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]