The Collaborative International Dictionary of English v.0.48:

Prerogative \Pre*rog"a*tive\, n. [F. pr['e]rogative, from L.
   praerogativa precedence in voting, preference, privilege, fr.
   praerogativus that is asked before others for his opinion,
   that votes before or first, fr. praerogare to ask before
   another; prae before + rogare to ask. See Rogation.]
   [1913 Webster]
   1. An exclusive or peculiar privilege; prior and indefeasible
      right; fundamental and essential possession; -- used
      generally of an official and hereditary right which may be
      asserted without question, and for the exercise of which
      there is no responsibility or accountability as to the
      fact and the manner of its exercise.
      [1913 Webster]

            The two faculties that are the prerogative of man --
            the powers of abstraction and imagination. --I.
                                                  Taylor.
      [1913 Webster]

            An unconstitutional exercise of his prerogative.
                                                  --Macaulay.
      [1913 Webster]

   2. Precedence; pre["e]minence; first rank. [Obs.]
      [1913 Webster]

            Then give me leave to have prerogative. --Shak.
      [1913 Webster]

   Note: The term came into general use in the conflicts between
         the Crown and Parliaments of Great Britain, especially
         in the time of the Stuarts.
         [1913 Webster]

   Prerogative Court (Eng. Law), a court which formerly had
      authority in the matter of wills and administrations,
      where the deceased left bona notabilia, or effects of the
      value of five pounds, in two or more different dioceses.
      --Blackstone.

   Prerogative office, the office in which wills proved in the
      Prerogative Court were registered.
      [1913 Webster]

   Syn: Privilege; right. See Privilege.
        [1913 Webster]

WordNet (r) 3.0 (2006):

prerogative
    n 1: a right reserved exclusively by a particular person or
         group (especially a hereditary or official right);
         "suffrage was the prerogative of white adult males" [syn:
         prerogative, privilege, perquisite, exclusive
         right]

Moby Thesaurus II by Grady Ward, 1.0:

81 Moby Thesaurus words for "prerogative":
   absolute power, absolutism, accomplishment, advantage, appanage,
   appurtenance, ascendancy, authority, authorization, birthright,
   claim, competence, competency, conjugal right,
   constituted authority, deanship, delegated authority, demand,
   divine right, droit, due, excellence, exemption, faculty, favor,
   franchise, greatness, immunity, inalienable right, incomparability,
   indirect authority, inherent authority, inimitability, interest,
   jus divinum, lawful authority, lead, legal authority, legitimacy,
   liberty, majority, natural right, one-upmanship, perquisite, power,
   precedence, predominance, predomination, preeminence,
   preponderance, prepotence, prepotency, prescription, prestige,
   presumptive right, pretense, pretension, priority, privilege,
   proper claim, property right, regality, right, right-of-way,
   rightful authority, royal prerogative, sanction, seniority, skill,
   success, superiority, the say, the say-so, title, transcendence,
   transcendency, vested authority, vested interest, vested right,
   vicarious authority, virtuosity



Bouvier's Law Dictionary, Revised 6th Ed (1856):

PREROGATIVE, English law. The royal prerogative is an arbitrary power vested
in the executive to do good and not evil. Rutherf. Inst. 279; Co. Litt. 90;
Chit. on Prerog.; Bac. Ab. h.t.



Bouvier's Law Dictionary, Revised 6th Ed (1856):

PREROGATIVE, civil law. The privilege, preeminence, or advantage which one
person has over another; thus a person vested with an office, is entitled to
all the rights, privileges, prerogatives, &c. which belong to it.



The Devil's Dictionary (1881-1906):

PREROGATIVE, n.  A sovereign's right to do wrong.