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Decisions with Uncertain Consequences—A Total Ordering on Loss-Distributions

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  • Stefan Rass
  • Sandra König
  • Stefan Schauer

Abstract

Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action can be modeled by a random variable, then the decision problem boils down to comparing different effects (random variables) by comparing their distribution functions. Although the full space of probability distributions cannot be ordered, a properly restricted subset of distributions can be totally ordered in a practically meaningful way. We call these loss-distributions, since they provide a substitute for the concept of loss-functions in decision theory. This article introduces the theory behind the necessary restrictions and the hereby constructible total ordering on random loss variables, which enables decisions under uncertainty of consequences. Using data obtained from simulations, we demonstrate the practical applicability of our approach.

Suggested Citation

  • Stefan Rass & Sandra König & Stefan Schauer, 2016. "Decisions with Uncertain Consequences—A Total Ordering on Loss-Distributions," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-23, December.
  • Handle: RePEc:plo:pone00:0168583
    DOI: 10.1371/journal.pone.0168583
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    References listed on IDEAS

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    1. Stefan Rass, 2015. "On Game-Theoretic Risk Management (Part Two) -- Algorithms to Compute Nash-Equilibria in Games with Distributions as Payoffs," Papers 1511.08591, arXiv.org, revised Apr 2020.
    2. Stefan Rass, 2015. "On Game-Theoretic Risk Management (Part One) -- Towards a Theory of Games with Payoffs that are Probability-Distributions," Papers 1506.07368, arXiv.org, revised Apr 2020.
    3. W Henry Chiu, 2010. "Skewness Preference, Risk Taking and Expected Utility Maximisation," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 35(2), pages 108-129, December.
    4. Busby, J.S. & Onggo, B.S.S. & Liu, Y., 2016. "Agent-based computational modelling of social risk responses," European Journal of Operational Research, Elsevier, vol. 251(3), pages 1029-1042.
    5. Eichner, Thomas & Wagener, Andreas, 2011. "Increases in skewness and three-moment preferences," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 109-113, March.
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