TY - JOUR

T1 - An iterative procedure for evaluating digraph competitions

AU - Borm, P.E.M.

AU - Brink, van den, R.

AU - Slikker, M.

PY - 2002

Y1 - 2002

N2 - A competition which is based on the results of (partial) pairwise comparisons can be modelled by means of a directed graph. Given initial weights on the nodes in such digraph competitions, we view the measurement of the importance (i.e., the cardinal ranking) of the nodes as an allocation problem where we redistribute the initial weights on the basis of insights from cooperative game theory. After describing the resulting procedure of redistributing the initial weights, an iterative process is described that repeats this procedure: at each step the allocation obtained in the previous step determines the new input weights. Existence and uniqueness of the limit is established for arbitrary digraphs. Applications to the evaluation of, e.g., sport competitions and paired comparison experiments are discussed.

AB - A competition which is based on the results of (partial) pairwise comparisons can be modelled by means of a directed graph. Given initial weights on the nodes in such digraph competitions, we view the measurement of the importance (i.e., the cardinal ranking) of the nodes as an allocation problem where we redistribute the initial weights on the basis of insights from cooperative game theory. After describing the resulting procedure of redistributing the initial weights, an iterative process is described that repeats this procedure: at each step the allocation obtained in the previous step determines the new input weights. Existence and uniqueness of the limit is established for arbitrary digraphs. Applications to the evaluation of, e.g., sport competitions and paired comparison experiments are discussed.

U2 - 10.1023/A:1016339832755

DO - 10.1023/A:1016339832755

M3 - Article

VL - 109

SP - 61

EP - 75

JO - Annals of Operations Research

JF - Annals of Operations Research

SN - 0254-5330

IS - 1-4

ER -