Skip to main content
SpringerLink
Log in

Entscheidungskalküle jenseits des subjektiven Erwartungsnutzens

Ein Plädoyer für die Verwendung unterer und oberer Wahrscheinlichkeiten

  • Entscheidungskalküle
  • Published:
Schmalenbachs Zeitschrift für betriebswirtschaftliche Forschung Aims and scope Submit manuscript

Summary

Starting point are the well-known empirical violations of axioms of Bernoulli Rationality and the discussion about its prescriptive exclusivity. The paper classifies non-expected utility models into categories which are suitable to model different kinds of violations, depending on whether they follow either Allais or Ellsberg. The argument is brought forward that a modification of Hurwicz’s Criterion is a good compromise, provided that lower and upper probabilities exist: the model is axiomatically founded, practicable — that means simply applicable, clearly interpretable and compatible with expected utility — and allows the modelling of an important class of descriptive violations. The new aspects of the article are firstly a frame of reference for the use of the models depending on the type of violation. Secondly, an axiomatic bracing of the modified Hurwicz Criterion is given by characterizing it as a special case of the Choquet expected utility when lower and upper state-probabilities occur. Thirdly, for these probabilities a clear interpretation is given within the classic probability framework.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literaturverzeichnis

  • Allais, Par M. (1953), Le Comportement De L’Homme Rationel Devant Le Risque: Critique Des Postulats et Axiomes de L’Ecole Americaine, in: Econometrica, Vol. 21, S. 503–546.

    Article  Google Scholar 

  • Anscombe, Francis J./Aumann, Robert J. (1963), A Definition of Subjective Probability, in: Annals of Mathematical Statistics, Vol. 34, S. 199–205.

    Article  Google Scholar 

  • Arrow, Kenneth J./Hurwicz, Leonid. (1972), Optimality Criterion for Decision Making under Ignorance, in: Carter, Charles F./Ford, James L. (Hrsg.), Uncertainty and Expectations in Economics, S. 1–11.

  • Bauer, Heinz. (1990), Maß- und Integrationstheorie.

  • Behnen, Konrad/Neuhaus, Georg. (1987), Grundkurs Stochastik.

  • Billot, Antoine. (1991), Cognitive Rationality and Alternative Belief Measures, in: Journal of Risk and Uncertainty, Vol. 4, S. 299–324.

    Article  Google Scholar 

  • Budescu, David V./Wallsten, Thomas S.. (1987), Subjective Estimation of Vague and Precise Uncertainties, in: Wright, Georg/Ayton, Peter (Hrsg.), Judgmental Forecasting, S. 63–82.

  • Camerer, Colin/ Weber, Martin. (1992), Recent Developments in Modeling Preferences, Uncertainty and Ambiguity, in: Journal of Risk and Uncertainty, Vol. 5, S. 325–370.

    Article  Google Scholar 

  • Chew, Soo H. (1989), Axiomatic Utility Theories with the Betweenness Property, in: Annals of Operations Research, Vol. 19, S. 273–298.

    Article  Google Scholar 

  • Curley, Shawn P./Yates, J. Frank/Abrams, Richard A. (1986), Psychological Sources of Ambiguity Avoidance, in: Organizational Behavior and Human Decision Processes, Vol. 38, S. 230–256.

    Article  Google Scholar 

  • Dempster, Arthur. (1967), Upper and Lower Probabilities Induced by a Multivalued Mapping, in: Annals of Mathematical Statistics, Vol. 38, S. 325–339.

    Article  Google Scholar 

  • Einhorn, Hillel J./ Hogarth, Robin M. (1985), Ambiguity and Uncertainty in Probabilistic Inference, in: Psychological Review, Vol. 92, S. 429–461.

    Article  Google Scholar 

  • Einhorn, Hillel J./Hogarth, Robin M.. (1986), Decision Making under Ambiguity, in: Hogarth, Robin M./Einhorn, Hillel J. (Hrsg.), Rational Choice, S. 41–66.

  • Eisenführ, Franz/Weber, Martin. (1994), Rationales Entscheiden, 2. Aufl.

