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Almost stochastic dominance under inconsistent utility and loss functions

  • Chunling Luo (a1), Zhou He (a1) and Chin Hon Tan (a1)


Current literature on stochastic dominance assumes utility/loss functions to be the same across random variables. However, decision models with inconsistent utility functions have been proposed in the literature. The use of inconsistent loss functions when comparing between two random variables can also be appropriate under other problem settings. In this paper we generalize almost stochastic dominance to problems with inconsistent utility/loss functions. In particular, we propose a set of conditions that is necessary and sufficient for clear preferences when the utility/loss functions are allowed to vary across different random variables.


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* Postal address: Department of Industrial & Systems Engineering, National University of Singapore, Singapore.
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[1] Becker, J. L. and Sarin, R. K. (1987). Lottery dependent utility. Manag. Sci. 33, 13671382.
[2] Becker, J. L. and Sarin, R. K. (1989). Decision analysis using lottery-dependent utility. J. Risk Uncertainty 2, 105117.
[3] Carlsson, C. et al. (2006). Are pharmaceuticals potent environmental pollutants?: Part I: Environmental risk assessments of selected active pharmaceutical ingredients. Sci. Total Environ. 364, 6787.
[4] Daniels, R. L. and Keller, L. R. (1990). An experimental evaluation of the descriptive validity of lottery-dependent utility theory. J. Risk Uncertainty 3, 115134.
[5] De La Cal, J. and Cárcamo, J. (2010). Inverse stochastic dominance, majorization, and mean order statistics. J. Appl. Prob. 47, 277292.
[6] Ferrari, B. et al. (2004). Environmental risk assessment of six human pharmaceuticals: are the current environmental risk assessment procedures sufficient for the protection of the aquatic environment? Environ. Toxicol. Chem. 23, 13441354.
[7] Komori, K., Suzuki, Y., Minamiyama, M. and Harada, A. (2013). Occurrence of selected pharmaceuticals in river water in Japan and assessment of their environmental risk. Environ. Monit. Assess. 185, 45294536.
[8] Leshno, M. and Levy, H. (2002). Preferred by "all" and preferred by "most" decision makers: almost stochastic dominance. Manag. Sci. 48, 10741085.
[9] Levy, H. (1992). Stochastic dominance and expected utility: survey and analysis. Manag. Sci. 38, 555593.
[10] Levy, H. (2016). Stochastic Dominance: Investment Decision Making Under Uncertainty, 3rd edn. Springer, Cham.
[11] Müller, A., Scarsini, M., Tsetlin, I. and Winkler, R. L. (2017). Between first- and second-order stochastic dominance. To appear in Manag. Sci. Available at
[12] Müller, A. and Stoyan, D. (2002). Comparison Methods for Stochastic Models and Risks. John Wiley, Chichester.
[13] Pal, A. et al. (2014). Emerging contaminants of public health significance as water quality indicator compounds in the urban water cycle. Environ. Internat. 71, 4662.
[14] Schmidt, U. (2001). Lottery dependent utility: a reexamination. Theory Decision 50, 3558.
[15] Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.
[16] Tan, C. H. (2015). Weighted almost stochastic dominance: revealing the preferences of most decision makers in the St. Petersburg paradox. Decision Anal. 12, 7480.
[17] Tan, C. H. and Luo, C. (2017). Clear preferences under partial distribution information. Decision Anal. 14, 6573.
[18] Tsetlin, I., Winkler, R. L., Huang, R. J. and Tzeng, L. Y. (2015). Generalized almost stochastic dominance. Operat. Res. 63, 363377.
[19] Tzeng, L. Y., Huang, R. J. and Shih, P.-T. (2013). Revisiting almost second-degree stochastic dominance. Manag. Sci. 59, 12501254.
[20] Yu, Y. (2009). Stochastic ordering of exponential family distributions and their mixtures. J. Appl. Prob. 46, 244254.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
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