Preference fusion when the number of alternatives exceeds two: indirect scoring procedures
<|reference_start|>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 {\em 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.<|reference_end|>
@article{chebotarev2006preference,
    title={Preference fusion when the number of alternatives exceeds two: indirect
  scoring procedures},
    author={Pavel Chebotarev and Elena Shamis},
    journal={Journal of the Franklin Institute, 336 (1999), No.2, 205-226.
  Erratum: 336 (1999) No.4, 747-748
  (http://dx.doi.org/10.1016/S0016-0032(99)00004-6)},
    year={2006},
    doi={10.1016/S0016-0032(98)00017-9},
    archivePrefix={arXiv},
    eprint={math/0602171},
    primaryClass={math.OC cs.MA math.CO}
}