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Probabilistic Lexicographic Preference Trees

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Algorithmic Decision Theory (ADT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13023))

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Abstract

We introduce probabilistic lexicographic preference trees (or PrLPTs for short). We show that they offer intuitive and often compact representations of non-deterministic qualitative preferences over alternatives in multi-attribute (or, combinatorial) binary domains. We specify how a PrLPT defines the probability that a given outcome has a given rank, and the probability that a given outcome is preferred to another one, and show how to compute these probabilities in polynomial time. We also show that computing outcomes that are optimal with the probability equal to or exceeding a given threshold for some classes of PrLP-trees is in P, but for some other classes the problem is NP-hard.

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Notes

  1. 1.

    Due to space restrictions, we provide a proof to the first of these results only.

  2. 2.

    We refer to the work by Lang et al. [11] for the definitions of ranks and dominance for LP-trees.

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Acknowledgements

This work was partially supported by the NSF grant IIS-1618783.

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Correspondence to Xudong Liu .

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Liu, X., Truszczynski, M. (2021). Probabilistic Lexicographic Preference Trees. In: Fotakis, D., Ríos Insua, D. (eds) Algorithmic Decision Theory. ADT 2021. Lecture Notes in Computer Science(), vol 13023. Springer, Cham. https://doi.org/10.1007/978-3-030-87756-9_6

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  • DOI: https://doi.org/10.1007/978-3-030-87756-9_6

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