The Concept of Objectives

  • J. Wilhelm
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 112)


Managerial decisions as well as decisions in politics or daily life may be interpreted as results of choice-making processes; in this context, to decide means to choose amongst known opportunities of action - alternatives.- The idea of externally given selection opportunities being submitted to a subjective procedure of choice-making turns out to be true in a world of perfect information only, perfect regarding every real and possible dimension; here the decision maker is informed of all past, present, and future relevant events, all possible activities, and can describe them in every important detail.


Decision Maker Utility Function Environmental Response Decision Situation Side Condition 
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  1. 1).
    Cf. the remarks made by Krümmel [1969, pp. 72–73].Google Scholar
  2. 1).
    ) Schneeweiß, [1967, p. 8], Radner [1964., p. 179].Google Scholar
  3. 2).
    ) Cf. Riemenschnitter [1972, p. 72] especially for the problems of so -called “dead knots” (“tote Knoten”) within decision trees.Google Scholar
  4. 1).
    ) For these problems we refer to Albach [1969, pp. 720–727] and the references given there.Google Scholar
  5. 2).
    ) For a definition of a measurable space and for all probability theoretic material we refer to Neveu [1969], here p. 27.Google Scholar
  6. 1).
    ) This classification of decision situations is due to Knight [1921, P. 233].Google Scholar
  7. 2).
    ) Cf. Keynes [1950, pp. 13–14], Carnap and Stegmüller [1959]. Axiomatical treatments of these problems may be found as a context of developing the expected-utility-hypothesis in Savage [1954], Pfanzagl [1968, pp. 195–196] and in Rabusseau and Reich [1972].Google Scholar
  8. 4).
    The basic model of decision theory assumes Ωa=Ω, A a=A, µa=µ for all a ε A, Cf. Schneeweiß [1967, p. 12].Google Scholar
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    ) For this terminology we refer to Klahr [1969, p. 596]Google Scholar
  10. 1).
    Hence, regarding points of view the following holds like before: different points of view may establish the same equivalence relation on the data-dimension space of (inline). Nevertheless in cases no confusion may arise we identify points of view and their corresponding equivalence relations.Google Scholar
  11. 1).
    For the notion of a universe we refer to Schubert [1970, p. 16]. For all topological notions not defined here or in the following and for all statements on topological material not proved here or in the following see Bourbaki [1965]. For the notion of the interval topology we refer to definition 1.8. to be found in our excursus on the Bernoulli-principle as well as to Pfanzagl [1968, p. 6l]. For an arbitrary ordered set M, by J M[we denote the corresponding interval topology.Google Scholar
  12. 2).
    Order-homomorphisms are mappings g: G + G’ with the property: for all a,bεG we have a≤γ⇒b => g(a)≤g(b); cf. definition 1.11.Google Scholar
  13. 3).
    ) For the concept of a category cf. Schubert [1970] or Lang [1965, p.Google Scholar
  14. 3).
    ) For the notion of a utility function is refered to Debreu [1959, p.55]. Regarding the terms ordinal and cardinal see Pfanzagl [1968, p. 74]. In our context these terms above all have respect to the isomorphisms of the category in question. Utility functions are special faithful order-homomorphisms (cf. def. 1.11.); continuous utility functions exist, if and only if the topology of G is separable (Pfanzagl [19685, p. 75], 4.2.3. Theorem).Google Scholar
  15. 1).
    * /z, is an abbreviation for the quotient set which is generated by z and the equality relation in R (cf. p. 8, footnote 1).Google Scholar
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    ) Cf. p. 12, footnote 1. For an example take the utility function of a consumer, Debreu [1959, pp. 55–57].Google Scholar
  17. 1).
    ) Heinen D-966] has made similar remarks in differing between so-called side conditions of type A and type B. This specification is of some importance to the problem of the so-called “goal-programming” also: here the problem is discussed that by setting “goals” (= side conditions of type B) the set of feasible actions may become empty. A first approach may be found in Balderstone [i960]. For further references we refer to p. 63 of these notes.Google Scholar
