From Incomplete Preferences to Ranking via Optimization
<|reference_start|>From Incomplete Preferences to Ranking via Optimization: We consider methods for aggregating preferences that are based on the resolution of discrete optimization problems. The preferences are represented by arbitrary binary relations (possibly weighted) or incomplete paired comparison matrices. This incomplete case remains practically unexplored so far. We examine the properties of several known methods and propose one new method. In particular, we test whether these methods obey a new axiom referred to as {\it Self-Consistent Monotonicity}. Some results are established that characterize solutions of the related optimization problems.<|reference_end|>
@article{chebotarev2006from,
    title={From Incomplete Preferences to Ranking via Optimization},
    author={Pavel Chebotarev and Elena Shamis},
    journal={A version of this paper was published as: P.Yu.Chebotarev,
  E.V.Shamis. Constructing an objective function for aggregating incomplete
  preferences, In: A.Tangian and J.Gruber, eds. Econometric Decision Models:
  Constructing Scalar-Valued Objective Functions. Lecture Notes in Economics
  and Mathematical Systems, Springer-Verlag, 1997, P.100-124},
    year={2006},
    archivePrefix={arXiv},
    eprint={math/0602552},
    primaryClass={math.OC cs.MA math.CO}
}