## 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.

Original language | English |
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Title of host publication | Algorithmic Decision Theory - 7th International Conference, ADT 2021, Proceedings |

Editors | Dimitris Fotakis, David Ríos Insua |

Pages | 86-100 |

Number of pages | 15 |

DOIs | |

State | Published - 2021 |

Event | 7th International Conference on Algorithmic Decision Theory, ADT 2021 - Toulouse, France Duration: Nov 3 2021 → Nov 5 2021 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 13023 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 7th International Conference on Algorithmic Decision Theory, ADT 2021 |
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Country/Territory | France |

City | Toulouse |

Period | 11/3/21 → 11/5/21 |

### Bibliographical note

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

Publisher Copyright:

© 2021, Springer Nature Switzerland AG.

## Keywords

- Lexicographic preference trees
- Preference representation and reasoning
- Probabilistic preference models

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science (all)