How much sorting does the justice system do?
In 1994, Americans experienced some 4.2 million serious violent crimes (murders, rapes, robberies, and aggravated assaults). In the same year, the justice system registered about 146,000 convictions for those serious violent crimes, and sent some 95,000 adjudicated felons to prison for them. On any given day in 1996, nearly 60 percent of offenders convicted of rape or sexual assault were on probation or parole rather than incarcerated. Similarly, on any given day in 1997, some 3.9 million persons were on probation or parole, including hundreds of thousands of persons convicted of a violent crime.
Suppose that, on average, every individual criminal was responsible for four serious violent crimes in 1994, and that the system caught, convicted, and imprisoned all of them. That would have added 1,000,000 serious violent felons — not 95,000 — to prison in 1994. Or suppose that all of the convicted sex offenders under the custody of corrections officials (i.e., on probation, on parole, or incarcerated) in the United States had been incarcerated in 1994. That would have increased the number of such offenders behind bars from about 99,000 to 234,000. Or imagine that all persons on probation for a violent crime in 1994 were incarcerated instead. That would have landed another 400,000 or so persons in prison.
US federal prisons, state prisons, and jails hold roughly 2 million prisoners. Is this number too high, too low, or just about right?
Arguing against further prison expansion is the principle of diminishing returns. That is, as noted above, if the most serious offenders are already in prison, then prison growth requires the criminal justice system to reach deeper into the pool of prison-eligible offenders, such that increases in incarceration are less and less cost-effective.
One of the most surprising, and significant, findings of this study is that this has not been the case with regard to the prison systems we surveyed when drug-only offenders are excluded. When drug-only offenders are included, however, it appears that the value of incarcerating the least “costly” half of inmates (least costly in terms of the social-costs of their offenses) is quite low.
I’m not sure that qualifies as surprising.
This isn’t diminishing returns; as long as the increases are less and less cost-effective, it’s diminishing marginal returns. Diminishing returns would be when so many people are incarcerated that there are hardly criminals left to throw in prison and most people being prosecuted are innocent.
Diminishing returns already means diminishing marginal returns. What you’re describing would be negative returns.
I saw the Wikipedia page too. They’ve got it wrong. I learned it like this in my first econ class (1997): At the outset of production, input increases and output increases. That’s increasing returns (obviously). With increasing input, higher additional output per unit input is increasing marginal returns. At some point the additional output per unit input starts to decline. It’s still increasing returns, but it’s diminishing marginal returns. Continuing to add more input will at some point mean that resources are so misused that diminishing returns will eventually set in.
We learned it with “utils” from eating hamburgers. At the beginning you love the hamburgers, and as you continue eating them, you love them more and more with every bite. After a few hamburgers, you’re still loving them, but each bite makes you love them less and less (diminishing marginal returns). Then after a while, as you continue eating, you begin to hate hamburgers (diminishing returns).
By my second econ class (2006), diminishing marginal returns and diminishing returns had already been conflated. The professor was taught as if they were the same thing, but we were using an old textbook that defined them correctly, and I had to teach a large group of my confused colleagues what the terms really meant. I suspect if it had been a business class, the proper distinction would have been made. Production during diminishing marginal returns can be profitable. But I don’t think a business would want to operate under diminishing returns.