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Minimax regret approaches for preference elicitation with rank-dependent aggregators

  • Original Article
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EURO Journal on Decision Processes

Abstract

Recently there has been a growing interest in non-linear aggregation models to represent the preferences of a decision maker in a multicriteria decision problem. Such models are expressive as they are able to represent synergies (positive and negative) between attributes or criteria, thus modeling different decision behaviors. They also make it possible to generate Pareto-optimal solutions that cannot be obtained by optimizing a linear combination of criteria. This is the case of rank-dependent aggregation functions such as Ordered Weighted Averages and their weighted extensions, but more generally of Choquet integrals. A key question is how to assess the parameters of such models to best fit decision maker’s behaviors or preferences. In this work, adopting a principled decision-theoretic approach, we consider the optimization problem induced by adaptive elicitation using the minimax regret criterion.

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Notes

  1. Linear optimizations are done under MatLab using the Gurobi solver on a machine with an Intel Core i7 CPU 3.60 GHz with 16 GB of memory.

  2. Linear optimizations are done using the Gurobi library of Java.

  3. Linear optimizations are done under MatLab using the Gurobi solver on a machine with an Intel Core i7 CPU 3.60 GHz with 16 GB of memory.

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Acknowledgments

This work is part of the ELICIT project supported by the French National Research Agency through the Idex Sorbonne Universités under Grant ANR-11-IDEX-0004-02.

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Authors and Affiliations

  1. Sorbonne Universités, UPMC Univ Paris 06, UMR 7606, LIP6 CNRS, UMR 7606, LIP6, 4 Place Jussieu, 75005, Paris, France

    Nawal Benabbou, Christophe Gonzales, Patrice Perny & Paolo Viappiani

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  1. Nawal Benabbou
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  2. Christophe Gonzales
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  3. Patrice Perny
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  4. Paolo Viappiani
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Correspondence to Patrice Perny.

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Benabbou, N., Gonzales, C., Perny, P. et al. Minimax regret approaches for preference elicitation with rank-dependent aggregators. EURO J Decis Process 3, 29–64 (2015). https://doi.org/10.1007/s40070-015-0040-6

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