Imprecise Sampling and Direct Decision Making

Abstract : In decision theory, uncertainty is generally modeled through probabilities or probabilityintervals. Data however, when collected by sampling, do not provide probabilities (resp.,lower/upper probabilities) but frequencies (resp., lower/upper frequencies). Discrepanciesbetween the former and the latter are taken into account by the model presented: axiomaticrequirements are shown to imply that the ordering of the decisions must only depend on aquadruple (GEU, u, U, N), where GEU is the generalized expected utility evaluation of thedecision that would result from the assimilation of frequencies to lower/upper probabilities;u and U are the utility levels of, respectively, the worst and the best reachable outcomes;and N is the size of the sample. Additional axioms are given that ensure the existence of anadditive utility representing the ordering.
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Christophe Gonzales, Jean-Yves Jaffray. Imprecise Sampling and Direct Decision Making. Annals of Operations Research, Springer Verlag, 1998, 80, pp.207-235. ⟨10.1023/A:1018963914548⟩. ⟨hal-01195567⟩

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