Abstract : Artin representations of fixed dimension of the absolute Galois group of rational numbers can be counted using their conductor, which is an arithmetic invariant associated to the isomorphism class of the representation. We show that the density of self-dual Artin representations among all Artin representations of dimension three is $0$ when counted in this manner, thus formalizing the notion that 'self-dual objects should occur rarely'. This generalizes previously known results in dimensions one and two.