The Collaborative International Dictionary of English v.0.48:

Eligibility \El`i*gi*bil"i*ty\, n. [Cf. F. ['e]ligibilit['e].]
   The quality of being eligible; eligibleness; as, the
   eligibility of a candidate; the eligibility of an offer of
   marriage.
   [1913 Webster]

WordNet (r) 3.0 (2006):

eligibility
    n 1: the quality or state of being eligible; "eligibility of a
         candidate for office"; "eligibility for a loan" [ant:
         ineligibility]

Moby Thesaurus II by Grady Ward, 1.0:

31 Moby Thesaurus words for "eligibility":
   acceptability, admissibility, admission, assimilation,
   completeness, comprehension, comprehensiveness, comprisal,
   coverage, desirability, eligible, embodiment, embracement,
   encompassment, envisagement, exhaustiveness, fitness, fittedness,
   inclusion, inclusiveness, incorporation, membership, openness,
   participation, qualification, reception, suitability, tolerance,
   toleration, whole, worthiness



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

ELIGIBILITY. Capacity to be elected.
     2. Citizens are in general eligible to all offices; the exceptions
arise from the want of those qualifications which the constitution requires;
these are such as regard his person, his property, or relations to the
state.
     3.- 1. In. general, no person is eligible to any office, until he has
attained the full age of twenty-one years; no one can be elected a senator
of the United States, who shall not have attained the age of thirty years,
been a 'citizen of th e United States nine years and who shall not be an
inhabitant of the, state for which he shall be chosen. Const. art. 1, s. 3.
No person, except a natural born citizen, or a citizen of the United States
at the time of the adoption of this constitution, is eligible to the office
of president, and no person shall be eligible to that office, who shall not
have attained the age of thirty-five years, and been fourteen years a
resident within the United States. Const. art. 2, s. 1.
     4.-2. A citizen may be ineligible in consequence of his relations to
the state; for example, holding an office incompatible with the office
sought. Vide Ineligibility. Because he has not paid the taxes the law
requires; because he has not resided a sufficient length of time in the
state.
     5.-3. He may be ineligible for want of certain property
qualifications required by some, law.