Is it better to have a criminal justice system that runs the risk of, in every 100 people being acquitted, that 1 will go on to commit a terrible future crime; or one that runs the risk of, in every 100 people being convicted, there being 1 who was innocent? Sorry about the tortured phrasing of my question...

Any realistic criminal justice system will make both types of error: T-errors (terrible future crime committed by one wrongly acquitted) and I-errors (innocent person wrongly convicted).

It seems morally more appropriate here to compare alternative systems feasible for the same society in terms of the total number of errors, not in terms of the ratios you focus on (ratio of T-errors to total number of acquitted, ratio of I-errors to total number of convicted). To see this, take a criminal justice system under which 100,000 are acquitted of whom 2000 are wrongly acquitted and go on to commit a terrible crime. Now suppose we modify this system so that many more innocent people are tried and properly acquitted. So now we have 200,000 acquitted of whom 2000 are wrongly acquitted and go on to commit a terrible crime. So we got the T-error rate from 2 percent down to 1 percent. But have we improved the system? Surely not.

So I rephrase your question this way: In designing our criminal justice system, should we give greater weight to avoiding T-errors or to avoiding I-errors?

There is a widely held view bearing on this question. In one famous formulation by William Blackstone (www.law.ucla.edu/volokh/guilty.htm), it says: “It is better that ten guilty persons escape than one innocent suffer.” I think what stands behind this view is the idea that we as a society bear a far weightier responsibility for harms to innocents that we directly bring about than for harms to innocents that we merely might have prevented.

This idea is familiar in pedestrian contexts. It would be wrong to kill one innocent person in order to save another. It would be wrong to harm one innocent person in order to rescue another from a similar harm. It would be wrong to risk the life of one innocent person to prevent a risk to the life of another (risks being equal). And it would be wrong to cause a risk of harm to one innocent person in order to prevent the same risk of harm to another. In all these cases, agents ought to give more weight to harms and risks of harm they directly bring about than to similar harms or risks of harm that they merely fail to prevent.

This almost answers the reformulated question: We should give greater weight to avoiding I-errors than to avoiding T-errors. I say "almost", because the average harm associated with errors of each kind may not be equal. So the conclusion might conceivably be overturned if the harm done by the average I-error is just a few days in jail without public stigma while the average harm resulting from the average T-error is a minor massacre. But this is not true in the real world. Here, in order seriously to reduce the number of terrible crimes committed by persons wrongly acquitted, we would have to make it easier to convict people accused of very serious crimes and then take those convicted out of circulation for very long periods or forever. And doing this will inevitably increase the number of innocent people who, wrongly convicted, are locked up for very long periods or even executed.

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