Characterizations of scoring methodsfor preference aggregation

The paper surveys more than forty characterizations of scoring methods for preferenceaggregation and contains one new result. A general scoring operator is self-consistent ifalternative i is assigned a greater score than j whenever i gets no worse (better) results ofcomparisons and its “opponents” are assigned, respectively, greater (no smaller) scores thanthose of j. We prove that self-consistency is satisfied if and only if the application of ascoring operator reduces to the solution of a homogeneous system of algebraic equationswith a monotone function on the left-hand side.