The dynamics of deterrence

The more credible you make a threat, the smaller the risk of actually having to carry it out. That may be the key to having less crime and less punishment.

Crime is a Bad Thing. So is punishment. Right now, the United States has too much of both.

One factor that leads people to break laws (or violate other rules where violation risks a sanction) is that they’re likely to get away with it. Given many violations and a limited capacity to sanction, the risk of being punished may be small. And once potential violators know that, the number of violations rises further, further reducing the risk of being punished for those who do violate, in a vicious circle.

But the circle can go the other way around. Increasing the number of sanctions in the face of any given violation rate will increase the risk of sanction for each violator. Some of them &#8212 the ones for whom violating was only marginally better than complying at the previous sanctions risk &#8212 will then go back to compliance, which further increases the risk for all the remaining violators, and so on.

So high violation rate/low punishment risk and low violation rate/high punishment risk may both be stable equilibria: the dynamics of crime and punishment &#8212 of deterrence &#8212 are a case where positive feedback can lead to “tipping” phenomena.

If you’re in charge of handing out the punishments in a situation at the high-violation-rate/low-punishment-risk equilibrium, and your goal is to reduce the violation rate, what can you do? If you could borrow some spare sanctions capacity for a while, you might be able to force the rate of violations down to a level where you no longer need the extra capacity to keep the situation under control.

But if you can’t do that &#8212 if no temporary surge capacity is available &#8212 perhaps you can get the same result by concentrating your threats, rather than allocating them at random among the violators. Pick out a number of potential offenders equal to the number of sanctions you have available, and tell them that they’re now in the zero-tolerance group: every violation by any one of them will be punished. You have enough capacity to carry out that threat, even if all of them violate.

Once they start to figure out that your threat was for real, they will reduce their offending activity. (That doesn’t require that they be perfectly rational, only that they dislike whatever you’re using as a sanction enough to want to avoid it.) As their violation rate falls, you will find yourself with more sanctions capacity than you need to punish violations within the zero-tolerance group, which allows you to increase the size of that group. Once the newly threatened people respond by reducing their violation rate, you can expand the group still further. And so on, until (ideally) the entire population of potential offenders is in the low-violation-rate/high-punishment-risk equilibrium.

The key is to establish and maintain the credibility of your deterrent threat. The more convincing the threat is, the less likely it is that you will have to carry it out. That’s the logic of “broken-windows” policing, of “coerced-abstinence” management of drug-involved offenders under community supervision, and of low-arrest crackdowns on open drug markets.

I’ll be giving talks on this theme at noon this Wednesday in Room 610T at John Jay College in New York (899 10th Avenue [@59th St.]) and again on Monday 12/18 at the Harvard Center for Risk Analysis. Both talks are open to the public, so come and heckle if you’re around.

Author: Mark Kleiman

Professor of Public Policy at the NYU Marron Institute for Urban Management and editor of the Journal of Drug Policy Analysis. Teaches about the methods of policy analysis about drug abuse control and crime control policy, working out the implications of two principles: that swift and certain sanctions don't have to be severe to be effective, and that well-designed threats usually don't have to be carried out. Books: Drugs and Drug Policy: What Everyone Needs to Know (with Jonathan Caulkins and Angela Hawken) When Brute Force Fails: How to Have Less Crime and Less Punishment (Princeton, 2009; named one of the "books of the year" by The Economist Against Excess: Drug Policy for Results (Basic, 1993) Marijuana: Costs of Abuse, Costs of Control (Greenwood, 1989) UCLA Homepage Curriculum Vitae Contact:

20 thoughts on “The dynamics of deterrence”

  1. Actually crime has been dropping for years. Mostly this is because there are fewer people in the crime-committing age group.. If you really want to stop crime, the easiest way would be to lock up everyone between thhe ages of fourteen and thirty.
    Failing that,t another effective way to fight crime is to create the sort of couuntry where everybody has a reasonable expectation of being able to get a living wage job.
    Which is not to say that the theory you present is wrong. Indeed it is exactly the principle behind effective classroom management at any public school.
    It only works, however, when the teacher is there.

  2. What about monitoring capacity? The model seems to assume that monitoring is costless, since if A1 complies under the deterministic strategy A2 will comply since he faces certain punishment. But if monitoring capacity limited, then it will be necessary to reduce monitoring of A2 to be sure of catching A1.
    More generally, shouldn't the probability of apprehending a given offender under the different scenarios come into play? By focusing on one potential offender we reduce the probability of catching the other, affecting his payoffs.

  3. I question the premise, "Crime is a Bad Thing." A substantial percentage of prosecutions in the U.S. are for victimless crimes — crimes involving drugs (except when sold to a minor), prostitution, gambling, pornography (except when produced with a minor) — and these acts may or may not be bad for the person who engages in them, depending on the circumstances, and should not be the law's concern in any event. Does the fact that prosecutions for these crimes foster disrespect for the law generally, and, in the case of drug crimes, is a major cause of other crimes, factor into the analysis?

