Republican David Vitter’s first television ad against his Nov. 21 runoff opponent Democrat John Bel Edwards takes aim at Edwards’ position on criminal justice — specifically, Edwards’ talking points about Louisiana’s high incarceration rate.

The ad claims Edwards, who is being backed by the Louisiana Sheriffs Association, wants to release “5,500 violent thugs” from prison — a position that Edwards says has been misconstrued and taken out of context.

In reality, both candidates support some form of prison reform, including the expansion of early release programs for nonviolent offenders.

Edwards and Vitter won the top two spots in Louisiana’s Oct. 24 primary, sending them to a head-to-head runoff to succeed Gov. Bobby Jindal, who can’t seek re-election due to term limits and has set off on a presidential campaign.

Lafayette Parish Sheriff Michael Neustrom, one of the sheriffs backing Edwards in the governor’s race, said he thinks progressive programs that aim to reduce the prison population responsibly are needed in Louisiana.

“We have to do things differently,” he said.

He said Louisiana prisons are overcrowded with minor, nonviolent offenders and that reform would be both economical and smart for the state. He noted that Texas could be a model for the types of reform that should be implemented here.

Louisiana has earned the dubious distinction of having — not just the nation’s — the world’s highest incarceration rate. There are nearly twice as many people jailed in Louisiana per capita as the national average. As of 2014, there were nearly 40,000 people behind bars in the state.

The prison system costs Louisiana nearly $350 million a year.

It’s an issue that the Louisiana Legislature has grappled with for several years, slowly winnowing away some of the mandatory minimum sentencing requirements implemented decades ago.

“We have to look at proven strategies that have been implemented elsewhere,” Edwards said in an interview Friday.

He said he thinks Louisiana should take a serious look at pretrial diversion programs, including sobriety and drug courts, as well as special programs for the mentally ill and veterans. Edwards is a military veteran.

“That’s the type of approach we should take,” he said, adding that the reduced costs on incarceration could be reinvested to reduce crime.

He said Vitter’s characterization of his views is misleading.

The 5,500 figure, which Edwards has noted in several speeches — not just the Southern University speech the Vitter ad cites — is the number of prisoners that puts Louisiana above the state with the No. 2 incarceration rate. He’s used it as a hypothetical number that Louisiana would need to reduce by just to get out of the No. 1 spot.

“I have never said I have a plan to release anybody,” he said, noting that the state has to set goals that it would like to achieve.

Asked about his views on sentencing reform and Louisiana’s high incarceration rate, Vitter referred reporters to his policy plan, “Together, Louisiana Strong.” The plan includes a chapter on “fighting violent crime and reforming criminal justice,” but it doesn’t specifically outline efforts to reduce Louisiana’s prison population.

It mentions that Vitter wants to implement “cost-effective work release and monitoring programs,” but doesn’t provide details on those ideas.

“I support common sense,” Vitter said Friday. “It is fundamentally different from John Bel Edwards.”

Vitter said he had not read recent legislative proposals that have aimed to reduce penalties for nonviolent offenses as a way to rein in the prison population.

He repeatedly characterized Edwards’ comments as a “proposal” that his opponent has made and said his main objection is to the figure named.

“We don’t need to pick an arbitrary number,” he said. “That’s a completely irresponsible proposal.”

He added that Mississippi’s rate shouldn’t even enter the discussion.

Follow Elizabeth Crisp on Twitter @elizabethcrisp. For more coverage of Louisiana state government and politics, follow our Politics blog at http://blogs.theadvocate.com/politicsblog.