The Collaborative International Dictionary of English v.0.48:

Irresponsibility \Ir`re*spon`si*bil"i*ty\, n. [Cf. F.
   irresponsabilit['e].]
   1. Lack of, or freedom from, responsibility or
      accountability.
      [1913 Webster]

   2. A trait causing one to act without a proper sense of
      responsibility; acting without giving proper weight to
      one's responsibilities.
      [PJC]

WordNet (r) 3.0 (2006):

irresponsibility
    n 1: a form of untrustworthiness; the trait of lacking a sense
         of responsibility and not feeling accountable for your
         actions [syn: irresponsibility, irresponsibleness]
         [ant: responsibility, responsibleness]