Shirley Jackson does not tell the reader who is in charge of the town in her story "The Lottery." What the reader does know is that Mr. Summers is in charge of the lottery event and proceedings. It is unclear if he has any official government leadership role.
The lottery was conducted—as were the square dances, the teen club, the Halloween program—by Mr. Summers, who had time and energy to devote to civic activities.
The above quote makes it clear that Mr. Summers is in charge of the lottery. That line cracks me up every single time that I read it, though. It says that Mr. Summers conducts all of the civic activities because he has time and energy for them. I too would have the time and energy if being in charge of those things made me exempt from the lottery. I would do an awful lot of things if it guaranteed I could never be stoned to death.
Mr. Summers is instrumental in changing the "chips" that the lottery uses. He convinces everybody that strips of paper are better than the wood pieces that were used when the village was small. Based on pieces of evidence like that, it's clear that Mr. Summers is the main man in charge of the lottery.
Because so much of the ritual had been forgotten or discarded, Mr. Summers had been successful in having slips of paper substituted for the chips of wood that had been used for generations. Chips of wood, Mr. Summers had argued, had been all very well when the village was tiny, but now that the population was more than three hundred and likely to keep on growing, it was necessary to use something that would fit more easily into he black box.