Abstract
Given information about which options a decision-maker definitely rejects from given finite sets of options, we study the implications for decision-making with E-admissibility. This means that from any finite set of options, we reject those options that no probability mass function compatible with the given information gives the highest expected utility. We use the mathematical framework of choice functions to specify choices and rejections, and specify the available information in the form of conditions on such functions. We characterise the most conservative extension of the given information to a choice function that makes choices based on E-admissibility, and provide an algorithm that computes this extension by solving linear feasibility problems.
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Notes
- 1.
Levi’s original definition considered credal sets that are convex, whereas we do not require this. In fact one of the strengths of our approach is that an assessment can lead to non-convex credal sets; see the example in Sect. 5 further on.
- 2.
It can for instance be considered as a linear programming problem, by adding the trivial objective function that is zero everywhere. Feeding this into a linear programming software package, the software will announce whether the problem is feasible. For a deeper understanding of how software solves such feasibility problems, we refer to the explanation of initial feasible solutions in Matoušek and Gärtner (2006, Sect. 5.6).
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Decadt, A., Erreygers, A., De Bock, J., de Cooman, G. (2023). Decision-Making with E-Admissibility Given a Finite Assessment of Choices. In: García-Escudero, L.A., et al. Building Bridges between Soft and Statistical Methodologies for Data Science . SMPS 2022. Advances in Intelligent Systems and Computing, vol 1433. Springer, Cham. https://doi.org/10.1007/978-3-031-15509-3_13
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