The best replacement for rule is act utilitarianism.

The best alternatives to rule are rated as following:
★★★★★  act utilitarianism
★★★  law
★★★  50 cent
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★★  policy
★★  regulation
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★★  eminem
★★  procedure
★★  congregational rule
★  indirect rule
★  standard
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★  act deontology
★  joyce rule
★  attwood
★  role
★  guideline
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  dillon\u0027s rule
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Speaking about rule, one probably shouldn't forget about minority rights.

Other search terms related to rule and their ratings are:
★★★★★ minority rights
★★★★ exceptions
★★★ pity
★★ ashanti
★ limits
★ trig functions
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