A model of correct and incorrect judgments assuming prosecutors and juries are machines of fixed accuracy, their errors completely uncorrelated
Copy and paste the following into Calca
Inputs:
juryAccuracy = 0.9081
prosecutorAccuracy = 0.90909090909090909090909
numberOfTrials = 70000
Outputs:
juryError = 1 - juryAccuracy
prosecutorError = 1 - prosecutorAccuracy
innocentConvicted = juryError * prosecutorError => 0.0084
guiltyConvicted = juryAccuracy * prosecutorAccuracy => 0.8255
guiltyAcquitted = juryError * prosecutorAccuracy => 0.0835
innocentAcquitted = juryAccuracy * prosecutorError => 0.0826
convictionRate = innocentConvicted + guiltyConvicted => 0.8339
acquittalRate = guiltyAcquitted + innocentAcquitted => 0.1661
percentageOfConvictionsThatAreWrong = 100 * innocentConvicted / convictionRate => 1.0019
percentageOfAcquittalsThatAreWrong = 100 * guiltyAcquitted / acquittalRate => 50.2983
GuiltyGoFreePerInnocentConvicted = guiltyAcquitted/innocentConvicted=> 10
convictions = convictionRate*numberOfTrials => 58,373
acquittals = acquittalRate*numberOfTrials=> 11,627
convictedAndGuilty = guiltyConvicted*numberOfTrials=> 57,788.1818
acquittedAndInnocent = guiltyAcquitted*numberOfTrials=>5,848.1818
convictedButInnocent = innocentConvicted*numberOfTrials =>584.8182
acquittedButGuilty = guiltyAcquitted*numberOfTrials=> 5,848.1818
(The below calculates the jury accuracy you must have, given the prosecutorial accuracy you entered above, to achieve the fixed conviction rate you enter below. So if you know how accurate prosecutors are and how often convictions occur, you can calculate how accurate juries are.)
fixedConvictionRate =0.7
juryAccuracyToYieldFixedConvictionRate = (1-prosecutorAccuracy-fixedConvictionRate)/(1-2*prosecutorAccuracy)=> 0.7444