Copeland Voting Fully Resists Constructive Control

Control and bribery are settings in which an external agent seeks to influence the outcome of an election. Faliszewski et al. [7] proved that Llull voting (which is here denoted by Copeland) and a variant (here denoted by Copeland) of Copeland voting are computationally resistant to many, yet not all, types of constructive control and that they also provide broad resistance to bribery. We study a parameterized version of Copeland voting, denoted by Copelandα, where the parameter α is a rational number between 0 and 1 that specifies how ties are valued in the pairwise comparisons of candidates in Copeland elections. We establish resistance or vulnerability results, in every previously studied control scenario, for Copelandα for each rational α, 0 < α < 1. In particular, we prove that Copeland, the system commonly referred to as “Copeland voting,” provides full resistance to constructive control. Among the systems with a polynomial-time winner problem, this is the first natural election system proven to have full resistance to constructive control. Results on bribery and fixed-parameter tractability of bounded-case control proven for Copeland and Copeland in [7] are extended to Copelandα for each rational α, 0 < α < 1; we also give results in more flexible models such as microbribery and extended control.