Tom R. Tyler, now a professor at Yale Law School, first framed the idea in his 1990 book, “Why People Obey the Law.” He wrote that people obey the law not because they fear punishment, as commonly thought. They obey it largely because they believe the authorities have the right to tell them what to do; in other words, the law has legitimacy.

And what gives the law legitimacy is how people are treated. “What people actually pay attention to when assessing behavior of people in legal authority is not how good they are in reducing crime or whether they get a ticket,” said Tracey Meares, also a professor at Yale Law School and a leading researcher of, and advocate for, procedural justice. “What people care about is how they’re treated and how they’re treated in particular ways.”

“All the research converges on the same basic points,” said David M. Kennedy, a professor at John Jay College of Criminal Justice in New York City. The National Network for Safe Communities, which he co-founded and directs, runs the pilot project that includes Stockton. “People want to believe whatever action police and authorities are taking is being done for good reason — that it’s equitable and fair rather than personal and prejudicial. They want to be treated with respect,” he said. “And they want to have a chance to speak their piece.”

“But you don’t learn this in the first instance from social science literature,” Kennedy continued. “You learn it from your mother.”

Although it was not reflected in the Republican convention that nominated Donald J. Trump for president last week, Americans have been experiencing a rare moment of bipartisan convergence on the toxicity of maximum-force policing. Procedural justice has become one of the most important strategies for changing direction — perhaps the most important. In 2014, the White House convened the President’s Task Force on 21st Century Policing, which published its report (pdf) last year. Its first recommendation: build trust and legitimacy, using procedural justice. Now many major police forces, including New York City’s, are starting to use it.

I talked to Sammy Nunez, the executive director of Fathers and Families of San Joaquin, and to Pastor Curtis Smith of People and Congregations Together. Both groups work with Stockton’s most vulnerable communities — among other things, to track police abuse and campaign against it. Both men said that while problems remain, Jones was doing a good job as police chief. “It’s a big change for me to say this,” said Nunez, “but I believe we do have an opportunity to actually change the department in Stockton.”

Jones began to try new approaches. The force began to work closely with clergy and the community. Then Jones learned about procedural justice. The Chicago Police Department had developed a course and was training all its officers. Stockton sent three officers to take the course, and then three more.