Alpern, Steve, Chen, Bo and Ostaszewski, Adam
(2020)
*A functional equation of tail-balance for continuous signals in the Condorcet jury theorem.*
Aequationes Mathematicae.
ISSN 0001-9054

Text (A functional equation of tail-balance for continuous signals in the Condorcet Jury Theorem)
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## 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 inÖnity (Condorcet, 1785). Recently, Alpern and Chen (2017a,b) 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 jurorís ìabilityî, and vote sequentially. This paper shows that, to mimic Condorcetís binary signal, such a distribution must satisfy a functional equation related to tail-balance, that is, to the ratio (t) of the probability that a mean-zero random variable satisÖes X > t given that jXj > t. In particular, we show that under natural symmetry assumptions the tail-balances (t) uniquely determine the signal distribution and so the distributions assumed in Alpern and Chen (2017a,b) are uniquely determined for (t) linear. 1 In

Item Type: | Article |
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Divisions: | Mathematics |

Date Deposited: | 03 Aug 2020 09:42 |

Last Modified: | 17 Sep 2020 14:30 |

URI: | http://eprints.lse.ac.uk/id/eprint/105845 |

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