legitimacy
The quality of being accepted as rightful, fair, or valid.
Legitimacy means having the right or authority to do something, or being considered valid and acceptable according to established rules or standards. When a government has legitimacy, people accept its right to make laws and decisions. When your teacher has legitimacy in the classroom, students recognize their authority to assign homework and maintain order.
The word appears in many contexts. A legitimate business operates legally and honestly, while a legitimate complaint is based on fair reasons that deserve attention. If someone questions the legitimacy of a game's outcome, they're wondering whether the result followed the rules properly.
Legitimacy often depends on how others view something. A king might claim legitimacy through a royal bloodline, while an elected president gains legitimacy through winning votes. In your own life, your legitimacy to speak on a topic comes from your knowledge and experience with it. If you've spent years studying piano, you have legitimate expertise to discuss music technique.
The opposite is illegitimate, meaning something lacks proper authority or validity. An illegitimate excuse for missing homework might be one that's obviously made up rather than genuine.
Notice that legitimacy is different from just having power. Someone might have the strength to take control, but without legitimacy, others won't truly accept their authority. Real legitimacy comes from being recognized as having the right to do what you're doing.