Parameterized complexity of control by voter selection in Maximin, Copeland, Borda, Bucklin, and Approval election systems

Elections are an important preference aggregation model in a variety of areas. Given a pool of n potential voters, the chair may strategically selecting k voters from the pool to feed to an election system, in order to control the final outcome of the election system. This type of control, called control by voter selection, is closely related to two already well-studied types of control, i.e., control by voter addition and control by voter deletion. This paper studies parameterized complexity of control by voter selection for five election systems, i.e., Maximin, Copelandα (0⩽α⩽1), Borda, Bucklin, and Approval. We prove that constructive/destructive control of Maximin, constructive/destructive control of Copelandα, constructive control of Borda, constructive control of Bucklin, and constructive control of Approval are all W[2]-hard, with respect to the parameter “number of selected voters”.