A prerogative is someone's special right or privilege. As Bobby Brown once sang, "I don't need permission / Make my own decisions / That's my prerogative."
Prerogative goes back to a Latin root for a group having the right to vote first (prae-, "pre-" + rogare, "to ask") and thus came to mean "privileged rank." In current use, it refers to a right or privilege held by any person or group. A near synonym is privilege, which puts more emphasis on the fact that others do not have it. The self-justifying phrase "That's my prerogative" (for example, in reference to changing one's mind) is quite common.