Abstract
An intuitively appealing “probability dominance” relation for random outcomes is defined and investigated. Its properties, strengths, and weaknesses relative to stochastic dominance and meanvariance dominance are studied. It is shown that the proposed probability dominance complements existing solution concepts and strengthens one's confidence in decision making under uncertainty. Fundamental characteristics of nondominated random payoffs and methods for identifying them, for both general and specific classes, are reported. Application pitfalls and possible extensions are also discussed.
Similar content being viewed by others
References
Fishburn, P. C.,Utility Theory for Decision Making, John Wiley and Sons, New York, New York, 1970.
Brumelle, S. L., andVickson, R. G.,A Unified Approach to Stochastic Dominance, Stochastic Optimization Models in Finance, Edited by W. T. Ziemba and R. G. Vickson, Academic Press, New York, New York, 1975.
Fishburn, P. C.,Stochastic Dominance without Transitive Preferences, Management Science, Vol. 24, pp. 1268–1277, 1978.
Fishburn, P. C.,Stochastic Dominance: Theory and Application, The Role and Effectiveness of Theories of Decision in Practice, Edited by D. J. White and K. C. Bowen, Hodder and Stoughton, London, England, pp. 60–72, 1975.
Hanoch, G., andLevy, H.,The Efficiency Analysis of Choices Involving Risk, Review of Economic Studies, Vol. 36, pp. 335–346, 1969.
Markowitz, H. M.,Portfolio Selection, Journal of Finance, Vol. 6, pp. 77–91, 1952.
Charnes, A., andCooper, W. W.,Chance-Constrained Programming, Management Science, Vol. 6, pp. 73–79, 1969.
Simon, H. A.,Administrative Behavior, The Macmillan Company, New York, New York, 1947.
Yu, P. L.,Behavior Bases and Habitual Domains of Human Decision/Behavior—Concepts and Applications, Proceedings of the Third Conference on Multiple Criteria Decision Making—Theory and Application, Edited by G. Fandel and T. Gal, Springer-Verlag, New York, New York, 1980.
Pitman, E. J. G.,The Closest Estimates of Statistical Parameters, Proceedings of the Cambridge Philosophical Society, Vol. 33, pp. 212–222, 1937.
Savage, L. J.,The Foundations of Statistics, John Wiley and Sons, New York, New York, 1954.
Wrather, C.,A Model of the General Bargaining Interaction with Application to Buyer/Seller Bargaining, PhD Dissertation, Graduate School of Business, University of Texas, Austin, Texas, 1980.
Libby, R., andFishburn, P. C.,Behavioral Models of Risk Taking in Business Decision: A Survey and Evaluation, Journal of Accounting Research, Vol. 15, pp. 272–292, 1977.
Blyth, C. R.,Some Probability Paradoxes in Choice from among Random Alternatives, Journal of the American Statistical Association, Vol. 67, pp. 366–373, 1972.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wrather, C., Yu, P.L. Probability dominance in random outcomes. J Optim Theory Appl 36, 315–334 (1982). https://doi.org/10.1007/BF00934350
Issue Date:
DOI: https://doi.org/10.1007/BF00934350