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Explaining robust additive utility models by sequences of preference swaps

Author

Listed:
  • K. Belahcene

    (LGI, CentraleSupélec, Université Paris-Saclay)

  • C. Labreuche

    (Thales Research & Technology)

  • N. Maudet

    (Sorbonne Universités, UPMC Univ Paris 06, CNRS)

  • V. Mousseau

    (LGI, CentraleSupélec, Université Paris-Saclay)

  • W. Ouerdane

    (LGI, CentraleSupélec, Université Paris-Saclay)

Abstract

As decision-aiding tools become more popular everyday—but at the same time more sophisticated—it is of utmost importance to develop their explanatory capabilities. Some decisions require careful explanations, which can be challenging to provide when the underlying mathematical model is complex. This is the case when recommendations are based on incomplete expression of preferences, as the decision-aiding tool has to infer despite this scarcity of information. This step is key in the process but hardly intelligible for the user. The robust additive utility model is a necessary preference relation which makes minimal assumptions, at the price of handling a collection of compatible utility functions, virtually impossible to exhibit to the user. This strength for the model is a challenge for the explanation. In this paper, we come up with an explanation engine based on sequences of preference swaps, that is, pairwise comparison of alternatives. The intuition is to confront the decision maker with “elementary” comparisons, thus building incremental explanations. Elementary here means that alternatives compared may only differ on two criteria. Technically, our explanation engine exploits some properties of the necessary preference relation that we unveil in the paper. Equipped with this, we explore the issues of the existence and length of the resulting sequences. We show in particular that in the general case, no bound can be given on the length of explanations, but that in binary domains, the sequences remain short.

Suggested Citation

  • K. Belahcene & C. Labreuche & N. Maudet & V. Mousseau & W. Ouerdane, 2017. "Explaining robust additive utility models by sequences of preference swaps," Theory and Decision, Springer, vol. 82(2), pages 151-183, February.
    • Handle: RePEc:kap:theord:v:82:y:2017:i:2:d:10.1007_s11238-016-9560-1
    DOI: 10.1007/s11238-016-9560-1
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    References listed on IDEAS

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    1. Greco, Salvatore & Mousseau, Vincent & Slowinski, Roman, 2008. "Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions," European Journal of Operational Research, Elsevier, vol. 191(2), pages 416-436, December.
    2. Spliet, Remy & Tervonen, Tommi, 2014. "Preference inference with general additive value models and holistic pair-wise statements," European Journal of Operational Research, Elsevier, vol. 232(3), pages 607-612.
    3. Carlos A. Bana e Costa & João C. Lourenço & Manuel P. Chagas & João C. Bana e Costa, 2008. "Development of Reusable Bid Evaluation Models for the Portuguese Electric Transmission Company," Decision Analysis, INFORMS, vol. 5(1), pages 22-42, March.
    4. Matthias Ehrgott & José Rui Figueira & Salvatore Greco (ed.), 2010. "Trends in Multiple Criteria Decision Analysis," International Series in Operations Research and Management Science, Springer, number 978-1-4419-5904-1, September.
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