Bounds on the competence of a homogeneous jury

Alexander Zaigraev, Serguei Kaniovski
2010 Theory and Decision  
In a homogeneous jury, the votes are exchangeable correlated Bernoulli random variables. We derive the bounds on a homogeneous jury's competence as the minimum and maximum probability of the jury being correct, which arise due to unknown correlations among the votes. The lower bound delineates the downside risk associated with entrusting decisions to the jury. In large and not-too-competent juries the lower bound may fall below the success probability of a fair coin flip-one half, while the
more » ... r bound may not reach a certainty. We also derive the bounds on the voting power of an individual juror as the minimum and maximum probability of her/his casting a decisive vote. The maximum is less than one, while the minimum of zero can be attained for infinitely many combinations of distribution moments.
doi:10.1007/s11238-010-9216-5 fatcat:lshimp6dgjdmtkahnamoerk7ii