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The Police Are not Stupid
But they are not smart either.

In 1996 Robert Jordan took a test in the hope of becoming a police officer in the town of New London, Connecticut. Jordan scored very well on the test, especially on the cognitive ability portion, but he was not given an interview. When he asked why, he was told that, having scored a 33 on the test, he was not asked to interview because departmental policy was to extend interviews only to applicants who scored between 20 or 27 on the test.
A 33 on this test is equivalent to a high IQ. Results between 20 and 27 indicate average to slightly-above-average IQ. This limits police officers to, at best, only slightly-above-average intelligence. This test, and the policy, was not limited to the New London police department and, in fact, is an un-examined component of police hiring all across the United States.
Robert Jordan sued on the basis of discrimination. The suit was dismissed since, according to the courts, intelligence is not a protected class as well as the notion that everybody who took the test was treated the in same manner. ABC news conducted a survey after the case in 2000 and found that across the nation, at that time the average test scores of hired police officers were between 21 and 22.
This policy of hiring at most only slightly-above-average intelligence, which is nationwide and still much in effect, exists on the theory that exceptionally intelligent police officers will too easily become bored with the job and leave after only a few years of costly training. Besides very little scientific basis for this theory, there are several misprisions: first that highly intelligent people are helpless before boredom and have little sense of duty and diligence; and secondly, that seasoned officers of average intelligence teaching raw recruits of average intelligence might not be the main driver of cost in training.
The problem, of course, has nothing to do with anyone of average or above-average intelligence in particular. Any sizeable group will have a large number of their personnel — perhaps even a majority — of average intelligence. The problem is the wholesale exclusion — indeed denial — of anybody well above average or exceptional intelligence.