The marginal utility of policing

In 2018, Rachael Rollins was elected District Attorney in Suffolk County, Massachusetts. Rollins immediately declared that she would not prosecute anyone for disorderly conduct, shoplifting, drug possession, drug sales, trespassing, and a number of other crimes. My reaction was that this was bound to be a disaster—Rollins was basically legalizing drug dealing and theft.

Then last year a big study was published of misdemeanor prosecutions in Suffolk County. This study looked at tens of thousands of misdemeanor prosecutions filed up until 2018 (i.e., before Rollins came into office). The authors exploited the random assignment of non-violent misdemeanor cases to different prosecutors—i.e. some prosecutors might file a shoplifting case 40% of the time, others file the same case against the same defendant 70% of the time. They found that:

for the marginal defendant, nonprosecution of a nonviolent misdemeanor offense leads to large reductions in the likelihood of a new criminal complaint over the next two years.

Rollins and other criminal justice “reformers” cited this study to declare that her decision to flatly refuse prosecution of all nonviolent misdemeanor crimes had been vindicated. Assuming this study is correct—and as far as I can tell, it is—is that the right conclusion to draw? I don’t think so.

A warning about what follows: I am going to talk about economic theory, and I am not a trained economist at all. Professor Aaron Chalfin at the University of Pennsylvania very generously agreed to give me some feedback on an early draft of this post and my basic explanation of these concepts, so I don’t think I’m butchering them too badly. But the fact remains that I am veering pretty far out of my lane here. There is also the possibility that, if you do know something about economics, you will find all of what follows to be painfully obvious.

The marginal utility of policing

I often argue proactive policing reduces crime. I point to evidence like Roland Fryer’s study of consent decrees, which found a pullback in policing was followed by a sharp increase in violent crime in Chicago and several other cities. But others who think I’m wrong can point to other evidence, like a study that found no change in crime in New York City when the NYPD pulled back on proactive policing in 2015.

I think the concept of marginal utility is the way to square this circle. Marginal utility is the idea that as you add a unit of X, it generates positive returns—but only up to a point. Once you add too much X, you start getting no return. If you keep adding units of X past that point (b), it actually makes things worse. You’re spending resources on X, but get no benefit, so adding X is now creating negative value.

Economists usually talk about marginal utility in terms of consumer products. For example, buying one TV for your house improves your quality of life. Buying two probably improves your quality of life, but not as much as the first one did. Buying a hundred TVs, however, is actually a net negative—it’s more TVs than you can ever use, you’re wasting money you could have spent on other stuff, and now your house is so full of useless TVs so you can’t do anything else that you like to do.

I suspect marginal utility explains a lot of conflicting evidence in criminal justice and policing. For example, consider a recent paper that found that adding more police officers reduces crime. The authors conclude that on average, “[e]ach additional police officer abates approximately 0.1 homicides” which is consistent with a lot of other studies. But there’s a caveat: cities with a black population of 27.26% or larger saw a return on the marginal additional police officer that was smaller or nonexistent. I expect this is just a function of marginal utility—Washington D.C., for example, has a large black population and also already has a very large police force, as does New York City. Adding an officer in D.C. or New York doesn’t get you the same kind of returns as adding an officer in San Francisco or Detroit.

Marginal utility has serious implications for people who think policing has no effect on crime. Many left-wing people looked at the NYPD study on proactive policing and concluded proactive policing has no impact on crime at all. But this is the wrong conclusion! The correct conclusion was that proactive policing in New York City had gone beyond the point of diminishing returns (b) such that each new stop had a zero or negative marginal utility. This makes a lot of sense if you think about it — NYPD’s “Stop and Frisk” program was enormous. They were doing tons of stops—probably way more than they needed to. But that doesn’t mean all the stops they were doing were worthless. It just means the marginal stop was worthless, and NYPD needed to reduce the number of stops until it reached the optimal number.

Importantly, I strongly suspect that the point of diminishing returns for each criminal justice intervention is probably different in every city and changes over time. Chicago has a very high violent crime rate, whereas crime in New York in 2015 was very low. Accordingly, it seems very likely that the optimal number (b) of Terry stops, arrests, police-officers-per-capita, etc. is going to be very different in each city. Chicago may need a lot more proactive policing even as New York needs less.

The problem of reducing X to zero

Marginal utility makes it clear why Rollins’ total non-prosecution scheme is so problematic and why the Suffolk County study doesn’t actually support it. Even if the marginal prosecution of a shoplifter is a net negative, that doesn’t mean prosecuting shoplifters is always completely worthless. It means there is an optimal number of shoplifting prosecutions, and we need to reduce shoplifting prosecutions until we reach the optimal number. It’s hypothetically possible the optimal number is “zero” — but this seems unlikely, and more importantly, it isn’t what the study shows.

The criminal justice system relies on any number of interventions: police presence, stops, arrests, prosecutions, and incarceration. And we now live in a weird space where policymakers seem very interested in reducing some of these things all the way down to zero: left-leaning “reform” types want to abolish police and prisons, completely cease the prosecution of certain crimes, or eliminate traffic stops. The logic of marginal utility strongly suggests this is virtually always the wrong approach. To take one very obvious example: in Seattle, the city suddenly reduced policing to zero in the “CHOP zone” — and crime exploded.

