Back to Search
Start Over
A functional equation of tail-balance for continuous signals in the Condorcet Jury Theorem.
- Source :
-
Aequationes Mathematicae . Feb2021, Vol. 95 Issue 1, p67-74. 8p. - Publication Year :
- 2021
-
Abstract
- Consider an odd-sized jury, which determines a majority verdict between two equiprobable states of Nature. If each juror independently receives a binary signal identifying the correct state with identical probability p, then the probability of a correct verdict tends to one as the jury size tends to infinity (Marquis de Condorcet in Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix, Imprim. Royale, Paris, 1785). Recently, Alpern and Chen (Eur J Oper Res 258:1072–1081, 2017, Theory Decis 83:259–282, 2017) developed a model where jurors sequentially receive independent signals from an interval according to a distribution which depends on the state of Nature and on the juror's "ability", and vote sequentially. This paper shows that, to mimic Condorcet's binary signal, such a distribution must satisfy a functional equation related to tail-balance, that is, to the ratio α (t) of the probability that a mean-zero random variable satisfies X > t given that | X | > t . In particular, we show that under natural symmetry assumptions the tail-balances α (t) uniquely determine the signal distribution and so the distributions assumed in Alpern and Chen (Eur J Oper Res 258:1072–1081, 2017, Theory Decis 83:259–282, 2017) are uniquely determined for α (t) linear. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FUNCTIONAL equations
*JURY
*JURORS
*INFINITY (Mathematics)
*VERDICTS
Subjects
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 95
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 148629616
- Full Text :
- https://doi.org/10.1007/s00010-020-00750-1