Abstract We investigate the computational complexity of electoral control in elections. Electoral control describes the scenario where the election chair seeks to alter the outcome of the election by structural changes such as adding, deleting, or replacing either candidates or voters. Such control actions have been studied in the literature for a lot of prominent voting rules. We complement those results by solving several open cases for Copeland $$^{\alpha }$$ α , maximin,k-veto, plurality with runoff, veto with runoff, Condorcet, fallback, range voting, and normalized range voting.

Standard (offline) control scenarios in elections (such as adding, deleting, or partitioning either voters or candidates) have been studied for many voting systems, natural and less natural ones, and the related control problems have been classified in terms of their complexity. However, for one of the most important natural voting systems, the Borda Count, only a few such complexity results are known. We reduce the number of missing cases by pinpointing the complexity of three control scenarios for Borda elections, including some that arguably are among the practically most relevant ones. We also study online candidate control, an interesting dynamical, partial-information model due to Hemaspaandra et al. (2012a), who mainly focused on general complexity bounds by constructing artificial voting systems—only recently they succeeded in classifying four problems of online candidate control for one natural voting system: sequential plurality (Hemaspaandra et al. 2016). We settle the complexity of another four natural cases: constructive and destructive online control by deleting and adding candidates in sequential Borda elections.