Condorcet's Paradox and The Condorcet Method
In 1785, Condorcet wrote Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix (Essay on the Application of Analysis to the Probability of Majority Decisions), one of his most important works. This work described several now famous results, including Condorcet's jury theorem, which states that if each member of a voting group is more likely than not to make a correct decision, the probability that the highest vote of the group is the correct decision increases as the number of members of the group increases, and Condorcet's paradox, which shows that majority preferences become intransitive with three or more options – it is possible for a certain electorate to express a preference for A over B, a preference for B over C, and a preference for C over A, all from the same set of ballots.
The paper also outlines a generic Condorcet method, designed to simulate pair-wise elections between all candidates in an election. He disagreed strongly with the alternative method of aggregating preferences put forth by Jean-Charles de Borda (based on summed rankings of alternatives). Condorcet was one of the first to systematically apply mathematics in the social sciences.
Read more about this topic: Marquis De Condorcet
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