Election control for VCR Euclidean preferences

Election control problems model situations where some entity (traditionally called the election chair) wants to ensure some agent's victory (the so-called, Constructive Control) or loss (the so-called Destructive Control) by either adding or deleting candidates or voters. Computational properties of deciding if such control actions can be successful is well-studied for many typical voting rules in various scenarios. In this paper we study complexity of election control problems for the Approval and Plurality Rules, focusing on the so-called VCR-elections (Voter-Candidate Range) which is a model where the agents of the election are identified with points in a metric space, and voters' preferences (as well as the candidates' charisma) are derived from their relative distance. We study the case of Euclidean metric in both one dimension (Euclidean preferences 'on a line') and two (Euclidean preferences 'in a plane') or more dimensions. This is joint work in progress with Jan Sznajd and Piotr Faliszewski.