A classical problem in Decision theory is to represent a preference preorder among random variables. The fundamental Debreu’s Theorem states that, in the discrete case, a preference satisfies the so-called Sure Thing Principle if and only if it can be represented by means of a function that can be additively decomposed along the states of the world where the random variables are defined. Such a representation suggests that every discrete random variable may be seen as a “histogram” (union of rectangles), i.e., a set. This approach leads to several fruitful consequences, both from a theoretical and an interpretative point of view. Moreover, an immediate link can be found with another alternative approach, according to which a decision maker sorts random variables depending on their probability of outperforming a given benchmark. This way, a unified approach for different points of view may be achieved.
Lingua originaleEnglish
Titolo della pubblicazione ospiteAnalyzing Risk through Probabilistic Modeling in Operations Research
Numero di pagine21
Stato di pubblicazionePubblicato - 2016


  • Debreu's theorem
  • Decision theory
  • Sure Thing Principle
  • histograms.
  • preference preorder


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