Abstract
When society is divided into two groups with different actual or perceived crime rates, maintaining a low crime rate, minimizing the total number of innocent individuals convicted of a crime and keeping the probability of wrongly convicting an innocent individual equal across groups are incompatible social goals. The model presented here fully develops these tradeoffs and then analyzes the results of a social welfare function containing all three goals. An empirical application of the model estimates that innocent black Americans would be roughly five times more likely to be wrongly convicted of a crime than innocent white Americans if society placed no value on equality when it comes to convictions. Estimates also reveal a similar upper bound for gender inequality.
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