Economic Theories on Condorcet Jury Theorem - Dictionary of Arguments

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Condorcet Jury Theorem: The Condorcet Jury Theorem posits that if each member of a jury has an independent probability of more than 50% of making the correct decision, then increasing the number of jurors will make the collective probability of a correct decision approach certainty. Conversely, if individual accuracy is below 50%, adding more jurors decreases the likelihood of a correct group decision. See also Decision theory, Decision-making processes, Jury theorem, Collective Intelligence. _____________ Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

> Economic Theories	> Condorcet Jury Theorem	Economic Theories on Condorcet Jury Theorem - Dictionary of Arguments 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. _____________ Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.	Economic Theories Parisi I Francesco Parisi (Ed) The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017

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