Californians took a leap of faith in 2014 when they voted to reduce penalties for certain low-level, non-violent crimes in hope that the change would lower the state’s highest-in-the-nation recidivism rate.

The resulting savings on prison costs would be put into mental health, drug rehabilitation, victims’ services, and school truancy and dropout prevention programs to help keep more people out of jails and prisons. Proponents also argued that it would free law enforcement to investigate and solve more serious crimes.

Here’s the good news: It’s working.

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Proposition 47 reduced penalties for personal illicit drug possession and for various forms of theft valued at no more than $950 — shoplifting, forgery, fraud, writing bad checks, receiving stolen property — from felonies punishable by prison to misdemeanors. Critics vehemently argued that it was a soft-on-crime approach that would increase violent crime and that innocent victims would pay the price.

But a year-long study by the Public Policy Institute of California found violent crime did not go up. Meanwhile, recidivism rates decreased by 3.1 percent due to Prop. 47. The measure isn’t perfect: It may be linked to a rise in thefts, primarily from motor vehicles, but it had no apparent effect on burglaries or stolen cars.

Only three of California’s 58 district attorneys had the courage to back the proposition. Kudos to Santa Clara County District Attorney Jeff Rosen, San Francisco DA George Gascon and Humboldt County DA Paul Gallegos for standing up to their colleagues who argued the measure would drive up crime.

In supporting the proposition in 2014, Rosen said “we need to be both smart and tough on crime. Since 1984, we have opened 22 prisons and just two state universities. Don’t we all wish it were the other way around?”

The PPIC report notes that California’s crime rates “remain comparable to the low rates observed in the 1960s, despite California’s more recent drastic reductions in its prison population.”

All told, the state’s prison population dropped from 135,000 in 2014 to just under 120,000 in 2016, and there were 40,000 fewer felony convictions in the state. That’s huge, given the fact that the average cost of housing California prisoners is $47,000 a year for those who committed non-violent and non-serious crimes.

The resulting savings is pumping about $100 million a year into city and county programs throughout the state specifically designed to treat, house and retrain those considered high-risk potential offenders. The Alameda County Health Care Services Agency and the Contra Costa Health Services Department each received $6 million last year to help people who had been impacted by the criminal justice system and had mental health or substance abuse issues.

California spent years focusing on arresting and imprisoning criminals. Proposition 47 points the state in a better direction, emphasizing crime prevention by giving criminals and potential offenders the help they need to be healthy, productive members of society.