Sincere‐Strategy Preference‐Based Approval Voting Fully Resists Constructive Control and Broadly Resists Destructive Control

Abstract

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.

Bypassing Combinatorial Protections: Polynomial-Time Algorithms for Single-Peaked Electorates

“…When β = 1, Copeland β is known as Llull, a system defined by the mystic Ramon Llull in the thirteenth century (see Hägele & Pukelsheim, 2001). Llull's election system is known to be remarkably resistant, computationally, to bribery and control attacks (Faliszewski et al, 2009a, although see also Erdélyi, Nowak, & Rothe, 2009, Erdélyi & Rothe, 2010, Erdélyi, Piras, & Rothe, 2011, for different highly resistant systems, and see Hemaspaandra, Hemaspaandra, & Rothe, 2009, regarding how extremely resistant artificial systems can be constructed).…”

Parameterized complexity of control problems in Maximin election

“…The (parameterized) computational complexity of control problems is still open for many elections, e.g., Borda [25] and Sincerestrategy Preference-based Approval [10]. In the future, we will study them.…”

“…Many papers were devoted to the computational analysis of the hardness of how an external agent or a group of voters can skew the result of elections. The most studied scenarios are control [1,10,16,18,22], manipulation [2,6], bribery [13,15], and lobbying [5,9]. This paper focuses on control.…”

Elections with Few Voters: Candidate Control Can Be Easy

“…Such election modifications could be either introducing some new candidates or voters or removing some existing candidates or voters from the election or partitioning candidates or voters (Bartholdi III, Tovey, & Trick, 1992;Erdélyi, Nowak, & Rothe, 2009;Faliszewski, Hemaspaandra, Hemaspaandra, & Rothe, 2009;Hemaspaandra, Hemaspaandra, & Rothe, 2007;Menton, 2013;Menton & Singh, 2013;Faliszewski, Hemaspaandra, Hemaspaandra, & Rothe, 2011;Parkes & Xia, 2012). We focus on the computational complexity of election control by adding and deleting candidates (that is, candidate control), for the case where the election involves only a few voters.…”