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Condorcet Jury Theorem | Condorcet | Parisi I 494 Condorcet Jury Theorem/Condorcet/Nitzan/Paroush: Condorcet (1785)(1) makes the following three-part statement: 1) The probability that a team of decision-makers would collectively make the correct decision is higher than the probability that any single member of the team makes such a decision. 2) This advantage of the team over the individual performance monotonically increases with the size of the team. Parisi I 495 3) There is a complete certainty that the team’s decision is right if the size of the team tends to infinity, that is, the probability of this event tends to one with the team’s size. A “Condorcet Jury Theorem” (henceforth, CJT) is a formulation of sufficient conditions that validate the above statements. There are many CJTs, but Laplace (1815)(2) was the first to propose such a theorem. >Condorcet Jury Theorem/Laplace. Parisi I 496 VsCondorcet: In contrast to the first two parts of Condorcet’s statement, the survival of the third part is somehow surprising. Many attempts have been made to prove the validity of the third part in case of heterogeneous teams (see Boland, 1989(3); Fey, 2003(4); Kanazawa, 1998(5); and Owen, Grofman, and Feld, 1989(6)). 1. De Condorcet, N. C. (1785). Essai sur l’application de l’analyse a la probabilite des decisions rendues a la pluralite des voix. Paris: De l’imprimerie royale. 2. Laplace, P. S. de (1815). Theorie analytique des probabilities. Paris: n.p. 3. Boland, P. J. (1989). “Majority systems and the Condorcet jury theorem.” The Statistician 38(3): 181–189. 4. Fey, M. (2003). “A note on the Condorcet jury theorem with supermajority rules.” Social Choice and Welfare 20(1): 27-32. 5. Kanazawa, S. (1998). “A brief note on a further refinement of Condorcet Jury Theorem for heterogenous groups.” Mathematical Social Sciences 35(1): 69-73. 6. Owen, G., B. Grofman, and S. Feld (1989). “Proving a distribution free generalization of the Condorcet jury theorem.” Mathematical Social Sciences 17(1): 1-16. Shmuel Nitzan and Jacob Paroush. “Collective Decision-making and the Jury Theorems”. In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University. |
Condo I N. de Condorcet Tableau historique des progrès de l’ esprit humain Paris 2004 Parisi I Francesco Parisi (Ed) The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017 |
Condorcet Jury Theorem | Economic Theories | Parisi I 494 Condorcet Jury Theorem/Economic theories/Nitzan/Paroush: Condorcet (1785)(1) makes the following three-part statement: 1) The probability that a team of decision-makers would collectively make the correct decision is higher than the probability that any single member of the team makes such a decision. 2) This advantage of the team over the individual performance monotonically increases with the size of the team. Parisi I 495 3) There is a complete certainty that the team’s decision is right if the size of the team tends to infinity, that is, the probability of this event tends to one with the team’s size. A “Condorcet Jury Theorem” (henceforth, CJT) is a formulation of sufficient conditions that validate the above statements. There are many CJTs, but Laplace (1815)(2) was the first to propose such a theorem. >Condorcet Jury Theorem/Laplace. Parisi I 496 VsCondorcet: In contrast to the first two parts of Condorcet’s statement, the survival of the third part is somehow surprising. Many attempts have been made to prove the validity of the third part in case of heterogeneous teams (see Boland, 1989(3); Fey, 2003(4); Kanazawa, 1998(5); and Owen, Grofman, and Feld, 1989(6)). In fact, the following is a well-known version of CJT: “If a team of decision-makers utilizes a simple majority rule, the decision would be perfectly correct in the limit given that the size of Parisi I 497 the team tends to infinity, even if the individual competencies, the pis, are different, provided that pi ≥ 1∕2+ε, where the value of ε is a positive constant regardless of how small it is.” The proof of the theorem relies on the proof of Laplace where P = 1∕2+ε combined with the fact that Π is an increasing function of the team members’ competencies. >Decision theory, >Decision-making processes. 1. De Condorcet, N. C. (1785). Essai sur l’application de l’analyse a la probabilite des decisions rendues a la pluralite des voix. Paris: De l’imprimerie royale. 2. Laplace, P. S. de (1815). Theorie analytique des probabilities. Paris: n.p. 3. Boland, P. J. (1989). “Majority systems and the Condorcet jury theorem.” The Statistician 38(3): 181–189. 4. Fey, M. (2003). “A note on the Condorcet jury theorem with supermajority rules.” Social Choice and Welfare 20(1): 27-32. 5. Kanazawa, S. (1998). “A brief note on a further refinement of Condorcet Jury Theorem for heterogenous groups.” Mathematical Social Sciences 35(1): 69-73. 6. Owen, G., B. Grofman, and S. Feld (1989). “Proving a distribution free generalization of the Condorcet jury theorem.” Mathematical Social Sciences 17(1): 1-16. Shmuel Nitzan and Jacob Paroush. “Collective Decision-making and the Jury Theorems”. In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University. |
Parisi I Francesco Parisi (Ed) The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017 |
Death | Condorcet | Habermas III 214 Death/Condorcet/Habermas: Condorcet (1795)(1) expects the hygienic and medical overcoming of misery and illness; he believes that "a time must come when death will only be the result of extraordinary circumstances". (1) Habermas: in other words: Condorcet believes in eternal life before death. This concept is representative of the historical philosophical thinking of the 18th century. However, it is precisely the radicalism that makes the fractures of historical philosophical thought come to the fore. HabermasVsCondorcet: For its linear concept of progress, Condorcet must presuppose that 1st the history of physics and the sciences oriented on its model can be reconstructed as a continuous path of development; Habermas III 215 2nd that all problems to which religious and philosophical teachings have so far provided answers can either be translated into problems that can be scientifically worked on or seen through as apparent problems. 3rd Condorcet presupposes the idea of a universal reason, which he himself cannot overlook as a child of the 18th century. VsCondorcet: This idea is first questioned by the Historical School and later by cultural anthropology. >Progress, >Technology, >Enlightenment, >Cultural anthropology. 1. Condorcet, Entwurf einer historischen Darstellung der Fortschritte des menschlichen Geistes, (Ed.) W. Alff, Frankfurt, 1963, p. 383. |
Condo I N. de Condorcet Tableau historique des progrès de l’ esprit humain Paris 2004 Ha I J. Habermas Der philosophische Diskurs der Moderne Frankfurt 1988 Ha III Jürgen Habermas Theorie des kommunikativen Handelns Bd. I Frankfurt/M. 1981 Ha IV Jürgen Habermas Theorie des kommunikativen Handelns Bd. II Frankfurt/M. 1981 |
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