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To be fair, there is legal precedent for cops not being too smart.

https://ny.prelawland.com/post/719662253773832192/too-smart-...

They're allowed to not hire someone if their IQ is too high. The stereotype is at the very least based on truth, and has been affirmed legally.

Too Smart for the Job: Jordan v. The City of New London

By Emma Babashak, Columbia University, Class of 2024 June 9, 2023 In the case of Robert Jordan v. City of New London and Keith Harrigan (2000), the plaintiff, Robert Jordan, alleged a violation of...

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People keep saying this and this case from 2000 is the one instance anybody has been able to cite. Most police agencies use standardized domain-specific written exams --- the PELLETB, NTN, IOS --- that are both not general cognitive exams and have no ceiling score.

This really seems like one of those too-perfect Internet myths that just isn't ever going to die. I think the balance of evidence is that if you picked any police department in the US out at random, it would have the opposite of the incentive claimed in your comment, and no ceiling on general cognitive ability whatsoever.

Sure, you can argue that despite being allowed to, most police departments do not discriminate in that way, but the legal precedent provides credence and legitimacy to the stereotype, regardless of its truthfulness, which is what I pointed out. I don't think any real data on this would be available, though, so I think most people (you and I included) just go by vibe, so in the absence of evidence one way or the other, the stereotypes will prevail, regardless of accuracy.
I would take the counterargument more seriously if anyone could name just one police department that administers IQ tests to applicants.