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Sincere‐Strategy Preference‐Based Approval Voting Fully Resists Constructive Control and Broadly Resists Destructive Control
Author(s) -
Erdélyi Gábor,
Nowak Markus,
Rothe Jörg
Publication year - 2009
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200810020
Subject(s) - voting , constructive , approval voting , preference , control (management) , anti plurality voting , computer science , cardinal voting systems , bullet voting , mathematical economics , disapproval voting , law and economics , computer security , operations research , political science , artificial intelligence , mathematics , law , economics , process (computing) , statistics , programming language , politics
We study sincere‐strategy preference‐based approval voting (SP‐AV), a system proposed by Brams and Sanver [1] and here adjusted so as to coerce admissibility of the votes (rather than excluding inadmissible votes a priori ), with respect to procedural control. In such control scenarios, an external agent seeks to change the outcome of an election via actions such as adding/deleting/partitioning either candidates or voters. SP‐AV combines the voters' preference rankings with their approvals of candidates, where in elections with at least two candidates the voters' approval strategies are adjusted – if needed – to approve of their most‐preferred candidate and to disapprove of their least‐preferred candidate. This rule coerces admissibility of the votes even in the presence of control actions, and hybridizes, in effect, approval with pluralitiy voting. We prove that this system is computationally resistant (i.e., the corresponding control problems are NP‐hard) to 19 out of 22 types of constructive and destructive control. Thus, SP‐AV has more resistances to control than is currently known for any other natural voting system with a polynomial‐time winner problem. In particular, SP‐AV is (after Copeland voting, see Faliszewski et al. [2, 3]) the second natural voting system with an easy winner‐determination procedure that is known to have full resistance to constructive control, and unlike Copeland voting it in addition displays broad resistance to destructive control (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)