Are Police Better People? Probably Not.

After reviewing the FCGDC data, it seems more likely that disparate black/white CJS outcomes are driven by police rather than judges or prosecutors. It seems the fundamental problem is that blacks are arrested at rates much higher than you would expect based on Fairfax County demographic information. There are a couple of ways to think about this. Perhaps (1) police officers tend to arrest blacks at lower level of confidence than whites with respect to suspected guilt. Perhaps (2) police arrest whites and blacks at comparable confidence levels but they target relatively black neighborhoods. Alternatively, (3) black populations may be associated with more crimes per capita than white populations. Given the relationship between income and criminality, it seems likely that the third option may have some truth – but it seems intuitively unlikely that this can account for the vast disparity between white and black arrest rates.

On the other hand, imagine that police officers maximize arrests at a certain level of confidence. Imagine that they have no bias against any particular group. In a highly stylized setting where a representative police officer can choose between patrolling two neighborhoods, identical in every way, he will be indifferent. Now suppose one neighborhood is somewhat poorer and the average inhabitant of that neighborhood is somewhat more likely to be involved in criminal activity. If this police officer is the ideal social agent (i.e. only cares about enforcing society’s laws), he will focus disproportionately on the poorer neighborhood. Specifically, he will patrol the poorer neighborhood until the marginal benefit of search (in arrests) equals the marginal cost (in time); at that point he will be indifferent between patrolling either neighborhood. In this scenario, the majority of arrests will come from the poorer neighborhood. If we assume the relative population size of the two neighborhoods is large compared to the size of the police force, we should expect a vast majority of arrests to come from the poorer neighborhood. If we add enough assumptions, we can create a scenario where the police behavior in Fairfax County today is “socially optimal” under the dubious meta-assumption that the Code of Virginia is optimally designed.

Can we test to see if reality approximates the story above? Yes. We already know that blacks and whites face comparable trial outcomes when controlling for income, so it’s unlikely that the average black defendant is more guilty than the average white defendant (i.e. the fact bundle against black defendants seems as strong as the bundle against white defendants on average). So what? The important takeaway from this fact is that one group doesn’t seem to commit crimes more conspicuously or hide crimes more adeptly; framed differently, it isn’t easier to search for either black or white criminals, although the density of criminals in one area may be relatively higher than that of another area. This makes reality look somewhat similar to the theoretical world outlined above. We also know that blacks are relatively more likely than whites to have charges against them dropped. This suggests support for police behavior hypothesis (1), police arrest blacks at lower confidence levels than whites. Reviewing the FCGDC police data itself, we find additional support for hypothesis (1) and (2).

With respect to the data, the distribution of average defendant win-rates associated with individual police officers is distributed fairly normally (we only looked at officers with at least 50 trials); but a histogram alone doesn’t tell us too much in this case. Maybe police arrest everyone at 50% confidence levels, and variation in defendant win-rates is more about whether the individual police officer is in the short-run or long-run. This is analogous to flipping a fair coin some number of times; over 50 trials, you may see a relatively large number of heads turn up. Over 1,000,000 trials, the Heads/Tails ratio should settle down at 1:1. Actually, we find that defendant win-rate by police officer doesn’t change much over time. A much more plausible story is that individual police officers arrest defendants at individual confidence levels. We also find substantial differences in black/white defendant win-rates across a number of police officers.

To sum up, even assuming the unexpectedly high level of black arrests is purely a function of crime density in poorer areas:

  • Individual police officers make arrests at dramatically differing levels of confidence.
  • A number of police seem to arrest blacks at lower levels of confidence than whites.

This is about the most charitable view of the arresting authorities one could reasonably give and it doesn’t exactly paint the police in a very flattering light.

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