On the complexity of the maximum satisfiability problem for Horn formulas
Information Processing Letters
The Minimum Satisfiability Problem
SIAM Journal on Discrete Mathematics
On the Complexity of Learning Lexicographic Strategies
The Journal of Machine Learning Research
Democratic approximation of lexicographic preference models
Proceedings of the 25th international conference on Machine learning
Journal of Artificial Intelligence Research
On graphical modeling of preference and importance
Journal of Artificial Intelligence Research
Learning conditionally lexicographic preference relations
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Faster extraction of high-level minimal unsatisfiable cores
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Aggregating dependency graphs into voting agendas in multi-issue elections
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Multi-agent soft constraint aggregation via sequential voting
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
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One approach to voting on several interrelated issues consists in using a language for compact preference representation, from which the voters' preferences are elicited and aggregated. A language usually comes with a domain restriction. We consider a well-known restriction, namely, conditionally lexicographic preferences, where both the relative importance between issues and the preference between values of an issue may depend on the values taken by more important issues. The naturally associated language consists in describing conditional importance and conditional preference by trees together with conditional preference tables. In this paper, we study the aggregation of conditionally lexicographic preferences, for several voting rules and several restrictions of the framework. We characterize computational complexity for some popular cases, and show that in many of them, computing the winner reduces in a very natural way to a maxsat problem.