Case Study Imagine a Small Town in Which There Has Recently Been

Essay

Case Study
Imagine a small town in which there has recently been a rash of murders that all bear the marks of the same culprit. The police investigation has gone nowhere and the town's sense of order is starting to break down. Residents are demanding that the sheriff find a culprit and threatening to exact vigilante justice on perceived criminals until a culprit is found. Given that the real murderer is unknown, the sheriff sees that she can only prevent chaos and bloodshed by framing someone who likely is not the murderer.
The sheriff has someone in mind who could be easily framed - a local man, Jim, who has been in and out of jail for other violent crimes like assault and robbery. He has no family and no one in town would protest if he were to be locked up. Moreover, he is a believable culprit and so would be easy to frame. The sheriff is fairly sure that he is not actually the murderer, and so she would likely be framing someone who, while not innocent overall, is innocent of these particular crimes. But she is not sure what else she can do to keep the peace.
-Does utilitarianism tell us that the sheriff is morally required to frame Jim? If so, is this a problem for utilitarianism? If not, how would the utilitarian explain this verdict?