  • Ellsberg, Daniel. (1961), Risk, Ambiguity, and the Savage Axioms, in: Quarterly Journal of Economics, Vol. 75, S. 643–669.

    Article  Google Scholar 

  • Epstein, Larry G.. (1992), Behavior under Risk: Recent Developments in Theory and Applications, in: Laffont, J. (Hrsg.), Advances in Economic Theory, S. 1–63.

  • Epstein, Larry G./ Zhang, Jiankang. (2001), Subjective Probabilities on Subjectively Unambiguous Events, in: Econometrica, Vol. 69, S. 265–306.

    Article  Google Scholar 

  • Fellner, William. (1961), Distortion of Subjective Probabilities as a Reaction to Uncertainty, in: Quarterly Journal of Economics, Vol. 75, S. 670–694.

    Article  Google Scholar 

  • Fox, Craig R./ Tversky, Amos. (1995), Ambiguity Aversion and Comparative Ignorance, in: Quarterly Journal of Economics, Vol. 110, S. 585–603.

    Article  Google Scholar 

  • Fox, Craig R./Weber, Martin. (2002), Ambiguity Aversion, Comparative Ignorance, and Decision Context, in: Organizational Behavior and Human Decision Processes, Vol. 88, S. 476–498.

    Article  Google Scholar 

  • Franke, Günter. (1978), Expected Utility with Ambiguous Probabilities and „Irrational“ Parameters, in: Theory and Decision, Vol. 9, S. 267–283.

    Article  Google Scholar 

  • Gärdenfors, Peter/ Sahlin, Nils-Eric. (1982), Unreliable Probabilities, Risk Taking, and Decision Making, in: Synthese, Vol. 53, S. 361–386.

    Article  Google Scholar 

  • Ghirardato, Paolo. (2001), Coping with Ignorance: Unforeseen Contingencies and Non-additive Uncertainty, in: Economic Theory, Vol. 17, S. 247–276.

    Article  Google Scholar 

  • Ghirardato, Paolo/ Marinacci, Massimo. (2002), Ambiguity Made Precise: A Comparative Foundation, in: Journal of Economic Theory, Vol. 102, S. 251–289.

    Article  Google Scholar 

  • Gierl, Heribert/ Helm, Roland/ Stumpp, Stefan. (2002), Markentreue und Kaufintervalle bei langlebigen Konsumgütern, in: zfbf, 54. Jg., S. 215–232.

    Google Scholar 

  • Gierl, Heribert/ Höser, Hans. (2002), Der Reihenfolgeeffekt auf Präferenzen, in: zfbf, 54. Jg., S. 3–18.

    Google Scholar 

  • Gilboa, Itzhak/Schmeidler, David. (1989), Maxmin Expected Utility with Non-Unique Prior, in: Journal of Mathematical Economics, Vol. 18, S. 141–153.

    Article  Google Scholar 

  • Gottinger, Hans W.. (1974), Subjektive Wahrscheinlichkeiten.

  • Hammond, Peter J. (1988), Consequentialist Foundations of Expected Utility, in: Theory and Decision, Vol. 25, S. 25–78.

    Article  Google Scholar 

  • Hax, Herbert. (1974), Entscheidungmodelle in der Unternehmung — Einführung in Operations Research.

  • Heath, Chip/ Tversky, Amos. (1991), Preference and Belief: Ambiguity and Competence in Choice under Uncertainty, in: Journal of Risk and Uncertainty, Vol. 4, S. 5–28.

    Article  Google Scholar 

  • Hilton, Ronald W. (1989), Failure of Blackwell’s Theorem Under Machina’s Generalization of Expected Utility Analyzis Without the Independence Axiom, in: Journal of Economic Behavior and Organization, Vol. 13, S. 233–244.

    Article  Google Scholar 

  • Janis, Irving L./Mann, Leon. (1977), Decision Making.

  • Kahn, Barbara E./ Sarin, Rakesh K. (1988), Modeling Ambiguity in Decisions under Uncertainty, in: Journal of Consumer Research, Vol. 15, S. 265–272.

    Article  Google Scholar 

  • Kahneman, Daniel/Slovic, Paul/Tversky, Amos. (Hrsg.) (1982), Judgment under Uncertainty: Heuristics and Biases.