  4. Bernard: Yes, the model abstracts away from the monitoring problem. That's still relevant to decisions about sentencing and handling probation violations, where sanctions capacity is scarce even compared to the number of detected violations. It's also relevant to the police decision about whether to arrest people openly committing offenses.
    Rilkefan: No, those equilibria are stable under fairly large perturbations. (If you prefer, they're "strong attractors.") There's an unstable tipping point in between. This is the standard "tipping" situation. A coin is stable heads up, stable tails up, and unstable on edge.
    Henry: You need to distinguish between acts that in your view shouldn't be crimes and acts without victims. Ask anyone who lives near a crack house or open-air drug market whether selling illicit drugs is victimless. But be prepared to duck. (Note that the same is true of taxes: New York City now has violent and disorderly street markets in untaxed cigarettes smurfed in from Indian reservations.) Yes, that's a reason to be careful about what we prohibit, regulate, and tax. But once the laws are in place, many of those crimes have victims.
    Not all of them, of course: An outcall prostitution service doesn't have the neighborhood impact of a brothel or streetcorner prostitution. Drug dealers who deliver based on calls to their cell phones (a common practice in some big cities) don't have the neighborhood impact of street dealers. Smart policing pays attention to those distinctions.

  5. Bernard, in that case monitoring resources might be the limiting factor, and monitoring could be skewed towards a selected 'zero-tolerance' group.

  6. "Ask anyone who lives near a crack house or open-air drug market whether selling illicit drugs is victimless." But it is not victimless only because the drugs are illicit. Ask anyone who lives near a liquor store whether selling legal alcoholic beverages is victimless.

  7. That sounds great policy-wise, but I can guess exactly when it would fail politically: as soon as someone is murdered by an ex-con from the non-zero-tolerance parollee pool. Not every such murder will be newsworthy enough to generate local-news outrage, but eventually you'll get a perfect storm: photogenic victim, just-released recidivist perpetrator, and a reporter with enough initiative to go to the local prison and find out how the perp got out so fast, even though the prison seemed to have enough space for lots of small-timers.
    You can imagine the local-TV interviews. "They had this monster locked up, but they let him out early to free up cells for shoplifters under this zero-tolerance random-flag program, and that's how he got out to kill my baby … "
    That's a pity, but my impression is that this is the fate of many long-term crime policy ideas. Am I wrong? Or is there a way around this sort of problem?

  8. Mark,
    Fair enough, where sanctions capacity is important. Do you know if prosecutors follow something like this strategy in plea bargaining? Is it an implication that they should?
    True, but that introduces two problems.
    One is determining the optimum use of monitoring resources (watching two people twelve hours a day may not cost the same as watching one for twenty-four hours).
    The other is that reducing monitoring of A2 to concentrate on A1 tilts A2's strategy in favor of offending, whereas costless monitoring assures that A2 will be apprehended.

  9. Henry: As I said, whether or not an activity ought to be illegal has no bearing on whether carrying it out illegally damages people. But in answer to your question, in the sort of poor neighborhoods that have destructive open drug markets, liquor stores are also loci of disorder, roundly hated by the neighbors.

  10. Ben,
    Previous posts on situations where this kind of policing has been used successfully have it focusing on non-violent crimes, usually the crimes that generate violence but for which not all involved are violent, like drugs. It might be useful to think of the excess capacity as capacity available while maintaining present enforcement ability for violent crime.

  11. What Ben M. said…
    Or to put it another way, even if this policy were effective, it violates the basic principle that "the punishment should fit the crime". Ben M. just points out a particular way that the punishment failing to fit the crime could become a major political issue.
    One could implement this idea with the initial "zero-tolerance" group being violators whose last name begins with the letter "A", and move to other letters of the alphabet as capacity becomes available. Of course, if implemented this way, the injustice of the policy would be obvious…

  12. The punishment does fit the crime, the idea isn't the death penalty for littering. "High punishment" refers to the rate of punishment, not the severity. It is a long post but this post should clear up any concerns Alex or Ben may have:
    In case that didn't work it is under "Drug Policy" and titled "The low-arrest drug crackdown".
    For another real, inadvertent example, look at the crime statistics for USC. In one of the worst neighborhoods one can imagine and it has lower crime numbers than UCLA, which is in arguably one of the better neighborhoods. How can this be? Because USC invests heavily to increase enforcement capacity making sure that crime is not an option due to the certainty of being caught. If you were to ask me I would suggest using the theories stated in this post and USC as the low crime starting point for efforts to clean up South Central.

