Economics Dictionary of ArgumentsHome
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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. | |||
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Pierre-Simon Laplace on Condorcet Jury Theorem - Dictionary of Arguments
Parisi I 495 Condorcet Jury Theorem/Laplace/Nitzan/Paroush: (Laplace, 1815(1)) Specification of the problem faced by the jury: 1) There are two alternatives. 2) The alternatives are symmetric. Specification of the decision rule applied by the team: 3) The team applies the simple majority rule. Specification of the properties of the jury members: 4) All members possess identical competencies. 5) The decisional competencies are fixed. 6) All members share identical preferences. Specification of the behavior of the jury members: 7) Voting is independent. 8) Voting is sincere. Parisi I 496 The core of Laplace’s proof is the calculation of the probability of making the right collective decision (to be denoted by Π), where Π is calculated by using Bernoulli’s theorem (1713). Laplace shows, first, that Π is larger than the probability of making the right decision P by any single member of the team; second, that Π is a monotone increasing function of the size of the team; and third, that Π tends to unity with the size of the team. Of course, besides the above conditions there is an additional trivial condition that the decisional capabilities of decision-makers are not worse than that of tossing a fair coin. Namely, the probability P of making the correct decision is not less than one-half. Other properties of Π are that it is monotone increasing and concave in the size of the team, n, and in the competence of the individuals, P. Thus, given the costs and benefits of the team members’ identical competence, one can find the optimal size of a team and the optimal individual’s competence by comparing marginal costs to marginal benefits. >Jury theorem, >Marginal costs, >Decision theory, >Decision-making processes. 1. Laplace, P. S. de (1815). Theorie analytique des probabilities. Paris: n.p. 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. |
Laplace, Pierre-Simon Parisi I Francesco Parisi (Ed) The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017 |
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