  • Kahneman, Daniel/ Tversky, Amos. (1979), Prospect Theory: An Analysis of Decision under Risk, in: Econometrica, Vol. 47, S. 263–291.

    Article  Google Scholar 

  • Karni, Edi/Schmeidler, David. (1991a), Utility Theory with Uncertainty, in: Hildenbrand, W./Sonnenschein, H. (Hrsg.), Handbook of Mathematical Economics Vol. IV, S. 1763–1825.

  • Karni, Edi/ Schmeidler, David. (1991b), Atemporal Dynamic Consistency and Expected Utility Theory, in: Journal of Economic Theory, Vol. 54, S. 401–408.

    Article  Google Scholar 

  • Keppe, Hans-Jürgen/ Weber, Martin. (1995), Judged Knowledge and Ambiguity Aversion, in: Theory and Decision, Vol. 39, S. 51–77.

    Article  Google Scholar 

  • Kofler, Eduard/Menges, Günter. (1976), Entscheidungen bei unvollständiger Information.

  • Kolmogoroff, Alexander N.. (1933), Grundbegriffe der Wahrscheinlichkeitsrechnung, in: Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 2, Heft 3, S. 1–62.

    Google Scholar 

  • Krelle, Wilhelm. (1968), Präferenz- und Entscheidungstheorie.

  • Laux, Helmut. (1976), Zur Entscheidung bei Fehlen objektiver Wahrscheinlichkeiten, in: Zeitschrift für Betriebswirtschaft, 46. Jg., S. 59–68.

    Google Scholar 

  • Lindstädt, Hagen. (2002), Das modifizierte Hurwicz-Kriterium für untere und obere Wahrscheinlichkeiten — ein Spezialfall des Choquet-Erwartungsnutzens, HHL-Arbeitspapier 57.

  • Maccheroni, Fabio. (2002), Maxmin under Risk, in: Economic Theory, Vol. 19, S. 823–831.

    Article  Google Scholar 

  • Machina, Mark J. (1989), Dynamic Consistency and Non-Expected Utility Models of Choice under Uncertainty, in: Journal of Economic Literature, Vol. 27, S. 1622–1668.

    Google Scholar 

  • March, James G. (1988), Variable Risk Preferences and Adaptive Aspirations, in: Journal of Economic Behavior and Organization, Vol. 9, S. 5–24.

    Article  Google Scholar 

  • Montesano, Aldo. (2001), Uncertainty with Partial Information on the Possibility of the Events, in: Theory and Decision, Vol. 51, S. 183–195.

    Article  Google Scholar 

  • Niehans, Jürg. (1948), Zur Preisbildung bei ungewissen Erwartungen, in: Schweizerische Zeitschrift für Volkswirtschaft und Staat, Vol. 84, S. 433–456.

    Google Scholar 

  • Osnabrügge, Gabriele/Stahlberg, Dagmar/Frey, Dieter. (1985), Die Theorie der kognizierten Kontrolle, in: Frey, Dieter/Irle, Martin (Hrsg.), Theorien der Sozialpsychologie, Band III: Motivations- und Informationsverarbeitungstheorien, S. 127–172.

  • Ott, Notburga (2001), Unsicherheit, Unschärfe und rationales Entscheiden.

  • Quiggin, John. (1982), A Theory of Anticipated Utility, in: Journal of Economic Behavior and Organization, Vol. 3, S. 323–343.

    Article  Google Scholar 

  • Raiffa, Howard. (1968), Decision Analysis: Introductory Lectures on Choices under Uncertainty. Rommelfanger, Heinrich (1994), Fuzzy Decision Support-Systeme.

  • Sarin, Rakesh/ Wakker, Peter. (1998), Revealed Likelihood and Knightian Uncertainty, in: Journal of Risk and Uncertainty, Vol. 16, S. 223–250.

    Article  Google Scholar 

  • Sarin, Rakesh/ Winkler, Robert L. (1992), Ambiguity and Decision Modeling: A Preference Based Approach, in: Journal of Risk and Uncertainty, Vol. 5, S. 389–407.

