The best replacement for representative democracy is republic.

The best alternatives to representative democracy are rated as following:
★★★★★  republic
★★★★  direct democracy
★★★  constitutional republic
★★  participatory democracy
★★  democracy
★★  democratic republic
★  direct
★  parliamentary democracy
★  constitutional democracy
★  pure democracy
  constitutional monarchy

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Speaking about representative democracy, one probably shouldn't forget about direct democracy.

Other search terms related to representative democracy and their ratings are:
★★★★★ direct democracy
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