Characterizations of scoring methods for preference aggregation
<|reference_start|>Characterizations of scoring methods for preference aggregation: The paper surveys more than forty characterizations of scoring methods for preference aggregation and contains one new result. A general scoring operator is {\it self-consistent} if alternative $i$ is assigned a greater score than $j$ whenever $i$ gets no worse (better) results of comparisons and its `opponents' are assigned respectively greater (no smaller) scores than those of $j$. We prove that self-consistency is satisfied if and only if the application of a scoring operator reduces to the solution of a homogeneous system of algebraic equations with a monotone function on the left-hand side.<|reference_end|>
@article{chebotarev2006characterizations,
    title={Characterizations of scoring methods for preference aggregation},
    author={Pavel Chebotarev and Elena Shamis},
    journal={Annals of Operations Research, 1998. V. 80. P.299-332},
    year={2006},
    archivePrefix={arXiv},
    eprint={math/0602522},
    primaryClass={math.OC cs.MA math.FA}
}