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    ) Simon [1957, p. 246]Google Scholar
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    ) Sauermann and Selten [1962, p. 577]Google Scholar
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    ) Simon [1957, pp. 250–252]Google Scholar
  21. 2).
    ) Accordingly, Sauermann and Selten [1962] try to develop a theory of adjusting the levels of aspiration to new decision situations and new information respectively.Google Scholar
  22. 3).
    An approach to derive levels of aspiration within the framework of the chance-constrained programming may be found in Naslund [1967, pp. 17–20]; opportunities of substituting objective-achievements by security aspirations are considered in Albach and Schiller [1970].Google Scholar
  23. 1).
    ) For references we refer to Schneeweiß [1967].Google Scholar
  24. 3).
    ) The first axiomatical treatment of the Bernoulli-principle is to be found in the fundamental work of von Neumann and Morgenstern [1946].Google Scholar
  25. 1).
    ) For a definition we refer to Neveu [1969, p. 4l], Definition 1.6.1.Google Scholar
  26. 2).
    ) Neveu [1969, p. 27], Definition 1.4.2.Google Scholar
  27. 1).
    ) Neveu [1969, p. 4l], Satz 1.6.1.Google Scholar
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    ) Neveu [1969, p. 41].Google Scholar
  29. 1).
    ) Bourbaki [1965, chap. 1, § 1, No 2].Google Scholar
  30. 2).
    ) Lenz [1961, p. 44].Google Scholar
  31. 1).
    ) Lenz [1961, p. 44]; gap = “Lttcke”, step = “Sprung”, cut = “Schnitt”.Google Scholar
  32. 2).
    Pfanzagl [1968, p. 62].Google Scholar
  33. 3).
    ) Pfanzagl [1968, p. 62], 3.4.5. Lemma.Google Scholar
  34. 1).
    ) Pishburn [1970, p. 112 and p. 138], theorem 8.4 and lemma 10.5.Google Scholar
  35. 1).
    ) Fishburn [1970, pp. 111–112], theorem 8.3, c 1 and c 2.Google Scholar
  36. 1).
    ) Bourbaki [1958, chap. 9, § 1, No 2]Google Scholar
  37. 1).
    ) This is the problem of statistical decision theory. Additionally, the problem of decision making under uncertainty (i.e. the lack of objective probabilities) used to be attacked by some autors in that way; cf. Hart [1942, pp. 110–118].Google Scholar
  38. 1).
    ) For the general form of those approaches we refer to Aumann [1964, P. 219].Google Scholar
  39. 2).
    ) Cf. def. 1.7..Google Scholar
  40. 1).
    ) AusgleiehsaktivLtäten in the sense of Riemenschnitter [1972, pp. 65–66].Google Scholar
  41. 1).
    ) These cases are called dead knots (tote Knoten) by Riemenschnitter [1972, p. 72].Google Scholar
  42. 2).
    ) In flexible planning models the actions in the sense of stiff planning models are replaced by strategies. A strategy is a sequence of actions in the sense of stiff planning, each of them related to certain events (Riemenschnitter C1972, p. 47]).Google Scholar
  43. 1).
    ) This makes sense if it is assumed that the planning horizon is fixed at that point, and no additional information is available after wards. For this assumption we refer to Krümmel [1964, p. 194].Google Scholar
  44. 4).
    ) We give the following references: Heinen [1966], Schmidt-Sudhoff [19 67], Bidlingmayer [1968]. Based on empirical investigations Kaplan, Dirlam and Lanzilotti [19581 and Raia [1965] have catalogued managerial objectives while at the same time pursuing real decisions.Google Scholar
  45. 2).
    ) Another important example consists of the conflict among the objectives of the heads of different departments. Planning the product range the production manager oftenly intends to reduce the number of different products, whereas the head of the marketing department looks for chances to sell a greater amount of products because of a manifold assortment of products he can supply, cf. Gutenberg [1968, Vol.1, pp. 153–154].Google Scholar
  46. 1).
    ) Cf. Krümmel [1964, p. 194].Google Scholar
  47. 2).
    ) “… it is possible to measure certain present characteristics of firms which are likely to influence their profit potential”, White [1960, p. 186].Google Scholar
  48. 3).
    ) As an example from an extensive literature we refer to Wundt [1965].Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1975

Authors and Affiliations

  • J. Wilhelm
    • 1
  1. 1.Institut für Gesellschafts- und WirtschaftswissenschaftenUniversität BoonBonnDeutschland

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