That's the problem - in the USA, detective and police are not two different occupations. You can only become a detective by being promoted from the ranks of policemen.

i.e. if the maximum IQ for a beat cop is 110, naturally the maximum IQ for a detective will also be 110.

The police union is mostly responsible for this, because they don't want people coming in from outside and skipping the grind to become detectives.

The pool of detectives is typically pulled from line police, isn't it? By restricting the IQ of those enforcing the laws, you're creating a poor candidate pool for detectives.

In France, detectives and police officers have to go the university to study the law and other subjects. I thought it was the same in most countries, isn't it?

In the U.S., different organizations have different standards. There are 2- and 4-year criminal justice university programs, but many police departments only require a high school diploma. A criminal justice degree or other related degree is usually a plus even if it's not required. As an example, the Minnesota State Patrol requires the applicants either have a 2- or 4-year degree in any subject or be a licensed peace officer (which could have happened through a criminal justice degree or through a police academy).

Most large cities have their own police academy or there's a regional academy that several cities use. Police academy is usually three or four months of intensive training that new recruits go through (a little like boot camp for the armed forces). After graduating from an academy, the officers are sometimes rotated through probationary assignments and then given a more permanent assignment.

Detectives and other specialists are generally promoted out of the ranks of police officers.

Not always. In the US, more common is a sort of police academy. Actual higher education is not really required.

Exactly, police departments do want to hire smart people, just not too many and they have to be the right kind of smart.

My brother is a cop and an inspector (detective for you in the US). He's smart but not at all bookish. So he's got the right "cop" personality and the fact that he was smart was a good thing.

Now that he's hiring cops, he's careful to only hire "smart" cops if he has a sergeant position opening up in a few years or if he's ok with them moving on to a new department in 3-5 years.

My uncle was a "dumb" cop for 25 years. He was quite happy writing tickets and arresting people for the bulk of his career. He only took a sergeant's job when street work got to hard on him physically.

I think you are describing something similar to the US Military where there are to "paths" into it: officers and enlisted.

In the US, there is one for police: police academy and then work your way up the ranks to detective, etc.

That isn't even close to being true. SNCOs and WOs need to be pretty clever, and they start off as E-1s. It works for the military, but then they aren't taking the short sighted position of filtering out folks who are "too smart" to be an E-1.

Uh, police detectives?