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Erschienen in: Theory and Decision 1/2016

02.11.2015

A Condorcet jury theorem for couples

verfasst von: Ingo Althöfer, Raphael Thiele

Erschienen in: Theory and Decision | Ausgabe 1/2016

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Abstract

The agents of a jury have to decide between a good and a bad option through simple majority voting. In this paper the jury consists of N independent couples. Each couple consists of two correlated agents of the same competence level. Different couples may have different competence levels. In addition, each agent is assumed to be better than completely random guessing. We prove tight lower and upper bounds for the quality of the majority decision. The lower bound is the same as the competence of majority voting of N independent agents. The upper bound cases for negatively correlated couples can be much better than the value for \(2 \, N\) independent agents.

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Literatur
Zurück zum Zitat Althöfer, I. (1991). Selective trees and majority systems: two experiments with commercial chess computers. In D. F. Beal (Ed.), Advances in Computer Chess 6 (pp. 37–59). Chichester: Ellis Horwood. Althöfer, I. (1991). Selective trees and majority systems: two experiments with commercial chess computers. In D. F. Beal (Ed.), Advances in Computer Chess 6 (pp. 37–59). Chichester: Ellis Horwood.
Zurück zum Zitat Althöfer, I. (1998). 13 Jahre 3-Hirn: Meine Schach-Experimente mit Mensch-Maschinen-Kombinationen. 3-Hirn-Verlag. Althöfer, I. (1998). 13 Jahre 3-Hirn: Meine Schach-Experimente mit Mensch-Maschinen-Kombinationen. 3-Hirn-Verlag.
Zurück zum Zitat Althöfer, I. (2004). Improved game play by multiple computer hints. Theoretical Computer Science, 313(3), 315–324.CrossRef Althöfer, I. (2004). Improved game play by multiple computer hints. Theoretical Computer Science, 313(3), 315–324.CrossRef
Zurück zum Zitat Bahadur, R. R. (1961). A Representation of the Joint Distribution of Responses to n Dichotomous Items. In H. Solomon (Ed.), Studies in Item Analysis and Prediction (pp. 158–168). Stanford: Stanford University Press. Bahadur, R. R. (1961). A Representation of the Joint Distribution of Responses to n Dichotomous Items. In H. Solomon (Ed.), Studies in Item Analysis and Prediction (pp. 158–168). Stanford: Stanford University Press.
Zurück zum Zitat Ben-Yashar, R., & Paroush, J. (2000). A nonasymptotic Condorcet jury theorem. Social Choice and Welfare, 17(2), 189–199.CrossRef Ben-Yashar, R., & Paroush, J. (2000). A nonasymptotic Condorcet jury theorem. Social Choice and Welfare, 17(2), 189–199.CrossRef
Zurück zum Zitat Berend, D., & Sapir, L. (2007). Monotonicity in Condorcet’s Jury Theorem with dependent voters. Social Choice and Welfare, 28(3), 507–528.CrossRef Berend, D., & Sapir, L. (2007). Monotonicity in Condorcet’s Jury Theorem with dependent voters. Social Choice and Welfare, 28(3), 507–528.CrossRef
Zurück zum Zitat Berg, S. (1993). Condorcet’s jury theorem, dependency among jurors. Social Choice and Welfare, 10(1), 87–95.CrossRef Berg, S. (1993). Condorcet’s jury theorem, dependency among jurors. Social Choice and Welfare, 10(1), 87–95.CrossRef
Zurück zum Zitat Boland, P. J., Proschan, F., & Tong, Y. L. (1989). Modelling dependence in simple and indirect majority systems. Journal of Applied Probability, 26(1), 81–88.CrossRef Boland, P. J., Proschan, F., & Tong, Y. L. (1989). Modelling dependence in simple and indirect majority systems. Journal of Applied Probability, 26(1), 81–88.CrossRef
Zurück zum Zitat Grofman, B. (1975). A comment on democratic theory: a preliminary mathematical model. Public Choice, 21(1), 99–103.CrossRef Grofman, B. (1975). A comment on democratic theory: a preliminary mathematical model. Public Choice, 21(1), 99–103.CrossRef
