Abstract
This chapter contains a survey of the theory of multiattribute value functions. A value function is a mathematical representation of human judgements which allows an analytical study of preferences and value judgements.
“Values are what we care about&values should be the driving force for our decision making. They should be the basis for the time and effort we spend thinking about decisions” (Keeney, 1992, p 3).
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References
Von Winterfeldt and Edwards (1986) use the term value tree. The same structure is called an objective hierarchy in Keeney and Raiffa (1976) and a fundamental objective hierarchy in Keeney (1992). These authors also provide techniques for identifying and structuring objectives.
Several other terms are used in place of those used here. Zeleny (1982) and Belton (1990) indicate the following possibilities: • objectives (goals, targets, aims, end, intents, purposes, missions, ambitions); • alternatives (options, decision options, actions, courses of action, choices, objects of choice, items, strategies, means); • attributes (criteria, performance indicators, yardsticks, standards, gauges, principles, norms, rules). The terms for alternatives may be used as synonyms without generating confusion. The different terms for objectives and attributes may imply particular interpretations, approaches and even fundamental theoretical differences. The interested reader is referred to Bouyssou (1990), Roy and Vincke (1984) and Keeney and Raiffa (1976), for some of the most significant distinctions made between these terms.
A formal definition of measurement requires the use of relational systems and of morphisms between relational systems. This is beyond the scope of this study: a precise treatment of the matter can be found in Man (1993).
For the sake of completeness, it should be noted that some additional technical assumptions are needed for proving the existence of v. The interested reader can find the complete results in the literature cited.
A strict definition of scale can be found in Mari (1993).
Roy and Vincke (1984) generalise the system of preference relations, allowing intransitivity and incomparability. This leads to approaches different from the value function approach.
As for the existence theorems, some additional technical conditions are necessary in order to prove the existence of the additive representation. These conditions are also slightly different for the bidimensional case and the general case for three and more attributes. The interested reader can find a detailed explanation in French (1988).
The proof requires an additional assumption, called “difference consistency”. Loosely speaking, difference consistency requires that if xi is preferred to xi’, all other things being equal, then the preference difference between xi and the worst level xi* is higher than the preference difference between xi’ and the same level. It also requires that if two options are indifferent, then the strength of preference between these options and a third one is equal.
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© 1997 Springer Science+Business Media Dordrecht
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Beinat, E. (1997). Multiattribute value function theory. In: Value Functions for Environmental Management. Environment & Management, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8885-0_2
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DOI: https://doi.org/10.1007/978-94-015-8885-0_2
Publisher Name: Springer, Dordrecht
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