The Collaborative International Dictionary of English v.0.48:

Perversity \Per*ver"si*ty\, n. [L. perversitas: cf. F.
   perversit['e].]
   The quality or state of being perverse; perverseness.
   [1913 Webster]

WordNet (r) 3.0 (2006):

perversity
    n 1: deliberate and stubborn unruliness and resistance to
         guidance or discipline [syn: contrariness, perversity,
         perverseness]
    2: deliberately deviating from what is good; "there will always
       be a few people who, through macho perversity, gain
       satisfaction from bullying and terrorism" [syn: perversity,
       perverseness]

Moby Thesaurus II by Grady Ward, 1.0:

61 Moby Thesaurus words for "perversity":
   antagonism, antipathy, antithesis, bearishness, bitchiness,
   cantankerousness, churlishness, clashing, collision, conflict,
   confrontation, contradiction, contradistinction, contraindication,
   contraposition, contrariety, contrariness, contrast,
   counterposition, crabbedness, crankiness, cross-purposes,
   crossness, crustiness, cussedness, difficultness, disagreeability,
   disagreement, discrepancy, dourness, excitability, fractiousness,
   frowardness, hostility, huffiness, huffishness, inconsistency,
   inimicalness, irascibility, irritability, meanness, oppositeness,
   opposition, opposure, oppugnance, oppugnancy, orneriness,
   perverseness, perversite, polarity, repugnance, showdown,
   snappishness, stuffiness, sulkiness, sullenness, testiness,
   ugliness, waspishness, waywardness, wrongheadedness