Papers

We study the performance of voting mechanisms from a utilitarian standpoint, under the recently introduced framework of metric-distortion, offering new insights along two main lines. First, if $d$ represents the doubling dimension of the metric space, we show that the distortion of STV is $O(d \log \log m)$, where $m$ represents the number of candidates. For doubling metrics this implies an exponential improvement over the lower bound for general metrics, and as a special case it effectively answers a question left open by Skowron and Elkind (AAAI '17) regarding the distortion of STV under low-dimensional Euclidean spaces. More broadly, this constitutes the first nexus between the performance of any voting rule and the ``intrinsic dimensionality'' of the underlying metric space. We also establish a nearly-matching lower bound, refining the construction of Skowron and Elkind. Moreover, motivated by the efficiency of STV, we investigate whether natural learning rules can lead to low-distortion outcomes. Specifically, we introduce simple, deterministic and decentralized exploration/exploitation dynamics, and we show that they converge to a candidate with $O(1)$ distortion.

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The practical scalability of many optimization algorithms for large extensive-form games is often limited by the games' huge payoff matrices. To ameliorate the issue, Zhang and Sandholm recently proposed a sparsification technique that factorizes the payoff matrix $\mathbf{A}$ into a sparser object $\mathbf{A} = \hat{\mathbf{A}} + \mathbf{U}\mathbf{V}^\top$, where the total combined number of nonzeros of $\hat{\mathbf{A}}$, $\mathbf{U}$, and $\mathbf{V}$, is significantly smaller. Such a factorization can be used in place of the original payoff matrix in many optimization algorithm, such as interior-point and second-order methods, thus increasing the size of games that can be handled. Their technique significantly sparsifies poker (end)games, standard benchmarks used in computational game theory, AI, and more broadly. We show that the existence of extremely sparse factorizations in poker games can be tied to their particular Kronecker-product structure. We clarify how such structure arises and introduce the connection between that structure and sparsification. By leveraging such structure, we give two ways of computing strong sparsifications of poker games (as well as any other game with a similar structure) that are i) orders of magnitude faster to compute, ii) more numerically stable, and iii) produce a dramatically smaller number of nonzeros than the prior technique. Our techniques enable---for the first time---effective computation of high-precision Nash equilibria and strategies subject to constraints on the amount of allowed randomization. Furthermore, they significantly speed up parallel first-order game-solving algorithms; we show state-of-the-art speed on a GPU.

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In the context of social choice theory, we develop a tableau-based calculus for reasoning about voting rules. This calculus can be used to obtain structured explanations for why a given set of axioms justifies a given election outcome for a given profile of voter preferences. We then show how to operationalise this calculus, using a combination of SAT solving and answer set programming, to arrive at a flexible framework for presenting human-readable justifications to users.

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When selecting multiple candidates based on approval preferences of agents, the proportional representation of agents' opinions is an important and well-studied desideratum. Existing criteria for evaluating the representativeness of outcomes focus on groups of agents and demand that sufficiently large and cohesive groups are "represented" in the sense that candidates approved by some group members are selected. Crucially, these criteria say nothing about the representation of individual agents, even if these agents are members of groups that deserve representation. In this paper, we formalize the concept of individual representation (IR) and explore to which extent, and under which circumstances, it can be achieved. We show that checking whether an IR outcome exists is computationally intractable, and we verify that all common approval-based voting rules may fail to provide IR even in cases where this is possible. We then focus on domain restrictions and establish an interesting contrast between "voter interval" and "candidate interval" preferences. This contrast can also be observed in our experimental results, where we analyze the attainability of IR for realistic preference profiles.

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Elkind et al. (AAAI, 2021) introduced a model for deliberative coalition formation, where a community wishes to identify a strongly supported proposal from a space of alternatives, in order to change the status quo. In their model, agents and proposals are points in a metric space, agents' preferences are determined by distances, and agents deliberate by dynamically forming coalitions around proposals that they prefer over the status quo. The deliberation process operates via k-compromise transitions, where agents from k (current) coalitions come together to form a larger coalition in order to support a (perhaps new) proposal, possibly leaving behind some of the dissenting agents from their old coalitions. A deliberation succeeds if it terminates by identifying a proposal with the largest possible support. For deliberation in d dimensions, Elkind et al. consider two variants of their model: in the Euclidean model, proposals and agent locations are points in R^d and the distance is measured according to ||...||_2; and in the hypercube model, proposals and agent locations are vertices of the d-dimensional hypercube and the metric is the Hamming distance. They show that in the continuous model 2-compromises are guaranteed to succeed, but in the discrete model for deliberation to succeed it may be necessary to use k-compromises with k >= d. We complement their analysis by (1) proving that in both models it is hard to find a proposal with a high degree of support, and even a 2-compromise transition may be hard to compute; (2) showing that a sequence of 2-compromise transitions may be exponentially long; (3) strengthening the lower bound on the size of the compromise for the d-hypercube model from d to 2^{\Omega(d)}.

