Lifting a preference order on elements of some universe to a preference order on subsets of this universe is often guided by postulated properties the lifted order should have. Wellknown impossibility results pose severe limits on when such liftings exist if all non-empty subsets of the universe are to be ordered. The extent to which these negative results carry over to other families of sets is not known. In this paper, we consider families of sets that induce connected subgraphs in graphs. For such families, common in applications, we study whether lifted orders satisfying the well-studied axioms of dominance and (strict) independence exist for every or, in another setting, for some underlying order on elements (strong and weak orderability). We characterize families that are strongly and weakly orderable under dominance and strict independence, and obtain a tight bound on the class of families that are strongly orderable under dominance and independence.
|Number of pages||51|
|Journal||Journal of Artificial Intelligence Research|
|State||Published - Dec 2019|
Bibliographical noteFunding Information:
This work was funded by the Austrian Science Fund (FWF) under grant number Y698 and by the NSF under grant number IIS-1618783.
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ASJC Scopus subject areas
- Artificial Intelligence