title: Decisions with Uncertain Consequences-A Total Ordering on Loss-Distributions.
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.
authors.affiliation: Universität Klagenfurt, Institute of Applied Informatics, Klagenfurt, Austria.
authors.forename: Stefan
authors.identifier: http://orcid.org/0000-0003-2821-2489
authors.initials: S
authors.lastname: Rass
authors.affiliation: Austrian Institute of Technology, Safety & Security Department, Klagenfurt, Austria.
authors.forename: Sandra
authors.initials: S
authors.lastname: König
authors.affiliation: Austrian Institute of Technology, Safety & Security Department, Klagenfurt, Austria.
authors.forename: Stefan
authors.initials: S
authors.lastname: Schauer
mesh_terms: D016494:Computer Security; D003657:Decision Making; D003662:Decision Theory; D006801:Humans; D007600:Judgment; D008962:Models, Theoretical; D011336:Probability; D018570:Risk Assessment; D045483:Rivers / Q000737:chemistry; D035501:Uncertainty; D014867:Water / Q000378:metabolism*
chemical_list: D014867:Water