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Following up on purely theoretical work of Bredereck et al. [AAAI 2020], we contribute further theoretical insights into adapting stable two-sided matchings to change. Moreover, we perform extensive empirical studies hinting at numerous practically useful properties. Our theoretical extensions include the study of new problems (that is, incremental variants of Almost Stable Marriage and Hospital Residents), focusing on their (parameterized) computational complexity and the equivalence of various change types (thus simplifying algorithmic and complexity-theoretic studies for various natural change scenarios). Our experimental findings reveal, for instance, that allowing the new matching to be blocked by a few pairs significantly decreases the difference between the old and the new matching.

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Federated learning (FL) performs the global model updating in a synchronous manner in that the FL server waits for a specific number of local models from distributed devices before computing and sharing a new global model. We propose asynchronous federated learning (AsyncFL), which allows each client to continuously upload its model based on its capabilities and the FL server to determine when to asynchronously update and broadcast the global model. The asynchronous model aggregation at the FL server is performed by the Boyer–Moore majority voting algorithm for the k-bit quantized weight values. The proposed FL can speed up the convergence of the global model learning early in the FL process and reduce data exchange once the model is converged.

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Over the last few years, researchers have put significant effort into understanding of the notion of proportional representation in committee election. In particular, recently they have proposed the notion of proportionality degree. We study the complexity of computing committees with a given proportionality degree and of testing if a given committee provides a particular one. This way, we complement recent studies that mostly focused on the notion of (extended) justified representation. We also study the problems of testing if a cohesive group of a given size exists and of counting such groups.

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In multiwinner approval voting, the goal is to select k-member committees based on voters' approval ballots. A well-studied concept of proportionality in this context is the justified representation (JR) axiom, which demands that no large cohesive group of voters remains unrepresented. However, the JR axiom may conflict with other desiderata, such as coverage (maximizing the number of voters who approve at least one committee member) or social welfare (maximizing the number of approvals obtained by committee members). In this work, we investigate the impact of imposing the JR axiom (as well as the more demanding EJR axiom) on social welfare and coverage. Our approach is threefold: we derive worst-case bounds on the loss of welfare/coverage that is caused by imposing JR, study the computational complexity of finding 'good' committees that provide JR (obtaining a hardness result, an approximation algorithm, and an exact algorithm for one-dimensional preferences), and examine this setting empirically on several synthetic datasets.

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We consider a setting where a group of individuals needs to make a number of independent decisions. The decisions should proportionally represent the views of the voters. We formulate new criteria of proportionality and analyse two rules, Proportional Approval Voting and Rule X, that are inspired by the corresponding approval-based committee election rules. We prove that the two rules provide very strong proportionality guarantees when applied to the setting of public decisions.

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We study the PAC learnability of multiwinner voting, focusing on the class of approval-based committee scoring (ABCS) rules. These are voting rules applied on profiles with approval ballots, where each voter approves some of the candidates. According to ABCS rules, each committee of $k$ candidates collects from each voter a score, that depends on the size of the voter's ballot and on the size of its intersection with the committee. Then, committees of maximum score are the winning ones. Our goal is to learn a target rule (i.e., to learn the corresponding scoring function) using information about the winning committees of a small number of sampled profiles. Despite the existence of exponentially many outcomes compared to single-winner elections, we show that the sample complexity is still low: a polynomial number of samples carries enough information for learning the target committee with high confidence and accuracy. Unfortunately, even simple tasks that need to be solved for learning from these samples are intractable. We prove that deciding whether there exists some ABCS rule that makes a given committee winning in a given profile is a computationally hard problem. Our results extend to the class of sequential Thiele rules, which have received attention due to their simplicity.

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We study extensions of the Election Isomorphism problem, focused on the existence of isomorphic subelections. Specifically, we propose the Subelection Isomorphism and the Maximum Common Subelection problems and study their computational complexity and approximability. Using our problems in experiments, we provide some insights into the nature of several statistical models of elections.

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The formation of stable coalitions is a central concern in multiagent systems. A considerable stream of research defines stability via the absence of beneficial deviations by single agents. Such deviations require an agent to improve her utility by joining another coalition while possibly imposing further restrictions on the consent of the agents in the welcoming as well as the abandoned coalition. While most of the literature focuses on unanimous consent, we also study consent decided by majority vote, and introduce two new stability notions that can be seen as local variants of popularity. We investigate these notions in additively separable hedonic games by pinpointing boundaries to computational complexity depending on the type of consent and restrictions on the utility functions. The latter restrictions shed new light on well-studied classes of games based on the appreciation of friends or the aversion to enemies. Many of our positive results follow from the Deviation Lemma, a general combinatorial observation, which can be leveraged to prove the convergence of simple and natural single-agent dynamics under fairly general conditions.

