Conditions under which random acquittal is better than acquitting the guilty to avoid convicting the innocent

One common approach to managing the inevitable erroneous convictions and erroneous acquittals produced by criminal justice systems is to employ various means (rules and procedures) to decrease the number of erroneous convictions at the expense of increasing, even many more times, the number of erroneous acquittals. Blackstone’s famous dictum (1765) that “[i]t is better that ten guilty persons escape than that one innocent suffer” (“the Blackstone ratio”), and others like it, have inspired this error distributing approach to error management. A mathematical analysis is provided demonstrating that, under certain conditions (“the R-conditions”), error distributing approaches result in criminal justice systems that function worse, by all quantitative measures (including the number of innocents convicted), than similar systems in which defendants are randomly acquitted. These results follow from one of a pair of derived fundamental equations applicable to all criminal justice systems, regardless of circumstance. Thus, the results hold irrespective of the means used to avoid convicting the guilty and challenge those who wish to engage in a particular error distributing approach to show that the R-conditions do not obtain for that approach (with reasonably convincing accuracy). Further, the results presented herein identify an upper bound to the Blackstone ratio, according to one conception of that ratio.