The best replacement for influence is power.

The best alternatives to influence are rated as following:
★★★★★  power
★★★★  authority
★★★★  control
★★  manipulation
★★  parental influence
★★  persuasion
★  inspiration
★  driving while intoxicated
★  effect
★  impact
★  rock music
★  affect
★  circle of concern
  motivation
  riot points
  trans effect
  informational influence
  family influence
  normative social influence
  duress
  fame
  coercion
  celebrity influence

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

Other search terms related to influence and their ratings are:
★★★★★ authority
★★ power
★ impact
You have in mind a companion for influence and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of influence in all years. Click on graph for more.
influence
power
authority