Abstract
Confronted with decisions involving many criteria in real life, people sometimes apply a ranking of importance to the criteria, instead of trying to balance the criteria on some common scale. The principle “first things first” is at the heart of any hierarchical procedure and one may ask for the reasons people are applying it. Beside empirical investigation, an answer may also be given by looking analytically for possible appealing features which hierarchical structures could possess. In this respect, not only the individual decision taker is of interest, but also his cultural environment, including e.g. the dictionary or the decimal system both being based on lexicographical ordering. It is the main result of the present paper that hierarchical decision procedures may be characterized by some specific stability property. Roughly speaking, the latter means that a decision taken in favor of one alternative against the other, is not upset by a small perturbation in the assessment of any of the criteria. For the result, we have to assume the decision rule under consideration yields decisions in sufficiently many cases of conflict between the different criteria. Without this assumption the stability property is not very demanding and it is shared by various different rules.
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References
Arrow, K.J., “Social Choice and Individual Values”, 2nd ed., Yale University Press, New Haven and London, 1963 (first edition 1951 ).
Fishburn, P.C., Axioms for lexicographic preferences, Rev. Econ.Studies 42 (1975), 415–419.
Fuchs, L., “Partially Ordered Algebraic Structures”, Pergamon Press, Oxford etc., 1963.
Krause, U., Recht und Gerechtigkeit, Ukonomie und Gesellschaft Jahrbuch 2: Wohlfahrt und Gerechtigkeit (1984), 158–172.
Roberts, F.S., “Measurement Theory”, Addison-Wesley, Reading, 1979.
Steedman, I. and Krause, U., Goethe’s Faust, Arrow’s possibility theorem and the individual decision taker, in: Elster, J. (ed.), “The Multiple Self”, Cambridge University Press, Cambridge, 1986.
Yu, P.L., “Multiple-Criteria Decision Making”, Plenum Press, New York and London, 1985.
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© 1987 Springer-Verlag Berlin Heidelberg
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Krause, U. (1987). Hierarchical Structures in Multicriteria Decision Making. In: Jahn, J., Krabs, W. (eds) Recent Advances and Historical Development of Vector Optimization. Lecture Notes in Economics and Mathematical Systems, vol 294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46618-2_12
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DOI: https://doi.org/10.1007/978-3-642-46618-2_12
Publisher Name: Springer, Berlin, Heidelberg
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