Election control considers the problem of an adversary who attempts to tamper with a voting process, in order to either ensure that their favored candidate wins (constructive control) or another candidate loses (destructive control). As online social networks have become significant sources of information for potential voters, a new tool in an attacker's arsenal is to effect control by harnessing social influence, for example, by spreading fake news and other forms of misinformation through online social media. We consider the computational problem of election control via social influence, studying the conditions under which finding good adversarial strategies is computationally feasible. We consider two objectives for the adversary in both the constructive and destructive control settings: probability and margin of victory (POV and MOV, respectively). We present several strong negative results, showing, for example, that the problem of maximizing POV is inapproximable for any constant factor. On the other hand, we present approximation algorithms which provide somewhat weaker approximation guarantees, such as bicriteria approximations for the POV objective and constant-factor approximations for MOV. Finally, we present mixed integer programming formulations for these problems. Experimental results show that our approximation algorithms often find near-optimal control strategies, indicating that election control through social influence is a salient threat to election integrity.
Our work is closely related to two research areas: election control and influence maximization. These bodies of work are separate: to our knowledge there is no previous work which considers election control social influence. The computational study of election control was started by @cite_0 , who considered constructive control. The destructive control setting was introduced by @cite_25 . A large body of work has studied election control under different settings and voting rules @cite_41 @cite_18 including bribing voters @cite_27 @cite_9 @cite_28 @cite_15 @cite_34 , adding or deleting voters @cite_32 @cite_31 @cite_8 @cite_40 , and adding or deleting candidates @cite_20 @cite_8 @cite_40 . Another topic is strategic behavior on the part of the voters themselves @cite_16 @cite_36 @cite_7 . The main difference between our work and previous work on election control is that we introduce and analyze social influence as a novel mechanism for both constructive and destructive control.
@cite_18 @cite_31 @cite_7 @cite_8 @cite_41 @cite_28 @cite_9 @cite_36 @cite_32 @cite_16 @cite_0 @cite_27 @cite_40 @cite_15 @cite_34 @cite_25 @cite_20
2950252656 2026607260 1644339822 103664523
We study the control complexity of fallback voting. Like manipulation and bribery, electoral control describes ways of changing the outcome of an election; unlike manipulation or bribery attempts, control actions---such as adding deleting partitioning either candidates or voters---modify the participative structure of an election. Via such actions one can try to either make a favorite candidate win ("constructive control") or prevent a despised candidate from winning ("destructive control"). Computational complexity can be used to protect elections from control attempts, i.e., proving an election system resistant to some type of control shows that the success of the corresponding control action, though not impossible, is computationally prohibitive. We show that fallback voting, an election system combining approval with majority voting, is resistant to each of the common types of candidate control and to each common type of constructive control. Among natural election systems with a polynomial-time winner problem, only plurality and sincere-strategy preference-based approval voting (SP-AV) were previously known to be fully resistant to candidate control, and only Copeland voting and SP-AV were previously known to be fully resistant to constructive control. However, plurality has fewer resistances to voter control, Copeland voting has fewer resistances to destructive control, and SP-AV (which like fallback voting has 19 out of 22 proven control resistances) is arguably less natural a system than fallback voting. Elections are a central model in a variety of areas. This paper studies parameterized computational complexity of five control problems in the Maximin election. We obtain the following results: constructive control by adding candidates is W[2]-hard with respect to the parameter ''number of added candidates''; both constructive and destructive control by adding deleting voters are W[1]-hard with respect to the parameter ''number of added deleted voters''. In this paper, we propose a framework to study a general class of strategic behavior in voting, which we call vote operations. We prove the following theorem: if we fix the number of alternatives, generate @math votes i.i.d. according to a distribution @math , and let @math go to infinity, then for any @math , with probability at least @math , the minimum number of operations that are needed for the strategic individual to achieve her goal falls into one of the following four categories: (1) 0, (2) @math , (3) @math , and (4) @math . This theorem holds for any set of vote operations, any individual vote distribution @math , and any integer generalized scoring rule, which includes (but is not limited to) almost all commonly studied voting rules, e.g., approval voting, all positional scoring rules (including Borda, plurality, and veto), plurality with runoff, Bucklin, Copeland, maximin, STV, and ranked pairs. We also show that many well-studied types of strategic behavior fall under our framework, including (but not limited to) constructive destructive manipulation, bribery, and control by adding deleting votes, margin of victory, and minimum manipulation coalition size. Therefore, our main theorem naturally applies to these problems. Control of elections refers to attempts by an agent to, via such actions as addition deletion partition of candidates or voters, ensure that a given candidate wins (Bartholdi, Tovey, & Trick 1992). An election system in which such an agent's computational task is NP-hard is said to be resistant to the given type of control. Aside from election systems with an NP-hard winner problem, the only systems known to be resistant to all the standard control types are highly artificial election systems created by hybridization (Hemaspaandra, Hemaspaandra, & Rothe 2007b). In this paper, we prove that an election system developed by the 13th century mystic Ramon Llull and the well-studied Copeland election system are both resistant to all the standard types of (constructive) electoral control other than one variant of addition of candidates. This is the most comprehensive resistance to control yet achieved by any natural election system whose winner problem is in P. In addition, we show that Llull and Copeland voting are very broadly resistant to bribery attacks, and we integrate the potential irrationality of voter preferences into many of our results.