Aggregating Conditionally Lexicographic Preferences on Multi-Issue Domains

One approach to voting on several interrelated issues consists in using a language for com-pact 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 impor-tance 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 restriction of the framework. We characterizes 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.