  13. If the punishment fitted the crime in drug cases, you'd be talking about a high rate of people recieving the equivalent of traffic tickets, not jail terms comparable to homicide cases.
    Drug offenses simply aren't that objectively serious, to warrent such harsh penalties. The penalties are harsh to compensate for the objective fact that punishment is rare. And punishment is rare for reasons inherent to any victimless crime: Where everybody involved in a transaction wants it to happen, the police have no easy way of enforcing the law. Normal techniques do not work.
    And so they resort to abnormal techniques, and we slowly decend into a police state.

  14. Does it strike anyone else that abstracting away the monitoring capacity is really assuming a can-opener, especially in situations where monitoring and sanctions come out of (more or less) the same budget? As you monitor a large and large group, unless you have arbitrary funds, your capacity for sanctions will decrease in an absolute as well as relative fashion.
    (Sanctions are also being abstracted to a significant extent here — do you simply need enough police officers to arrest and book all of the members of your zero-tolerance group, or enough cells to hold them for longish stretches, or that plus enough prosecutors and lawyers to process them in a reasonable time, or what? Depending on your criminal population and the strength of the incentives for criminal behavior, the low-offense, high-punishment-risk state could be subject to rapid tipping if a bunch of criminals all do the math and decide that, as for flocking prey species, there's safety in numbers.)
    Ultimately I think some of the commenters touch on another game-theoretic question, namely how you maintain the low-offense, high-punishment-risk state of affairs once achieved. Public budgets being what they are, the temptation for some low-crime jurisdictions to think they could do with less monitoring and sanctions capacity will always be with us. Not only does that risk a return to the high-offense, low-punishment-risk condition, but it poses a risk of unemployment for the folks in the monitoring and sanctions industries. So perhaps the next thing to figure out is the equilibrium level of crime and punishment that will keep police, judges and jailers in their jobs without to much risk of big shakeups to combat perceived ineffectiveness.

  15. What's the model for the coin flipping over in the first place, then? An interruption in local gravity? And the idea is that there's some Higgs potential – mexican-hat shaped – so pushing in the normal direction is useless, and one instead needs to push in a different direction?

  16. Brett
    You make a good point about the excessive use of police resources on drug cases.
    I think we have to distinguish on different drugs.
    Heroin we can manage addicts on a government-supplied scheme (incidentally cutting the skids out from under the Taliban). This is already under trial in Europe, and in fact was the rule in Britain before 1970. The long term consequences of (clean) heroin addiction are actually fairly benign– and remission is common.
    Marijuana has harmful long term consequences (psychosis!) but in small doses is relatively harmless, and has therapeutic applications which are being ignored because of its criminal status. It's also less addictive than alcohol.
    So another candidate for some form of regulation.
    'E' (MDMA) probably has serious long term consequences, but is basically a youth/club drug. The Dutch police offer free quality testing in the clubs. It's probably less harmful to young people than alcohol abuse. Again a tick for tolerance.
    Tobacco, alcohol, caffeine are all addictive, but we know where we are on these.
    On crack cocaine, and crystal meths, I have struggled to find a way that we can manage the enormous harm the drug can cause to users, their families, and society around them. Here, I think, zero tolerance is more appropriate.

  17. Anybody who's familiar with the history of Prohibition will be aware of the way it shifted alcohol consumption away from wine and beer, to hard liquor. And will be aware of how consumption patterns have gradually reverted after repeal.
    Some of the most dangerous of the illegal drugs are consumed largely as a result of the war on drugs distorting consumer preferences, and especially distorting producers' preferences. (Some rather nasty "designer" drugs have come from the war driven search for compounds whose precursors haven't yet been restricted.)
    The flip side of that is that the pharmaceutical industry's enormous research resources have, thanks to Prohibition Mk II, NOT been devoted to discovering safer recreational drugs.
    In short, it's a serious mistake to presume that consumption patterns under the government's increasingly heavy thumb are the same, only a bit lower, as they would be in a legal market. We have every reason to suppose they wouldn't be.
    Remember, the primary way people used to consume cocaine was in… Coca cola. Not snorted or shot into their veins. Caffeine is a cocaine substitute. I suspect that in a drug free market, caffeine would be displaced by something like Modafinil, even more effective and safe.

  18. As much as some of us would like this to be an issue of why we can't get high on the way to work, thats really not the point of this post. Nor is the fear that actual subject of this post may be used to throw pot using teenager in prison for life. It is about effective use of resources to combat crime as a whole, and more specifically violent crime. Don't get me wrong, I tend to agree with a lot of what is being said but it seems remarkably off-topic.
    While I suppose a two dimensional Higg's Potential models a situation of two stable extrema, but an interruption in local gravity? I think that would be ignoring the effect of the measurement.

  19. My question was how one finds oneself in one extremum – either there has been huge noise or an extraordinary force applied, or the potential was time-dependent – else a crime-ridden area had to have contained a critical criminal density forever.

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