If your principal overlooks cheating on standardized tests because it makes his school look better, he is guilty of connivance, or allowing an unethical act to take place.

If your siblings conspire to play a prank on you, you could say they are conniving to trick you. If your mother knew about it, but chose to allow the act to happen, you'd probably be pretty angry at her connivance. Or you could follow the old saying, "Don't get mad, get even!"

Definitions of connivance
  1. noun
    agreement on a secret plot
    synonyms: collusion
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    type of:
    the verbal act of agreeing
  2. noun
    (law) tacit approval of someone's wrongdoing
    synonyms: secret approval, tacit consent
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    type of:
    approval, commendation
    a message expressing a favorable opinion
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