Preference fusion when the number of alternatives exceeds two: indirect scoring procedures

We consider the problem of aggregation of incomplete preferences represented by arbitrary binary relations or incomplete paired comparison matrices. For a number of indirect scoring procedures we examine whether or not they satisfy the axiom of self-consistent monotonicity. The class of win–loss combining scoring procedures is introduced which contains a majority of known scoring procedures. Two main results are established. According to the first one, every win–loss combining scoring procedure breaks self-consistent monotonicity. The second result provides a sufficient condition of satisfying self-consistent monotonicity.