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Characterizations of scoring methods for preference aggregation

Pavel Chebotarev·Elena Shamis
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Abstract

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.

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Pavel Chebotarev, Elena Shamis. 2006-02-23. Characterizations of scoring methods for preference aggregation. https://arxiv.org/abs/math/0602522

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