Zurück zum Zitat Grofman, B., Owen, G., & Feld, S. (1983). Thirteen theorems in search of the truth. Theory and Decision, 15(3), 261–278.CrossRef Grofman, B., Owen, G., & Feld, S. (1983). Thirteen theorems in search of the truth. Theory and Decision, 15(3), 261–278.CrossRef
Zurück zum Zitat Kaniovski, S. (2010). Aggregation of correlated votes and Condorcet’s Jury Theorem. Theory and Decision, 69(3), 453–468.CrossRef Kaniovski, S. (2010). Aggregation of correlated votes and Condorcet’s Jury Theorem. Theory and Decision, 69(3), 453–468.CrossRef
Zurück zum Zitat Kaniovski, S., & Zaigraev, A. (2011). Optimal jury design for homogeneous juries with correlated votes. Theory and Decision, 71(4), 439–459.CrossRef Kaniovski, S., & Zaigraev, A. (2011). Optimal jury design for homogeneous juries with correlated votes. Theory and Decision, 71(4), 439–459.CrossRef
Zurück zum Zitat Kocay, W., & Kreher, D. L. (2005). Graphs, algorithms and optimization. Boca Raton: Chapman & Hall / CRC Press. Kocay, W., & Kreher, D. L. (2005). Graphs, algorithms and optimization. Boca Raton: Chapman & Hall / CRC Press.
Zurück zum Zitat Ladha, K. K. (1992). The Condorcet Jury Theorem, Free Speech, and Correlated Votes. American Journal of Political Science, 36(3), 617–634.CrossRef Ladha, K. K. (1992). The Condorcet Jury Theorem, Free Speech, and Correlated Votes. American Journal of Political Science, 36(3), 617–634.CrossRef
Zurück zum Zitat Ladha, K. K. (1993). Condorcet’s jury theorem in light of de Finetti’s theorem. Social Choice and Welfare, 10(1), 69–85.CrossRef Ladha, K. K. (1993). Condorcet’s jury theorem in light of de Finetti’s theorem. Social Choice and Welfare, 10(1), 69–85.CrossRef
Zurück zum Zitat Ladha, K. K. (1995). Information pooling through majority-rule voting: Condorcet’s jury theorem with correlated votes. Journal of Economic Behavior & Organization, 26(3), 353–372.CrossRef Ladha, K. K. (1995). Information pooling through majority-rule voting: Condorcet’s jury theorem with correlated votes. Journal of Economic Behavior & Organization, 26(3), 353–372.CrossRef
Zurück zum Zitat Miller, R. N. (1986). Information, electorates, and democracy: some extensions and interpretations of the Condorcet Jury theorem. In B. Grofman & G. Owen (Eds.), Information pooling and group decision making. Greenwich: JAI Press. Miller, R. N. (1986). Information, electorates, and democracy: some extensions and interpretations of the Condorcet Jury theorem. In B. Grofman & G. Owen (Eds.), Information pooling and group decision making. Greenwich: JAI Press.
Zurück zum Zitat Owen, G., Grofman, B., & Feld, S. L. (1989). Proving a distribution-free generalization of the Condorcet Jury Theorem. Mathematical Social Sciences, 17(1), 1–16.CrossRef Owen, G., Grofman, B., & Feld, S. L. (1989). Proving a distribution-free generalization of the Condorcet Jury Theorem. Mathematical Social Sciences, 17(1), 1–16.CrossRef
Zurück zum Zitat Zaigraev, A., & Kaniovski, S. (2012). Bounds on the competence of a homogeneous jury. Theory and Decision, 72(1), 89–112.CrossRef Zaigraev, A., & Kaniovski, S. (2012). Bounds on the competence of a homogeneous jury. Theory and Decision, 72(1), 89–112.CrossRef
Zurück zum Zitat Zaigraev, A., & Kaniovski, S. (2013). A note on the probability of at least k successes in n correlated binary trials. Operations Research Letters, 41(1), 116–120.CrossRef Zaigraev, A., & Kaniovski, S. (2013). A note on the probability of at least k successes in n correlated binary trials. Operations Research Letters, 41(1), 116–120.CrossRef
Metadaten
Titel
A Condorcet jury theorem for couples
verfasst von
Ingo Althöfer
Raphael Thiele
Publikationsdatum
02.11.2015
Verlag
Springer US
Erschienen in
Theory and Decision / Ausgabe 1/2016
Print ISSN: 0040-5833
Elektronische ISSN: 1573-7187
DOI
https://doi.org/10.1007/s11238-015-9521-0

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