On the Tree Representations of Dichotomous Preferences

We study numerous restricted domains of dichotomous preferences with respect to some tree structures. Particularly, we study the relationships among these domains and the ones proposed by Elkind and Lackner [2015]. We also show that recognizing all the restricted domains proposed in this paper is polynomial-time solvable. Finally, we explore the complexity of winner determination for several important approval-based multiwinner voting rules when restricted to these domains.