compulsion

noun3

1. •
   The use of authority, influence, or other power to force (compel) a person or persons to act.

   • From the opening of the City & South London Railway independent electric locomotives were used under compulsion of the Board of Trade. — 1941
2. •
   An irrational need or irresistible urge to perform some action, often despite negative consequences.

   • During the basketball game, I had a sudden compulsion to have a smoke.
3. •
   The lawful use of violence (i.e. by the administration).