We study sincere-strategy preference-based approval voting (SP-AV), a systemproposed by Brams and Sanver [Electoral Studies, 25(2):287-305, 2006], and hereadjusted so as to coerce admissibility of the votes (rather than excludinginadmissible votes a priori), with respect to procedural control. In suchcontrol scenarios, an external agent seeks to change the outcome of an electionvia actions such as adding/deleting/partitioning either candidates or voters.SP-AV combines the voters' preference rankings with their approvals ofcandidates, where in elections with at least two candidates the voters'approval strategies are adjusted--if needed--to approve of their most-preferredcandidate and to disapprove of their least-preferred candidate. This rulecoerces admissibility of the votes even in the presence of control actions, andhybridizes, in effect, approval with pluralitiy voting. We prove that this system is computationally resistant (i.e., thecorresponding control problems are NP-hard) to 19 out of 22 types ofconstructive and destructive control. Thus, SP-AV has more resistances tocontrol than is currently known for any other natural voting system with apolynomial-time winner problem. In particular, SP-AV is (after Copeland voting,see Faliszewski et al. [AAIM-2008, Springer LNCS 5034, pp. 165-176, 2008]) thesecond natural voting system with an easy winner-determination procedure thatis known to have full resistance to constructive control, and unlike Copelandvoting it in addition displays broad resistance to destructive control.
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