's Jury Theorem

Condorcet's jury theorem is a political science theorem about the relative probability of a given group of individuals arriving at a correct decision. The theorem was first expressed by the Marquis de Condorcet in his 1785 work Essay on the Application of Analysis to the Probability of Majority Decisions.

The assumptions of the simplest version of the theorem are that a group wishes to reach a decision by majority vote. One of the two outcomes of the vote is correct, and each voter has an independent probability p of voting for the correct decision. The theorem asks how many voters we should include in the group. The result depends on whether p is greater than or less than 1/2:

  • If p is greater than 1/2 (each voter is more likely to vote correctly), then adding more voters increases the probability that the majority decision is correct. In the limit, the probability that the majority votes correctly approaches 1 as the number of voters increases.
  • On the other hand, if p is less than 1/2 (each voter is more likely to vote incorrectly), then adding more voters makes things worse: the optimal jury consists of a single voter.
- That's from Wikipedia

In other words, the wisdom of crowds depends on each individual sapiens' "enhanced" wisdom. If most people are knowledgeable, then the crowd's wisdom works, but if most people are leading just a "busy" self-centered life or worse biased view of the world, then the wisdom of the crowd goes down the drain. 

This has huge consequences on democracy, the free market, and yeah, civilization as we know. 

I rest my case.  It's amazing how we made it this far. 



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