Aggregating Probabilities across Offe nces in Criminal Law

A defendant is charged with four unrelated offences, allegedly committed in four different times and places. The probability that he committed each one of the offences is .9. Assume that the minimum threshold required for conviction is .95. Under prevailing criminal law the defendant would be acquitted of all four charges since no offence can be attributed to him. However, a simple calculation reveals that the probability that the defendant committed no offence at all is .01% only! Consequently it seems that convicting the person for at least one offence without specifying what this offence is would be just and efficient. We argue that in such cases, and under certain conditions, efficient deterrence will be better achieved if courts would aggregate probabilities across different offences, and would be willing to convict defendants even for unspecified offences. We also show under what conditions aggregating probabilities will yield less, rather than more, convictions.

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