Those supporting the initiative said opening shops that sold alcohol on the reservation would allow the tribe to keep a share of Pine Ridge’s money on the reservation that is now being spent in liquor stores in towns bordering it. Further, they argued that the tax proceeds from alcohol sales could be used to bolster the Oglala Sioux’s alcohol treatment programs. It remained unclear how much money allowing alcohol sales would produce for the reservation, which is one of the poorest places in the country and has unemployment rates estimated at more than 80 percent.

“Not legalizing it is just the status quo,” said Robert Ecoffey, 58, who worked in law enforcement on the tribe and served as a superintendent for the Bureau of Indian Affairs. “You have all of the issues and none of the resources to help deal with it.”

But that argument was unconvincing to Mr. Brewer.

“We’re going to use alcohol money to spend on alcohol issues,” he said. “That doesn’t make sense to me. I consider this blood money that the tribe will be getting. I hate to accept it.”

Solving the alcohol problem, he said, requires educating children, returning to the roots of tribal culture and creating jobs through economic development. Instead, he said, the tribal council, the federal government and the people of Pine Ridge have turned a blind eye to the problem.

The United States government has traditionally banned alcohol on reservations, but during the past 20 years, as more tribes have opened casinos — which are the leading economic drivers on many reservations — those prohibitions have been relaxed by tribes. Still, many reservations continue to limit alcohol sales and consumption to casinos.

Even the smell of alcohol on a person’s breath in Pine Ridge has been cause for arrest. But despite the ban, alcohol — particularly beer — is plentiful on Pine Ridge. Most comes from stores that sell alcohol in the tiny town of Whiteclay, just across the Nebraska border from the reservation. Four stores in Whiteclay sell millions of cans of beer and malt liquor a year, almost all of it to the Oglala Sioux of Pine Ridge. Lawsuits, boycotts, police safety checks and protests organized by the tribe have all failed to close the stores or to put a significant dent in their business.