A paddywagon is a vehicle used by police to transport large groups of people who are arrested. It may be descended from the archaic racial epithet "Paddy", meaning any Irish person. A common means of demeaning the Irish is to assert that they were frequently arrested, supposedly due to excessive alcohol consumption and the concomitant disruptive behavior--thus, a wagon for carrying "Paddies" became a paddywagon. The other possibility is that the name demotes the police who in New York were (still are?) overwhelmingly Irish for a time.
See also: stereotype, List of common phrases based on stereotypes
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