Max Policing Is Disproportionate

NYT: Minneapolis Police Use Force Against Black People at 7 Times the Rate of Whites … most use of force happens in areas where more black people live. Although crime rates are higher in those areas, black people are also subject to police force more often than white people in some mostly white and wealthy neighborhoods, though the total number of episodes in those areas is small. (More)

Star Slate Codex: When restricted to index crimes, dozens of individual-level studies have shown that a simple direct influence of race on pretrial release, plea bargaining, conviction, sentence length, and the death penalty among adults is small to nonexistent once legally relevant variables (e.g. prior record) are controlled.

in 62% of studies, police are not searching blacks disproportionately to the amount of crimes committed or presumed “indicators of suspiciousness”. In 38% of studies, they are. … there are two possible hypotheses here: either police are biased, or black people actually commit these crimes at higher rates than other groups. The second hypothesis has been strongly supported by crime victimization surveys,

Blacks appear to be arrested for drug use at a rate four times that of whites. Adjusting for known confounds reduces their rate to twice that of whites. However, other theorized confounders could mean that the real relative risk is anywhere between two and parity. … the people shot by police are less black than the people shooting police or the violent shooters police are presumably worried about. … 24% of blacks charged with drug dealing are acquitted, compared to only 14% of whites. … There seems to be a strong racial bias in capital punishment and a moderate racial bias in sentence length and decision to jail. (More)

The race and policing literature usually asks if the relative rates of stopping, arrest, conviction, sentences, etc. are disproportionate to race, after controlling for relevant factors like crime rates. I know this not just from the above Star Slate Codex review, but also because I’ve supervised many related research papers while teach grad law & economics.

In that context, the NYT article is crazy biased, as it just reports raw race correlations without controlling for anything. Surely NYT crime reporters know better; they should have at least noted relative black/white crime rates in Minneapolis.

The point of my post here, however, is just to point out that we shouldn’t expect proportionate stops, arrests, etc. in the context of policing designed to max crime reduction.

Imagine you are a police charged with cutting crime in your area. Or more realistically, as you don’t control courts or prosecution, you seek to max the number of crimes you charge that are convicted, weighted by their severity (perhaps proxied by sentence severity). Given this goal, you survey a world of possible and reported crimes, and for each one you estimate the chances that a crime happened there, and if so your chance of finding enough evidence to achieve a conviction. In such a situation, your efforts are often disproportionate.

For example, consider two possible murders, one with 10 and the other with 100 plausible suspects. If you put more effort into investigating that first murder, then each suspect there will get a disproportionate fraction of your attention, relative to their chance of guilt.

As another example, imagine a stream of cars passes you, and you pick which of them to stop. You put each car into a class with which you associate a prior rate of success in finding evidence of crime, weighted by crime importance. As you have limited time, you will limit yourself to stopping the car classes with the highest prior rate of success. This can result in a disproportionate relation between the rate of crime and stopping.

Policing that maxes crime detection and prosecution will not in general effect all people, groups, and situations in linear proportion to their rate or chances of committing crimes, perhaps weighted by severity. It will instead focus on the people, groups, and situations with the very highest rates of crime, and lowest costs of finding and collecting sufficient evidence of those crimes. And often that will produce rates of arrest, etc. that are disproportionate to crime rates.

We do know of one situation where maximizing police effort is proportionate to crime rates: when the chance to find sufficient evidence of crime uncovered goes as the logarithm of police effort re each possible crime. This is when every time you double your effort into a possible crime, say putting in two hours instead of one, you increase your chance of finding sufficient evidence on that crime by the same small amount (say 0.1%).

But while there may be situations where this applies, logarithmic dependence hardly seems a general feature of policing. For example, we we know that it fails at the high end, as the chance of conviction can’t exceed 100%. And it fails at the low end when there are fixed costs to start any investigation whatsoever.

We thus expect disproportionate crime-fighting efforts aimed at groups with higher crime rates, and especially at groups with the highest crime rates for identifiable subgroups. The variance, not just the average, matters a lot; the high tails of these distributions should dominate.

People who are poor, unskilled, and impulsive, and who mix more closely with other such folks, are likely to put in less effort, end less expertise, into hiding their crimes. As a result, police effort is likely to detect such crimes more easily. So police who are tasked with finding crimes are likely to focus their efforts more on these people. If you think that is a problem, an obvious solution would be to prioritize policing of the rich, skilled, and self-controlled. If police seek to max fines or sentence severity, why then increase the fines or sentences of such convictions.

But before you do that, ask yourself honestly: are the crimes of the rich actually more socially harmful? It makes more sense to me to just make punishments proportional to our best estimates of their social harm, regardless of who does the crime. And it makes sense to have punishments compensate for lower probabilities of conviction, to maintain the same expected punishment for someone who commits a crime.

But otherwise, if the poor are actually causing more harm, or making it easier to catch their crimes, well it makes sense to me to pursue those crimes more. Even disproportionately.