A Different Way to Look at Random Variables: Do Decision Makers Look at Functions or at Sets?

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Author(s): Erio Castagnoli (Bocconi University, Italy), Marzia De Donno (University of Parma, Italy), Gino Favero (University of Parma, Italy)and Paola Modesti (University of Parma, Italy)
Copyright: 2016
Pages: 21
Source title: Analyzing Risk through Probabilistic Modeling in Operations Research
Source Author(s)/Editor(s): Dariusz Jacek Jakóbczak (Technical University of Koszalin, Poland)
DOI: 10.4018/978-1-4666-9458-3.ch008

Keywords: Business & Management / Business Science Reference / Management Science / Operations and Service Management

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Abstract

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.

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