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Multiattributive decision theory: who are the best?

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Author(s): Hartmann H. Scheiblechner

Journal: Psychological Test and Assessment Modeling
ISSN 2190-0493

Volume: 55;
Issue: 2;
Start page: 207;
Date: 2013;
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Keywords: Decision theory | ranking | scoring | d-dimensional isotonic probabilistic model

ABSTRACT
A rank ordering of preference of multiattributive choice alternatives is suggested. The choice alternatives are characterised by several attributes (dimensions) which themselves are assumed to be given by strict partial orders (rank orders with possibly ties, or “rating scales”). A dominance relation is defined on the alternatives: an alternative dominates another if it is at least as good as the other in all dimensions and strictly superior in at least one dimension. The result is a multidimensional partial order. The problem is to choose a single best or a given number of best alternatives from the choice set. The solution must not involve comparisons of ranks of different dimensions, if the decision maker is a single individual, or of rank orders of different individuals, if the decision maker is a social group (social choice function). The (modified) percentile rank score (Scheiblechner, 2002, 2003) is suggested as scaling function. The performance of the (modified) percentile score is illustrated by the examples of the results of the competitors of the decathlon of Olympic Games at Beijing 2007 and World Championships at Berlin 2009.
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