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kevin
@k3vin-wang
The Condorcet Jury Theorem is named after the 18th-century French philosopher and mathematician, Marquis de Condorcet. It is related to the broader ideas of collective intelligence and social information aggregation. This theorem has been influential in discussions about the epistemic reasons for democracy and the design of decision-making bodies. When a group of individuals independently makes a decision between two options, and each person is more likely to be right than wrong, majority voting is generally correct. As the size of the group increases, the likelihood of the majority being correct also increases. It applies in the following conditions: • There is an odd number of voters • Each person has a greater than 50% chance of being correct • People make decisions independently • There are only two possible answers (right/wrong) As the number of people in the group increases, the accuracy of the majority vote approaches 100%.
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kevin
@k3vin-wang
This theorem has implications for decision-making in various fields: • Ensemble learning in machine learning: Combining multiple models can improve accuracy. • Democratic theory: Provides a mathematical argument for the wisdom of crowds. Limitations: • The theorem assumes independence, but in the real world, this may not hold due to shared information or mutual influence. • It assumes that each individual is more likely to be correct than wrong, which may not always be true. • In practice, increasing the group size might introduce coordination problems or dilute individual responsibility. Assuming each individual has a probability p > 0.5 of being correct: • The probability that the majority is correct is higher than p • As the number of voters n approaches infinity, the probability of a correct majority decision approaches 1 • As n increases, the chances of a majority error decrease • As n increases, the binomial distribution of correct votes becomes more concentrated above 50%
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