One thing that came to mind is the fact that he is a ruler and not just a judge. If he we just a judge, then his decision would be much easier because it is his sole responsibility to protect the innocent and punish the guilty.
But when you take into account that he is also in charge of protecting the members of the town it gets trickier. You then really have to decide whether you are willing to kill one to probably save many, or protect the one at the possible loss of others.
Some people might think that imprisoning all four of them is a better solution because at least then the innocent man isn't killed. There are two problems I have with this though. First, you are still judging an innocent man as if he we guilty, and changing his life for the worse. Another problem that could result from simply imprisoning them is that you would then most likely have to imprison all other future murderers. People might be more willing to kill if they know they will only be going to prison.