The gradually escalating levels of destructive obedience in the milgram experiments best illustrate one of the potential dangers of the phenomenon.

I believe the answer is: the foot-in-the-door phenomenon

the foot-in-the-door phenomenon describe a situation when a person become more compelled to agree toward a big request after previously agreed to do smaller request first. In the Milgram experiment, the subject agreed to imposed higher voltage to other after previously agreed to give smaller voltage