Generalization of the weighted voting method using penalty functions constructed via faithful restricted dissimilarity functions

Generalization of the weighted voting method using penalty functions constructed via faithful restricted dissimilarity functions

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Article ID: iaor20128032
Volume: 225
Issue: 3
Start Page Number: 472
End Page Number: 478
Publication Date: Mar 2013
Journal: European Journal of Operational Research
Authors: , , , ,
Keywords: penalty functions, preference modelling, voting systems
Abstract:

In this paper we present a generalization of the weighted voting method used in the exploitation phase of decision making problems represented by preference relations. For each row of the preference relation we take the aggregation function (from a given set) that provides the value which is the least dissimilar with all the elements in that row. Such a value is obtained by means of the selected penalty function. The relation between the concepts of penalty function and dissimilarity has prompted us to study a construction method for penalty functions from the well‐known restricted dissimilarity functions. The development of this method has led us to consider under which conditions restricted dissimilarity functions are faithful. We present a characterization theorem of such functions using automorphisms. Finally, we also consider under which conditions we can build penalty functions from Kolmogoroff and Nagumo aggregation functions. In this setting, we propose a new generalization of the weighted voting method in terms of one single variable functions. We conclude with a real, illustrative medical case, conclusions and future research lines.

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