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Preference Elicitation and Robust Optimization with Multi-Attribute Quasi-Concave Choice Functions.
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This paper considers ambiguity in choice functions over a multi-attribute prospect space and proposes two approaches based respectively on the support functions and level functions of quasi-concave functions to develop tractable formulations of the maximin preference robust optimization model.Abstract:
Decision maker's preferences are often captured by some choice functions which are used to rank prospects. In this paper, we consider ambiguity in choice functions over a multi-attribute prospect space. Our main result is a robust preference model where the optimal decision is based on the worst-case choice function from an ambiguity set constructed through preference elicitation with pairwise comparisons of prospects. Differing from existing works in the area, our focus is on quasi-concave choice functions rather than concave functions and this enables us to cover a wide range of utility/risk preference problems including multi-attribute expected utility and $S$-shaped aspirational risk preferences. The robust choice function is increasing and quasi-concave but not necessarily translation invariant, a key property of monetary risk measures. We propose two approaches based respectively on the support functions and level functions of quasi-concave functions to develop tractable formulations of the maximin preference robust optimization model. The former gives rise to a mixed integer linear programming problem whereas the latter is equivalent to solving a sequence of convex risk minimization problems. To assess the effectiveness of the proposed robust preference optimization model and numerical schemes, we apply them to a security budget allocation problem and report some preliminary results from experiments.read more
Citations
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Preference Robust Distortion Risk Measure and Its Application
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References
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TL;DR: Theory of games and economic behavior as mentioned in this paper is the classic work upon which modern-day game theory is based, and it has been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations.
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Coherent Measures of Risk
TL;DR: In this paper, the authors present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "coherent", and demonstrate the universality of scenario-based methods for providing coherent measures.
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Comparison Methods for Stochastic Models and Risks
Alfred Müller,Dietrich Stoyan +1 more
TL;DR: In this article, the authors present an univariate Stochastic model for queuing systems and compare its properties with those of other non-stochastic models and compare risks.
Journal ArticleDOI
Multiattribute and single-attribute utility functions for the health utilities index mark 3 system.
David Feeny,William Furlong,George W. Torrance,Charles H. Goldsmith,Zenglong Zhu,S DePauw,Margaret Denton,Michael H. Boyle +7 more
TL;DR: The HUI3 scoring function has strong theoretical and empirical foundations and performs well in predicting directly measured scores and provides a practical way to obtain utility scores based on community preferences.