The best replacement for initiative is referendum.

The best alternatives to initiative are rated as following:
★★★★★  referendum
★★★★  guilt
★  project
★  program
★  initiation
★  guilt erikson
★  goal
  proposition
  autonomy
  at the initiative
  take the initiative
  strategy
  self motivation
  global trust
  potential social initiative
  campaign
  clean air act
  resolve
  popular referendum
  shame and guilt
  one with everything

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Speaking about initiative, one probably shouldn't forget about referendum.

Other search terms related to initiative and their ratings are:
★★★★★ referendum
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Google Trends

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initiative
referendum
guilt