THESE days, it’s practically unheard-of for those on the left to embrace ideas promoted by the likes of the Koch brothers and the conservative Heritage Foundation. But it would be a shame if partisan distrust kept Democrats from supporting a proposal favored by the right: a measure that would bolster the idea that a criminal conviction should require proof of what lawyers call “mens rea” — literally, a guilty mind. That’s because it can be harnessed to aid some of those who are especially ill treated by the criminal justice system: the poor and racial minorities.

As a legal principle, mens rea means that causing harm should not be enough to constitute a crime; knowingly causing harm should be. Walking away from the baggage carousel with a suitcase you mistook for your own isn’t theft; it’s theft only if you knew you didn’t own it. Ordinary citizens may assume that this common-sense requirement is already the law of the land. And indeed law students are taught that prosecutors must prove not just that a defendant did something bad, but also that his frame of mind made him culpable when he did it.

But over the years, exceptions to the principle have become common because mens rea requirements have not been consistently detailed in laws. In one often-cited case, the president of a company that mistakenly shipped mislabeled drugs was convicted of a crime even though he had no way of knowing that the labels were incorrect. In another, a truck driver crossing the Canadian border into Washington to deliver cases of beer was convicted of drug trafficking even though prosecutors produced no evidence that he knew or should have known that the truck had a secret compartment filled with drugs. In these cases and many more like them, the prosecution secured conviction without showing that the defendant had a guilty mind.

Congress is now considering a measure sponsored by Representative James Sensenbrenner, Republican of Wisconsin, that would require that mens rea be proven in many more cases. For instance, a law making it a crime to mislabel drugs would automatically be interpreted as criminalizing knowing mislabeling. The measure would not affect statutes that make clear that no mental state need be shown for guilt — for example, laws criminalizing sex with minors.

The provision is part of a sweeping criminal justice bill that includes important reforms sought by liberals, including reduced sentences for minor crimes. Democrats, however, oppose the mens rea provision on the ground that it would weaken efforts to prosecute corporate executives whose companies have caused harm. Their opposition is a major stumbling block to passage of the larger bill. But suspicions about Republican motivations should not turn liberals against these changes, because strengthening mens rea requirements will also help poor and minority people.

Consider a New York law banning “gravity knives” — folding knives that open with a flick of the wrist — that lacks mens rea protections. The statute does not require proof that a defendant knew her knife was a gravity knife, much less that gravity knives are banned in the state. As a result, the law has been used by the police in New York City to pick up thousands of people, most of them minorities, even if they had the knives for innocent purposes. And in Baltimore, Freddie Gray died in a police van after being arrested for violating a very similar statute that also lacked a mens rea requirement.

The Justice Department opposes the proposed mens rea measure on the ground that it would have prevented convictions of corporate executives whose products caused harm. But it is entirely possible that the government could have proven mens rea had it been required to try. Furthermore, criminal conviction is not the only way to make corporations pay for their harms: Tort liabilities and civil penalties are not constrained by mens rea requirements.

Senator Patrick Leahy, Democrat of Vermont, opposes strengthening mens rea requirements across the board, arguing that each problematic statute should be revised individually. But it would take years to revamp thousands of laws. The history of New York’s effort to revise its gravity-knife ban underscores the problem: A proposal to require proof of “unlawful intent” in gravity-knife cases passed the New York State Assembly in 2015 but stalled in the State Senate.

The greatest impact of the federal legislation might be in encouraging changes at the state level, where poor and minority defendants are most frequently prosecuted. Ohio and Michigan have already passed mens rea reform laws. And in the wake of federal legislation, other states, including New York, would likely follow their lead.

Democrats should push for even more sweeping changes to unjust “felony murder” laws, which permit murder convictions for anyone participating in a felony in which someone dies, even if no one involved could have been expected to foresee that happening. We know that adolescents are far less aware than adults of the risks their conduct involves, but since felony murder does not require proof of mens rea, adolescent defendants can’t offer evidence of their distorted perceptions of risk.

For liberals, the right’s proposal offers a chance to strike a blow for justice for ordinary people. No one should be convicted of a crime — or even stopped by the police — without evidence of a criminal state of mind.

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