But other criminologists, skeptical that the 1994 law had such a big effect, are unconvinced that any new federal law would have much sway. My colleague Erik Eckholm detailed the arguments of those who question whether the 1994 bill played a decisive part in driving state imprisonment higher. (Their main argument is that the states were already sending far more people to prison before the passage of the bill.)

There are other objections to something like the Brennan proposal. Its $20 billion in grants works out to $2 billion a year, which some critics call too small to matter, given that states and counties spend some $200 billion a year on criminal justice and about $70 billion on corrections. Ms. Chettiar of the Brennan Center notes that the federal government has frequently used dollars to prod state policy.

And there are political calculations. John Pfaff, a law professor at Fordham University, contends that it makes little sense to spend the limited political capital that might exist to overhaul criminal justice on federal legislation that, in his view, is unlikely to significantly change states’ behavior. In his research, Mr. Pfaff has shown how state and county prosecutors have driven prison populations higher by filing more cases than they used to. Any measures to reduce state prison populations, according to Mr. Pfaff, need to focus on prosecutors and the prosecuted. Such measures might include making it harder for county law enforcement officials to send people to state prisons that the counties do not pay for.

Helping defendants could also reduce the number of people in state prisons, which was 1.35 million in 2014. One reason that prosecutors send more people to prison might be that many defendants don’t get competent legal help from public defenders, who have overwhelming caseloads. Mr. Pfaff proposes that the federal government spend $4 billion a year on public defenders in the state and county systems, which he says might be a shield against overzealous prosecutors.

But law enforcement data does not clarify for criminologists which types of cases prosecutors have emphasized. Did the increase in the prison population come from a more aggressive pursuit of violent offenses, or nonviolent ones? Without knowing this, it’s hard to say whether a measure that, say, seeks to press district attorneys to reduce imprisonment and sentences for nonviolent offenses would have much effect on the overall prison population.

Such questions may not be answered soon. But the debate over the large prison population has taken on such a prominence in this presidential campaign that it might not be long before the candidates start asking more detailed questions about its causes — and what can be done to address them.