We consider the problem of predicting winners in elections given complete knowledge about all possible candidates, all possible voters (together with their preferences), but in the case where it is uncertain either which candidates exactly register for the election or which voters cast their votes. Under reasonable assumptions our problems reduce to counting variants of election control problems. We either give polynomial-time algorithms or prove #P-completeness results for counting variants of control by adding/deleting candidates/voters for Plurality, k -Approval, Approval, Condorcet, and Maximin voting rules.

Approval-like voting rules, such as Sincere-Strategy Preference-Based Approval voting (SP-AV), the Bucklin rule (an adaptive variant of k-Approval voting), and the Fallback rule (an adaptive variant of SP-AV) have many desirable properties: for example, they are easy to understand and encourage the candidates to choose electoral platforms that have a broad appeal. In this paper, we investigate both classic and parameterized computational complexity of electoral campaign management under such rules. We focus on two methods that can be used to promote a given candidate: asking voters to move this candidate upwards in their preference order or asking them to change the number of candidates they approve of. We show that finding an optimal campaign management strategy of the first type is easy for both Bucklin and Fallback. In contrast, the second method is computationally hard even if the degree to which we need to affect the votes is small. Nevertheless, we identify a large class of scenarios that admit a fixed-parameter tractable algorithm.

The conventional model of coalition formation considers every possible subset of agents as a potential coalition. However, in many real-world applications, there are inherent constraints on feasible coalitions: for instance, certain agents may be prohibited from being in the same coalition, or the coalition structure may be required to consist of coalitions of the same size. In this paper, we present the first systematic study of constrained coalition formation (CCF). We propose a general framework for this problem, and identify an important class of CCF settings, where the constraints specify which groups of agents should/should not work together. We describe a procedure that transforms such constraints into a structured input that allows coalition formation algorithms to identify, without any redundant computations, all the feasible coalitions. We then use this procedure to develop an algorithm for generating an optimal (welfare-maximizing) constrained coalition structure, and show that it outperforms existing state-of-the-art approaches by several orders of magnitude.

AI’s War on Manipulation: Are We Winning?

We provide an overview of more than two decades of work, mostly in AI, that studies computational complexity as a barrier against manipulation in elections. We provide an overview of more than two decades of work, mostly in AI, that studies computational complexity as a barrier against manipulation in elections.

Friedgut, Kalai, and Nisan also assume that there is a single manipulator. In the first part of the survey we discussed worstcase Their main insight is that a completely random hardness as a barrier against manipulation in manipulation may succeed with nonnegligible elections.

We explore the relationship between two approaches to rationalizing voting rules: the maximum likelihood estimation (MLE) framework originally suggested by Condorcet and recently studied by Conitzer, Rognlie, and Xia, and the distance rationalizability (DR) framework of Elkind, Faliszewski, and Slinko. The former views voting as an attempt to reconstruct the correct ordering of the candidates given noisy estimates (i.e., votes), while the latter explains voting as search for the nearest consensus outcome. We provide conditions under which an MLE interpretation of a voting rule coincides with its DR interpretation, and classify a number of classic voting rules, such as Kemeny, Plurality, Borda and Single Transferable Vote (STV), according to how well they fit each of these frameworks. The classification we obtain is more precise than the ones that result from using MLE or DR alone: indeed, we show that the MLE approach can be used to guide our search for a more refined notion of distance rationalizability and vice versa.

We study the computational complexity of the counting version of the Possible-Winner problem for elections. In the Possible-Winner problem we are given a profile of voters, each with a partial preference order, and ask if there are linear extensions of the votes such that a designated candidate wins. We also analyze a special case of Possible-Winner, the Manipulation problem. We provide polynomial-time algorithms for counting manipulations in a class of scoring protocols and in several other voting rules. We show #P-hardness of the counting variant of Possible-Winner for plurality and veto and give a simple yet general and practically useful randomized algorithm for a variant of Possible-Winner for all voting rules for which a winner can be computed in polynomial time.

We consider the problem of manipulating elections via cloning candidates. In our model, a manipulator can replace each candidate c by one or more clones, i.e., new candidates that are so similar to  c  that each voter simply replaces  c  in his vote with the block of  c 's clones. The outcome of the resulting election may then depend on how each voter orders the clones within the block. We formalize what it means for a cloning manipulation to be successful (which turns out to be a surprisingly delicate issue), and, for a number of prominent voting rules, characterize the preference profiles for which a successful cloning manipulation exists. We also consider the model where there is a cost associated with producing each clone, and study the complexity of finding a minimum-cost cloning manipulation. Finally, we compare cloning with the related problem of control via adding candidates.