With more national focus on those drawbacks, not all voters are enthusiastic about beefing up police forces, even in cities with sharply increasing homicide numbers.Last week, residents of Austin, Texas, rejected by a wide margin a ballot measure that would have required the city to hire hundreds more officers.

Opponents pointed out that while Austin had a record high number of homicides, cities with far more police officers per capita, including Atlanta, Chicago and Milwaukee, had experienced greater increases in their homicide rates, and cities with fewer officers per capita, including Raleigh, N.C., and El Paso, had seen homicides decline.

“If I read this margin of victory correctly, I think people understand that there is going to be crime, but are more willing to solve the question of why these things are happening as opposed to just responding to them when they do,” said Chas Moore, executive director of the Austin Justice Coalition, which opposed the measure.

Because the causes of crime vary from place to place, it can be extraordinarily difficult to disentangle the benefits of hiring more officers in any one city. After a rise in gun violence in Chicago in 2016, for example, the city announced that it would hire almost 1,000 additional officers, a number officials said was justified by a “top to bottom” staffing analysis that watchdog groups have not been able to obtain. Shootings began to fall before those officers were recruited and trained.

“As long as Chicago has a cold winter, crime is going to drop,” said Tracy Siska, the executive director of the Chicago Justice Project, adding that gun violence in 2016 was abnormally high. “So you can’t say that crime went down because they hired all these new officers — no, no, no.”

Chicago’s crime numbers did fall in 2019, the year that the force reached its peak of 13,353 officers, according to data from the city’s Office of Inspector General. But the next year, the coronavirus pandemic and an increase in gun purchases appeared to play a much larger role, making it hard once again to isolate the effects of the police force size. Overall, crime plummeted while the number of shootings surged.

There is also the question — left largely unanswered by existing studies — of how the added officers are being deployed.