What would a utilitarian have us do in this case if we were the sheriff? In other words, should we lie, according to utilitarianism? What considerations would a utilitarian identify as important to think about in this case? Would a Kantian agree with the utilitarian's advice here? Why or why not?

Imagine a scenario where there has been a serious crime in a town and the Sheriff is trying to prevent serious rioting. He knows that this rioting is likely to bring about destruction, injury and maybe even death. The problem is that he has no leads; he has not the slightest idea who committed the crime. However, he can prevent these riots by lying to the town and framing an innocent man. No one will miss the man and he is hated in the town. If he frames and jails this innocent man, convincing people to believe that it was this man that committed the crime, then the town will be placated and people will not riot.