This is a fascinating topic. I would say that societies do not have to choose a group of people to punish, but from the perspective of history this is exactly what happens. There are three reasons why this takes place.
First, generally speaking people do not like to take responsibility. So, if something goes wrong, there is something in humanity that loves to blame others. It almost seems like a biological necessity.
Second, we live in a precarious world where often times things do go wrong. Think of all the wars, the terrorism abroad and even at home - not to mention other social problems, such as poverty. In this context, scapegoating is common.
Finally, for society to move on with a sense of resolve, too often blame is assigned to a group. "The Lottery" does a masterful job in showing that this happens. The only point that I take issue with Jackson is that it is not always random. Those in power usually choose whom they will single out.