Dumb cop/reasonable cop routine
A dumb cop/reasonable cop routine was a negotiating maneuver in which two parties manipulated another by posing as a stupid person and their more intelligent, rational partner.
In 2381, Carol Freeman believed Grand Nagus Rom and First clerk Leeta were employing this routine to get a better deal on their Federation membership application, but Admiral Vassery didn't heed her warning. (LD: "Parth Ferengi's Heart Place")