Margin of Victory in Tournaments: Structural and Experimental Results
M. Brill, U. Schmidt-Kraepelin, W. Suksompong
AAAI 2021
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.
Remarks: The paper is about tournaments but uses preference-like data to generate them. There is a journal version: Markus Brill, Ulrike Schmidt-Kraepelin, Warut Suksompong: Margin of victory for tournament solutions. Artif. Intell. 302: 103600 (2022).
Experiments:
| Election type |
Culture |
Candidates |
Voters |
Instances |
Parameters |
| Ordinal |
Impartial Culture |
{5, 10, 15, 20, 25, 30} |
{51} |
100 |
None |
| Ordinal |
Mallows |
{5, 10, 15, 20, 25, 30} |
{51} |
100 |
$\phi = 0.95$ |
| Ordinal |
Urn Model |
{5, 10, 15, 20, 25, 30} |
{51} |
100 |
adding 10 copies of a vote after sampling it ($\alpha = \frac{10}{m!}$) |