"special right or privilege granted to someone; characteristic right inhering in one's nature, office, or position," late 14c., prerogatif, (in Anglo-Latin from late 13c.), from Old French prerogative (14c.) and directly from Medieval Latin prerogativa "special right," from Latin praerogativa "prerogative, previous choice or election, privilege."
This was originally (with tribus, centuria) "unit of 100 voters who by lot voted first in the Roman comita," noun use of fem. of praerogativus (adj.) "chosen to vote first, that is asked before," from praerogere "ask before others," from prae "before" (see pre-) + rogare "to ask, ask a favor," apparently a figurative use of a PIE verb meaning literally "to stretch out (the hand)," from root *reg- "move in a straight line." In Middle English also "an innate faculty or property which especially distinguishes someone or something."