    Article  Google Scholar 

  • Savage, Leonard J. (1951), The Theory of Statistical Decision, in: Journal of the American Statistical Association, Vol. 46, S. 55–67.

    Article  Google Scholar 

  • Savage, Leonard J.. (1954), The Foundations of Statistics.

  • Schmeidler, David. (1986), Integral Representation without Additivity, in: Proceedings of the American Mathematical Society, Vol. 97, S. 255–261.

    Article  Google Scholar 

  • Schmeidler, David. (1989), Subjective Probability and Expected Utility without Additivity, in: Econometrica, Vol. 57, S. 571–587.

    Article  Google Scholar 

  • Schmidt, Ulrich. (2002), Ist das Unabhängigkeitsaxiom eine notwendige Voraussetzung der präskriptiven Entscheidungstheorie?, in: Zeitschrift für Betriebswirtschaft, 72. Jg., S. 317–329.

    Google Scholar 

  • Schneeweiß, Hans. (1963), Kritische Bemerkungen zur Kritik am Wahrscheinlichkeitssubjektivismus, in: Statistische Hefte, Vol. 4, S. 203–220.

    Article  Google Scholar 

  • Smith, Vernon L. (1969), Measuring Nonmonetary Utilities in Uncertain Choices: The Ellsberg Urn, in: Quarterly Journal of Economics, Vol. 83, S. 324–329.

    Article  Google Scholar 

  • Spengler, Thomas. (1992), Lineare Entscheidungsmodelle zur Organisations- und Personalplanung.

  • Spengler, Thomas. (1999), Grundlagen und Ansätze der strategischen Personalplanung mit vagen Informationen.

  • Tversky, Amos/ Kahneman, Daniel. (1992), Advances in Prospect Theory: Cumulative Representation of Uncertainty, in: Journal of Risk and Uncertainty, Vol. 5, S. 297–323.

    Article  Google Scholar 

  • Wakker, Peter. (1988), Nonexpected Utility as Aversion to Information, in: Journal of Behavioral Decision Making, Vol. 1, 169–175.

    Article  Google Scholar 

  • Wakker, Peter. (2001), Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-thing Principle, in: Econometrica, Vol. 69, S. 1039–1059.

    Article  Google Scholar 

  • Wald, Abraham. (1945), Statistical Decision Functions which Minimize Maximum Risk, in: Annals of Mathematics, Vol. 46, S. 265–280.

    Article  Google Scholar 

  • Winkler, Robert L. (1991), Ambiguity, Probability, Preference, and Decision Analysis, in: Journal of Risk and Uncertainty, Vol. 4, S. 285–297.

    Article  Google Scholar 

  • Yaari, Menahem E.. (1985), On the Role of ‚Dutch Books‘ in the Theory of Choice Under Risk, in: Nancy L. Schwartz Memorial Lecture.

  • Yaari, Menahem E. (1987), The Dual Theory of Choice under Risk, in: Econometrica, Vol. 55, S. 95–116.

    Article  Google Scholar 

  • Yager, Ronald R./Kacprzyk, Janusz/Fedrizzi, Mario. (Hrsg.) (1994), Advances in the Dempster-Shafer Theory of Evidence.

Download references

Author information

Authors and Affiliations

  1. Lehrstuhl für Strategisches Management und Organisation, HHL, Leipzig Graduate School of Management - Handelshochschule Leipzig, Jahnallee 59, 04109, Leipzig, Deutschland

    Hagen Lindstädt (Professor Dr.)

Authors
  1. Hagen Lindstädt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hagen Lindstädt.

Additional information

Der Autor dankt den Herren Hugo Kossbiel, Pierfrancesco La Mura, Gerhard Muche, Thomas Spengler, Michael Wolff und einem anonymen Gutachter für wertvolle Hinweise.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lindstädt, H. Entscheidungskalküle jenseits des subjektiven Erwartungsnutzens. Schmalenbachs Z betriebswirtsch Forsch 56, 495–519 (2004). https://doi.org/10.1007/BF03372747

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03372747

JEL-Classification

Keywords

Search

Navigation