I avoid commenting on incarceration and bail reform issues because it isn’t something I know a ton about. But I will say that I also think marginal utility should be given weight when people talk about incarceration and pretrial detention. Imagine the average sentence for a certain felony is nine years in prison, with almost all sentences falling between eight years and ten years. Criminologists exploit natural variations in sentencing and examine public safety outcomes. They find that each additional year of incarceration is actually having a net-negative effect on public safety: incarceration is criminogenic and expensive, and this outweighs its crime-stopping incapacitation and deterrence effects.

A “progressive” prosecutor might see this study finding that “incarceration for offense X is criminogenic” and conclude that incarceration is always bad. He may sharply reduce sentences for this crime — maybe even down to zero! — because he thinks the relationship between incarceration and public safety is negative and linear:

But what if the optimal sentence (the sentence which maximizes incapacitation and deterrence effects while minimizing criminogenic effects) is actually six years, and it is only beyond that point that each additional year of incarceration has negative crime-fighting utility? If so, the progressive prosecutor’s choice to jump from Point A (nine-year sentences) to Point B (zero-year sentences) will have a disastrous impact on public safety, because each marginal year of incarceration was having a beneficial public safety effect until the sixth year:

In this hypothetical scenario, the data wasn’t “wrong” — the criminologists were right that every marginal year of incarceration was having a negative effect on public safety. The error was linear thinking. The fact that a marginal year of incarceration currently has a negative effect doesn’t mean incarceration is always a net negative, so if you suddenly reduce incarceration to zero or near-zero you’ll kick off a crime wave.

It’s also very possible, of course, for this same error of linear thinking to run in the opposite direction. A person who is “tough on crime” may be encouraged by evidence that a particular crackdown is working, and so go hog-wild on incarceration or stop-and-frisk because they incorrectly believe the public safety returns are limitless.

Caveats and conclusions

There are several important caveats to the idea I’m putting forward here.

First, second-order effects (which I write about a lot on this blog) mean that when we’re talking about the utility of any particular public safety intervention, it seems very likely that weird things happen at the extremes. If a prosecutor tells police they won’t prosecute a certain crime at all, police may simply stop arresting people for that crime.Also, uncertainty matters, and criminals will adjust their behavior once they learn that committing a certain crime never results in an arrest or prosecution.

Incarceration in particular probably has really strong effects at the extremes. My experience was that the average criminal really didn’t want to go to jail. So the difference between zero days in jail and one day in jail is probably pretty significant in terms of deterrent value. But once he’s already in jail, the difference between one day in jail and two days in jail matters a lot less. So the return (in terms of deterrence and incapacitation minus criminogenic effects and system costs) on the marginal day of incarceration (for the first ten days) probably looks more like this:

If this is correct, you can probably reduce misdemeanor sentences from ten to five days without having much of a negative impact on public safety. But if you reduce them all the way to zero, bad things are going to happen.

Second, I doubt that the marginal utility of any particular criminal justice intervention is fixed. It’s possible to increase the utility of any particular intervention — for example, police stopping a gang member on probation for a gun crime is a more valuable stop, from a public safety perspective, than stopping an 80-year old grandmother with no criminal record. Another example might be improving returns on incarceration by rehabilitating offenders through inpatient drug treatment. In the same vein, the marginal year a repeat offender spends in prison is surely far more effective than the marginal year a first-time offender spends in prison:

The descriptive statistics in the Suffolk County study that Rollins liked says the marginal misdemeanor case in which a defendant was “prosecuted” lasted for six months, involved no jail time/bail, and 77% of the defendants prosecuted were never formally convicted. So here, you’ve got here all the costs of prosecution (arrest record, making defendants come into court, criminal justice system costs) with basically none of the deterrent or incapacitation benefits that would come from jail time or a formal conviction. It’s not surprising, then, that the marginal prosecution was worthless. I would love to see the same study done on cases where the marginal defendant was actually convicted, or better yet, sentenced to a day or more in jail.

Third, and perhaps most importantly, not everything can be measured in purely utilitarian terms. Issues of morality and justice have to be taken into account. It is probably not efficient to incarcerate Anders Brevik for life, and yet seeing as how he murdered 77 people, I would say the sentence he received in Norway (21 years) is not sufficient. Similarly, it’s possible that expending the resources it takes to solve every single murder is very inefficient for police (or even a net negative) from a crime-prevention standpoint, since the resources used there could have been put to better use in other areas. But as a matter of justice, solving every murder seems very important and worthwhile. Justice is hard to quantify.

My main point is this: making sudden and dramatic changes to policing will probably always turn out badly, and should be avoided. You may think police are too heavily involved in providing mental health services, but taking police out of mental health calls completely? That’s going to turn out badly. Police may be making too many traffic stops, but completely banning them? That’s also going to turn out badly. Even if you are very convinced that a particular criminal justice intervention isn’t useful right now, that doesn’t mean it is always worthless. Changes to policing should be implemented gradually, with a careful eye towards identifying the optimal level of police intervention—not simply eliminating it.

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