A practice I often noticed on the I-90 in New York State (Or I-25 where I now live) is that people speed on the highway until they see a police officer with a speed gun (or with flashing lights writing a ticket to some poor driver on the side of the road), and then they slow down and drive at the speed limit for a while.
What I don’t understand is that the probability of two police officers one after the other is very low (lower than the probability of having one), so shouldn’t people speed up after they see a police officer with a speed gun?
This is an interesting observation and although I don’t have data on this, I agree with you that the occurrence of multiple police officers on the highway is most likely negatively correlated. This means that if you see one, you are less likely to see another immediately after. And you are right that this suggests that rationally, people should speed up immediately after passing a police officer.
While the act of slowing down after passing a police officer might be irrational, I suspect that people generally want to be law abiding and don’t want to take too much risk while driving. So seeing a police car serves as a reminder of these two basic ideas.
Here is an experiment that could be fun to do:
In one condition simply and inconspicuously measure speed of passing cars at multiple places along the highway.
In a second condition, do the same but in addition have a visible police car between two of the places where you are measuring speed. The idea being that people will slow down after passing the police-which is your point.
In a third condition we will have a sign that reads “Reminder: the speed limit is 55 MPH. Drive safely.” I suspect that this sign will also reduce speed, but the question is whether it will reduce speed to the same degree as the police car. If it does, then we will know that the speed reduction effect is fully due to the reminder function and not to the fear of being caught (though of course it is possible that they will both work).
Maybe some police department will help us do this.