TL;DR
This paper explores the margin of victory concept in tournament solutions, providing structural insights and experimental evidence on how it refines winner sets across different stochastic models.
Contribution
It offers new structural properties of the margin of victory and demonstrates its effectiveness in refining winners in various tournament models.
Findings
MoV exhibits monotonicity and consistency properties
Experimental results show MoV refines winner sets significantly
Structural insights improve understanding of tournament solutions
Abstract
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.
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