Why high accuracy rate really matters

Your editorial "State can't rewrite federal worker law" displays a poor understanding of probability that is unfortunately all too common in America today. Achieving 99-percent accuracy for the E-Verify may or may not be possible, but at its current level of accuracy, estimated at 94 percent, a person receiving a "not verified" result has a less than 50 percent chance of actually being an undocumented immigrant. That means that over one half of the people refused jobs by E-Verify will actually be legal workers. The key to understanding why is Bayes' Theorem: P(A|X) = P(X|A)*P(A)/(P(X|A)*P(A) + P(X|~A)*P(~A))

In English, what this says is that the probability that a person is an undocumented worker given an "unverified" result is equal to the probability of a unverified result for an undocumented worker (94 percent) times the probability that a given worker is undocumented (which we'll estimate to be 5 percent), divided by the sum of that same value plus the probability of an unverified result for a documented worker (6 percent) times the probability that a worker is documented (95 percent). According to the latest estimates from Department of Homeland Security, the percentage of the U.S. population consisting of illegal immigrants is around 3.6 percent, (11 million out of 300 million), but it is likely that a greater number of those illegal immigrants are of working age than legal citizens, so I used an estimate of 5 percent instead. Calculate all that out and you get a result of 45 percent.

So the probability that a worker given an "unverified" result by E-Verify is actually an illegal immigrant is only 45 percent. Does that seem fair to you? At an accuracy rate of 99 percent, that probability is raised to 83 percent, which is a much more acceptable level. Of course, the supremacy clause probably makes all of this irrelevant, but I can't resist an opportunity to teach people about Bayes' Theorem.

Eric Russell

Chicago