Skip to main content
SpringerLink
Log in
Book cover

International Conference on Algorithmic Decision Theory

ADT 2021: Algorithmic Decision Theory pp 86–100Cite as

Probabilistic Lexicographic Preference Trees

  • Conference paper
  • First Online:

  • 600 Accesses

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

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.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

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.

References

  1. Bigot, D., Zanuttini, B., Fargier, H., Mengin, J.: Probabilistic conditional preference networks. In: Proceedings of the Conference on Uncertainty in Artificial Intelligence (2013)

    Google Scholar 

  2. Booth, R., Chevaleyre, Y., Lang, J., Mengin, J., Sombattheera, C.: Learning conditionally lexicographic preference relations. In: ECAI, pp. 269–274 (2010)

    Google Scholar 

  3. Boutilier, C., Brafman, R., Domshlak, C., Hoos, H., Poole, D.: CP-nets: a tool for representing and reasoning with conditional ceteris paribus preference statements. J. Artif. Intell. Res. 21, 135–191 (2004)

    Google Scholar 

  4. Bouveret, S., Endriss, U., Lang, J.: Conditional importance networks: a graphical language for representing ordinal, monotonic preferences over sets of goods. In: IJCAI (2009)

    Google Scholar 

  5. Colman, A.M., Stirk, J.A.: Singleton bias and lexicographic preferences among equally valued alternatives. J. Econ. Behav. Org. 40(4), 337–351 (1999)

    Google Scholar 

  6. Cornelio, C., Grandi, U., Goldsmith, J., Mattei, N., Rossi, F., Venable, K.B.: Reasoning with PCP-nets in a multi-agent context. In: AAMAS, pp. 969–977 (2015)

    Google Scholar 

  7. De Saint-Cyr, F.D., Lang, J., Schiex, T.: Penalty logic and its link with Dempster-Shafer theory. In: Uncertainty Proceedings 1994, pp. 204–211. Elsevier (1994)

    Google Scholar 

  8. Dubois, D., Lang, J., Prade, H.: Possibilistic logic. In: Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 439–513. Oxford University Press (1994)

    Google Scholar 

  9. Fishburn, P.C.: Utilities and decision rules: a survey’, lexicographic orders. Manag. Sci. 20, 1442–1471 (1974)

    Google Scholar 

  10. Ford, J.K., Schmitt, N., Schechtman, S.L., Hults, B.M., Doherty, M.L.: Process tracing methods: contributions, problems, and neglected research questions. Organ. Behav. Hum. Decis. Process. 43(1), 75–117 (1989)

    Google Scholar 

  11. Lang, J., Mengin, J., Xia, L.: Voting on multi-issue domains with conditionally lexicographic preferences. Artif. Intell. 265, 18–44 (2018)

    Google Scholar 

  12. Liu, X., Truszczynski, M.: Learning partial lexicographic preference trees over combinatorial domains. In: Proceedings of the 29th AAAI Conference on Artificial Intelligence (AAAI), pp. 1539–1545. AAAI Press (2015)

    Google Scholar 

  13. Liu, X., Truszczynski, M.: Reasoning with preference trees over combinatorial domains. In: Walsh, T. (ed.) ADT 2015. LNCS, vol. 9346, pp. 19–34. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23114-3_2

  14. Liu, X., Truszczynski, M.: Voting-based ensemble learning for partial lexicographic preference forests over combinatorial domains. Ann. Math. Artif. Intell. 87(1–2), 137–155 (2019)

    Google Scholar 

  15. Lukasiewicz, T., Martinez, M.V., Simari, G.I.: Probabilistic preference logic networks. In: ECAI, pp. 561–566 (2014)

    Google Scholar 

  16. Moshkovich, H., Mechitov, A., Olson, D.: Verbal decision analysis. In: Multiple Criteria Decision Analysis: State of the Art Surveys. ISOR, vol. 78, pp. 609–633. Springer, New York (2005). https://doi.org/10.1007/0-387-23081-5_15

  17. Westenberg, M.R.M., Koele, P.: Multi-attribute evaluation processes: methodological and conceptual issues. Acta Psychol. 87(2–3), 65–84 (1994)

    Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

  1. School of Computing, University of North Florida, Jacksonville, USA

    Xudong Liu

  2. Department of Computer Science, University of Kentucky, Lexington, USA

    Miroslaw Truszczynski

Authors
  1. Xudong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miroslaw Truszczynski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xudong Liu .

Editor information

Editors and Affiliations

  1. National Technical University of Athens, Athens, Greece

    Dimitris Fotakis

  2. Consejo Superior de Investigaciones Cientificas, Madrid, Madrid, Spain

    David Ríos Insua

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-87755-2

  • Online ISBN: 978-3-030-87756-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation