Intransitivity in multiple solutions of Kemeny Ranking Problem

2013 Joint IMEKO (International Measurement Confederation) TC1-TC7-TC13 Symposium: Measurement Across Physical and Behavioural Sciences

Muravyov, S.V.^1 ; Marinushkina, I.A.^1

Department of Computer-aided Measurement Systems and Metrology, National Research Tomsk Polytechnic University, Tomsk 634050, Russia^1

关键词: Intransitivity;    Linear order;    Multiple solutions;    Optimal solutions;    Ranking problems;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/459/1/012006/pdf
DOI  :  10.1088/1742-6596/459/1/012006

来源: IOP

【 摘 要 】

Kemeny rule is one of deeply justified ways to solve the problem allowing to find such a linear order (Kemeny ranking) of alternatives that a distance from it to the initial rankings (input preference profile) is minimal. The approach can give considerably more than one optimal solutions. The multiple solutions (output profile) can involve intransitivity of the input profile. Favorable obstacle in dealing with intransitive output profile is that the intransitive cycles are lexicographically ordered what can help when algorithmically revealing them.