  Tournament solutions are standard tools for identifying winners based on
pairwise comparisons between competing alternatives. The recently studied
notion of margin of victory (MoV) offers a general method for refining the
winner set of any given tournament solution, thereby increasing the
discriminative power of the solution. In this paper, we reveal a number of
structural insights on the MoV by investigating fundamental properties such as
monotonicity and consistency with respect to the covering relation.
Furthermore, we provide experimental evidence on the extent to which the MoV
notion refines winner sets in tournaments generated according to various
stochastic models.
