A tournament solution based on dominating-set-relaxed partitions

We introduce a tournament solution by assigning scores to alternatives according to their positions in the dominating-set-relaxed partitions. The solution set can be achieved in polynomial time (cubic time complexity) and satisfies Condorcet consistency, Smith’s consistency, and monotonicity. It is contained in the uncovered set and, as a consequence, it is a Pareto-optimal tournament solution (that is, when the binary relation of the tournament is interpreted as a majority preference relation, the social choice rule induced by the proposed solution is Pareto-optimal). When the alternative set is specifically divisible with respect to each alternative in the sense of dominating-set-relaxed partitions (e.g., when the binary relation used to define the tournament guarantees a dominating set), the solution set coincides with that of Copeland method. However, this is not true for general situations. In addition, similar to the Copeland method, the proposed solution is neither externally stable nor composition-consistent.