Sheriff Joe Arpaio of Arizona’s Maricopa County is being sued by the Dept of Justice for discrimination through the use of profiling. When ol’ Sheriff Joe stops a car for some traffic, licensing, or other safety violation, it seems that he puts the occupants through an immigration check nine times more frequently when they are Hispanics, than when they are not. This to the feds and other soft heads is clear discrimination through profiling; is it not? Let’s return to the sheriff after a couple of preliminaries.
Most people who put their feelings on the back burner for a bit and revert to reason will agree that discrimination occurs when some benefit or sanction is directed toward a segment of population that is out of kilter with the proportion of the population having an attribute that legally deserves the benefit or sanction.
Let’s say that 15% of county residences have a specific building code violation, and county winds up writing citations and fining 25% of residences for that violation. It is clear that 10% of residences have been discriminated against since they can show that no violation existed on their properties.
Also if a population of equally developmentally handicapped people were supposed to get a certain subsidy, and upon examination it was later found that payments went excessively to a subset of the handicapped that had another attribute (say, they were all tall) not contemplated in the law, then the subset without the secondary attribute (the short ones) suffered discrimination.
It gets a little dicier when we start dealing with realworld uncertainties, and when we have to allocate scarce resources to achieve a certain objective. And this brings us to some of Sheriff Joe’s problems. So let’s get a few numbers under our belt (they may be off a bit, depending on your source, but I tried to get them all from the Census Bureau, so they should work for this discussion.)
So here’s the problem. If Sheriff Joe stops a car at random for some reason, the base rate or probability that it contains an illegal is at least P(illegal) = 500,000/6,400,000 = 0.078 or 7.8%. He then walks up to the car and sees it contains one or more Hispanics. Now the question arises ‘what’s the chance or probability that the car contains an illegal, given that its occupant(s) is/are Hispanic?’ This probability, written as P(illegal|Hispanic), is critical because going through a legal residency check is a hassle for both the deputy and the car’s occupants, and it takes time and money to complete. It also has an obvious public relations cost as we can see.
If it turns out that P(illegal|Hispanic) is sufficiently large, then the deputy should go through the hassle to check the occupants for legal residency since s/he has reasonable cause to suspect illegals. So let’s compute the needed probability from the formula discovered by the Reverend Bayes which was introduced here and here. We repeat it below in the needed form.
To calculate the above formula we need the likelihood ratio for the ‘evidence’ (i.e. occupant(s) Hispanic) that impact the deputy’s hunch (or hypothesis) of illegals in the car. This ratio is obtained by simply dividing the probability that the occupants are Hispanics, given that they are illegals, by the probability that the occupants are Hispanics, given that they are NOT illegals. The first term (numerator) we calculate as P(Hispanic|illegal) = 0.999, the almost certainty argued above. The second (denominator), from the data above, is P(Hispanic|NOT illegal) = (1.9M – 0.5M)/(6.4M – 0.5M) = 0.237. So that gives us the desired likelihood ratio L(Hispanic|illegal) = 0.999/0.237 = 4.210. Sticking this and P(illegal) = 0.078 into the above formula, and recalling that P(legal) = 1 – P(illegal), gives us the sought for answer, P(illegal| Hispanic) = 0.263, or more than one chance in four that an Arizona car containing Hispanic occupants has at least one illegal alien among them.
It is clear that with just the evidence of Hispanic car occupancy in Arizona, the deputy should check the legal residence status of the occupants because there most certainly exists reasonable cause to believe that an (illegal entry) crime has been committed. Intuition tells us that the numbers are correct and in the ballpark because of Arizona’s 1.9M Hispanics, 0.5M are illegals. Sheriff Joe didn’t even need Bayes to figure out what his deputies should do.
But, of course, that is not the end of it, and I’ll add more to this numerical noodling another time.
For now we can wonder at what level of certainty that a crime has been committed does it become reasonable to investigate further. Should such actions be pursued when the chances are about one in four, how about one in twenty, how about nine out of ten? At what level does discrimination, and against whom, begin or end? When we take out arbitrary feelings from the discussion, it has been my experience that the progressive mind is nowhere to be found. Perhaps we live in a new age.
(BTW, we can dismiss that butt stupid congressman who outraged on camera last week that during those traffic stops Sheriff Arpaio’s deputies “are treating those immigrants as if they were criminals!” Well no s&*t Red Ryder.)