We consider two basic aspects of juries that must decide on guilt verdicts, namely the size of juries and their composition in situations where society consists of sub-populations. We refer to the actual jury that needs to provide a verdict as the `first jury', and as their judgement should reflect that of society, we consider an imaginary `second jury' to represent society. The focus is mostly on a lower probability of a guilty verdict by the second jury, conditional on a guilty verdict by the first jury, under suitable exchangeability assumptions between this second jury and the first jury. Using a lower probability of a guilty verdict naturally provides a `benefit of doubt to the defendant' robustness of the inference. By use of a predictive approach, no assumptions on the guilt of a defendant are required, which distinguishes this approach from those presented before. The statistical inferences used in this paper are relatively straightforward, as only cases are considered where the lower probabilities according to Coolen's Nonparametric Predictive Inference for Bernoulli random quantities and Walley's Imprecise Beta Model coincide.
Keywords. Imprecise Beta Model, lower probability, Nonparametric Predictive Inference, representation of subgroups
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Authors addresses:
Frank Coolen
Dept of Mathematical Sciences
Durham University
Durham, DH1 3LE
Brett Houlding
Department of Mathematical Sciences, Durham University,
Durham,
DH1 3LE,
UK
Steven Parkinson
229 Scar Lane, Golcar, Huddersfield,
West Yorkshire
HD7 4AU
E-mail addresses:
| Frank Coolen | frank.coolen@durham.ac.uk |
| Brett Houlding | brett.houlding@durham.ac.uk |
| Steven Parkinson | s.g.parkinson@durham.ac.uk |