Full-text resources of CEJSH and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl


2014 | 178 | 74-92

Article title

Propozycja hybrydy reguł Hurwicza i Bayesa w podejmowaniu decyzji w warunkach niepewności


Title variants

A Hybrid of the Hurwicz and Bayes Rules in the Decision Making Under Uncertainty

Languages of publication



The Hurwicz rule and the Bayes rule are classical approaches applied in the decision making under uncertainty. This situation occurs when the decision maker may choose one of several alternatives and he or she is only able to assign to each of them an interval of potential payoffs or a set of possible profits. In both cases the answer obtained depends on the state of nature (scenario) which will happen, but in the first case the set of scenarios is infinite and in the second one - it is finite. The Hurwicz measure, with the aid of the coefficient of pessimism and the coefficient of optimism, enables to find the optimal pure strategy when the decision selected is performed only once. Meanwhile the Bayes criterion is designed to indicate the optimal pure or mixed strategy when the variant chosen is performed once or many times. In the first part of the article the author analyzes the Hurwicz rule and illustrates cases when the use of this criterion leads to quite unexpected results which seem to be contradictory with the logic and do not reflect the decision maker's preferences. In the second part a proposal of an approach for optimal pure strategy searching (by means of formulas considering both the coefficients of pessimism and optimism, as well as the whole set of payoffs) is presented. This procedure (H+B rule) combines elements of the Hurwicz criterion and the Bayes criterion, but is deprived of disadvantages typical of the Hurwicz rule. The rule suggested takes into consideration both extreme payoffs and intermediate payoffs, which enables to receive rational recommendations for a larger spectrum of decision problems. The H+B rule may be applied in the decision making process under uncertainty when the number of potential scenarios and the set of possible payoffs are finite, however a slight modification of the equations proposed enables to use this procedure in problems with continuous payoffs.






Physical description



  • Basili M., 2006: A Rational Decision Rule with Extreme Events. "Risk Analysis", Vol. 26, 1721-1728.
  • Basili M., Chateauneuf A., Fontini F., 2008: Precautionary Principle as a Rule of Choice with Optimism on Windfall Gains and Pessimism on Catastrophic Losses. "Ecological Economics", Vol. 67, 485-491.
  • Basili M., Zappia C., 2010: Ambiguity and Uncertainty in Ellsberg and Shackle. "Cambridge Journal of Economics", 34(3), 449-474.
  • Dominiak C., 2006: Multicriteria Decision Aid under Uncertainty. W: Multiple Criteria Decision Making' 05. T. Trzaskalik (ed.). Publisher of the Karol Adamiecki University of Economics, Katowice.
  • Dominiak C., 2009: Multicriteria Decision Aiding Procedure under Risk and Uncertainty. W: Multiple Criteria Decision Making' 08. T. Trzaskalik (ed.). Publisher of the Karol Adamiecki University of Economics, Katowice.
  • Ellsberg D., 2001: Risk, Ambiguity and Decision. Garland Publishing, New York, NY, USA.
  • Gaspars-Wieloch H., 2013: Modifications of the Hurwicz's Decision Rule. "Central European Journal of Operations Research", Springer, DOI 10.1007/s10100-013-0302-y, May.
  • Gaspars-Wieloch H., 2012: Ograniczona skuteczność metod optymalizacyjnych w rozwiązywaniu ekonomicznych problemów decyzyjnych. "Ekonomista", 3, 303-324.
  • Ghirardato P., Maccheroni F., Marinacci M., 2004: Differentiating Ambiguity and Ambiguity Attitude. "Journal of Economic Theory", Vol. 118, 133-173.
  • Gilboa I., 2009: Theory of Decision under Uncertainty. Cambridge University Press.
  • Groenewald M.E., Pretorius P.D., 2011: Comparison of Decision-making under Uncertainty Investment Strategies with the Money Market. "Journal of Financial Studies and Research".
  • Hurwicz L., 1952: A Criterion for Decision Making under Uncertainty. "Technical Report 355", Cowles Commission.
  • Hurwicz L., 1951: The Generalized Bayes Minimax Principle: A Criterion for Decision Making Under Uncertainty. Cowles Commission, "Discussion Paper Statistics 335".
  • Huynh V.N., Hu C., Nakamori Y., Kreinovich V., 2007: On Decision Making under Interval Uncertainty: A New Justification of Hurwicz Optimism-Pessimism Approach and Its Use in Group Decision Making. "Departmental Technical Reports (CS)", Paper 107.
  • Ignasiak E. (red.), 1996: Badania operacyjne. Polskie Wydawnictwo Ekonomiczne, Warszawa.
  • Kaufmann A., Faure R., 1974: Invitations a la recherche operationnelle. Paris, Dunod.
  • Knight F.H., 1921: Risk, Uncertainty, Profit. Hart, Schaffner & Marx, Houghton Mifflin Co Boston, MA.
  • Marinacci M., 2002: Probabilistic Sophistication and Multiple Priors. "Econometrica", Vol. 70, 755-764.
  • Nakamura K., 1986: Preference Relations on a Set of Fuzzy Utilities as a Basis for Decision Making. "Fuzzy Sets and Systems", Vol. 20, 147-162.
  • Neumann J., Morgenstern O., 1944: Theory of Games and Economic Behavior. Princeton University Press.
  • Pazek K., Rozman C., 2009: Decision Making under Conditions of Uncertainty in Agriculture: A Case Study of Oil Crops. "Poljoprivreda (Osijek)", Vol. 15(1), 45-50.
  • Piasecki K., 1990: Decyzje i wiarygodne prognozy. Zeszyty Naukowe nr 106, Akademia Ekonomiczna, Poznań.
  • Render B., Stair R.M., Hanna M.E., 2006: Quantitative Analysis for Management. Pearson Prentice Hall, Upper Saddle River, New Jersey.
  • Savage L.J., 1961: The Foundations of Statistics Reconsidered. W: Studies in Subjective Probability. H.E. Kyburg, H.E. Smokler (eds.). New York, Wiley, 173-188.
  • Siddiqui A., Chronopoulos M.: Optimal Investment and Operational Decision Making under Risk Aversion and Uncertainty. "European Journal Operations Research" (w druku).
  • Sikora W. (red.), 2008: Badania operacyjne. Polskie Wydawnictwo Ekonomiczne, Warszawa.
  • Trzaskalik T., 2008: Wprowadzenie do badań operacyjnych z komputerem. Wydanie II zmienione. Polskie Wydawnictwo Ekonomiczne, Warszawa.
  • Wald A., 1950a: Basic Ideas of a General Theory of Statistical Decisions Rules. W: Selected Papers in Statistics and Probability. A. Wald (ed.). McGraw-Hill, New York, 656-668.
  • Wald A., 1950b: Statistical Decision Functions. Wiley, New York.

Document Type

Publication order reference



YADDA identifier

JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.