Margin of victory for tournament solutions

Tournament solutions are frequently used to select winners from a set of alternatives based on pairwise comparisons between alternatives. Prior work has shown that several common tournament tend large winner sets and therefore have low discriminative power. In this paper, we propose general framework for refining solutions. order distinguish winning alternatives, also non-winning ones, introduce the notion margin victory (MoV) MoV is robustness measure individual alternatives: For winners, captures distance dropping out set, non-winners, entering set. each case, measured in terms which would be reversed achieve desired outcome. solutions, including top cycle, uncovered Banks determine complexity computing provide worst-case bounds both non-winners. Our results can viewed perspective bribery manipulation.