"The Lottery" by Shirley Jackson was published in 1948, not long after the end of World War II when the world was still dealing with the Holocaust, concentration camps and the atomic bomb aftereffects. The society in the story just as in real life was a patriarchal one, with women in the subordinate role. We as readers are reminded that Tess is subordinate to her husband when he tells her to shut up. This story really does reduce the ordinary people by one because a sacrifice of a person is required each year. The one way I see that it keeps the society functioning is that this lottery is tradition, and therefore change is bad meaning that all things in the society must stay the same. That would mean that society must function as it always has with the same rules and traditions. I'm not sure that it would really reduce the population as a whole as each woman is under pressure to produce as many children as possible to reduce the risk to the family if their family name is chosen.
The lottery is more like a sacrifice than like a device to reduce the population. It is associated with the ancient human sacrifices that were expected to help insure good crops. Therefore it doesn't seem as if the superstition is concerned with reducing the population but with sacrificing part of the population, that is, sacrificing something of value to the community. It isn't a very effective way of reducing the population, anyway, since it only eliminates one person per year. The lottery in Shirley Jackson's story really doesn't make much sense--but maybe that is just part of the overall stupidity and ignorance and blindness exhibited by these people. Speaking of blindness, I am reminded of the short novel The Country of the Blind, by H. G. Wells, which deserves to be better known. It is covered in eNotes. See the reference link below. It is about an explorer who encounters an isolated land where all the inhabitants are congenitally blind. They think there is something wrong with him because he can see what they take to be hallucinations, i.e., everything that is visible.
It occurs to me that, rather than being intended to reduce the population, the lottery might originally have been intended to increase it. When Tessie Hutchinson is about to be stoned to death she keeps protesting that it isn't fair. The lottery really isn't fair if you consider the way it works.
The first drawing selects a family. Then the second drawing selects the member of that family--regardless of age--who is to be killed by the crowd. It would be a tremendous advantage to belong to a big family and a tremendous disadvantage to belong to a small family. Some couples could have as many as eight or ten children. Even if that family was selected in the first drawing, each member would still have a big chance of not beinig selected in the second drawing. So there would be an incentive for married couples to have as many children as possible, although they might have to end up stoning one of their own children to death. That doesn't seem to be a big concern in this strange community.
A single adult male might be under extreme pressure to get married, because if his name was selected in the first drawing he would still have a fifty-fifty chance of escaping stoning if his wife's name was selected in the second drawing. And if they had a child, his chances of escaping stoning would be even greater.