On the Complexity of the Two-Stage Majoritarian Rule

Abstract: Sequential voting rules have been extensively used in parliamentary and legislative decision making. After observing that the prevalent successive and the amendment rules fail several fundamental axioms, Horan and Sprumont [2021] proposed very recently a two-stage sequential rule which satisfies a variety of desirable properties. This paper examines this rule by investigating the complexity of Agenda Control, Coalition Manipulation, Possible Winner, Necessary Winner, and eight standard election control problems. Our study offers a comprehensive understanding of the complexity landscape of these problems.