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Participatory budgeting (PB) is a democratic process where citizens jointly decide on how to allocate public funds to indivisible projects. In this work, we focus on PB processes where citizens may provide additional money to projects they want to see funded. We introduce a formal framework for this kind of PB with donations. Our framework also allows for diversity constraints, meaning that each project belongs to one or more types, and there are lower and upper bounds on the number of projects of the same type that can be funded. We propose three general classes of methods for aggregating the citizens’ preferences in the presence of donations and analyze their axiomatic properties. Furthermore, we investigate the computational complexity of determining the outcome of a PB process with donations and of finding a citizen’s optimal donation strategy.

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We consider a sequential blocked matching (SBM) model where strategic agents repeatedly report ordinal preferences over a set of services to a central planner. The planner’s goal is to elicit agents’ true preferences and design a policy that matches services to agents in order to maximize the expected social welfare with the added constraint that each matched service can be blocked or unavailable for a number of time periods. Naturally, SBM models the repeated allocation of reusable services to a set of agents where each allocated service becomes unavailable for a fixed duration We first consider the offline SBM setting, where the strategic agents are aware of their true preferences. We measure the performance of any policy by distortion, the worst-case multiplicative approximation guaranteed by any policy. For the setting with s services, we establish lower bounds of Ω(s) and Ω(√s) on the distortions of any deterministic and randomised mechanisms, respectively. We complement these results by providing approximately truthful, measured by incentive ratio, deterministic and randomised policies based on random serial dictatorship which match our lower bounds. Our results show that there is a significant improvement if one considers the class of randomised policies. Finally, we consider the online SBM setting with bandit feedback where each agent is initially unaware of her true preferences, and the planner must facilitate each agent in the learning of their preferences through the matching of services over time. We design an approximately truthful mechanism based on the Explore-then-Commit paradigm, which achieves logarithmic dynamic approximate regret.

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We investigate approval-based committee voting with incomplete information about the approval preferences of voters. We consider several models of incompleteness where each voter partitions the set of candidates into approved, disapproved, and unknown candidates, possibly with ordinal preference constraints among candidates in the latter category. This captures scenarios where voters have not evaluated all candidates and/or it is unknown where voters draw the threshold between approved and disapproved candidates. We study the complexity of some fundamental computational problems for a number of classic approval-based committee voting rules including Proportional Approval Voting and Chamberlin-Courant. These problems include that of determining whether a given set of candidates is a possible or necessary winning committee, whether it forms a committee that possibly or necessarily satisfies representation axioms, and whether a given candidate is possibly or necessarily a member of the winning committee.

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Liquid democracy is a novel paradigm for collective decision-making that gives agents the choice between casting a direct vote or delegating their vote to another agent. We consider a generalization of the standard liquid democracy setting by allowing agents to specify multiple potential delegates, together with a preference ranking among them. This generalization increases the number of possible delegation paths and enables higher participation rates because fewer votes are lost due to delegation cycles or abstaining agents. In order to implement this generalization of liquid democracy, we need to find a principled way of choosing between multiple delegation paths. In this paper, we provide a thorough axiomatic analysis of the space of delegation rules, i.e., functions assigning a feasible delegation path to each delegating agent. In particular, we prove axiomatic characterizations as well as an impossibility result for delegation rules. We also analyze requirements on delegation rules that have been suggested by practitioners, and introduce novel rules with attractive properties. By performing an extensive experimental analysis on synthetic as well as real-world data, we compare delegation rules with respect to several quantitative criteria relating to the chosen paths and the resulting distribution of voting power. Our experiments reveal that delegation rules can be aligned on a spectrum reflecting an inherent trade-off between competing objectives.

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We extend the recently introduced framework of metric distortion to multiwinner voting. In this framework, n agents and m alternatives are located in an underlying metric space. The exact distances between agents and alternatives are unknown. Instead, each agent provides a ranking of the alternatives, ordered from the closest to the farthest. Typically, the goal is to select a single alternative that approximately minimizes the total distance from the agents, and the worst-case approximation ratio is termed distortion. In the case of multiwinner voting, the goal is to select a committee of k alternatives that (approximately) minimizes the total cost to all agents. We consider the scenario where the cost of an agent for a committee is her distance from the q-th closest alternative in the committee. We reveal a surprising trichotomy on the distortion of multiwinner voting rules in terms of k and q: The distortion is unbounded when q <= k/3, asymptotically linear in the number of agents when k/3 < q <= k/2, and constant when q > k/2.

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