The best replacement for compulsion is addiction.

The best alternatives to compulsion are rated as following:
★★★★★  addiction
★★★  obsession
★★  craving
★★  duress
★  tic
★  compunction
★  habit
  impulse
  coercion
  impulsion

Your alternative for compulsion is not listed? Suggest!
Speaking about compulsion, one probably shouldn't forget about obsession.

Other search terms related to compulsion and their ratings are:
★★★★★ obsession
★ ocd
You have in mind a companion for compulsion and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of compulsion in all years. Click on graph for more.
compulsion
addiction
obsession