arXiv subjects

Edith Elkind

Publications and source records attributed to Edith Elkind.

At least 19 recordsLinked to original sources

arXiv2026

Multiwinner Voting with Spatial Preferences under Incomplete Information

In multiwinner elections with many candidates, as in participatory budgeting or large-scale recommendation, voters cannot plausibly evaluate every candidate, yet standard proportional-fairness guarantees such as EJR+ are stated for fully specified approval ballots. We ask whether strong proportional representation can still be guaranteed while eliciting only a little from each voter. We study this in a spatial model, the Axis-aligned Random Rectangle Voter (ARRV) model, in which candidates occupy a $d$-dimensional issue space and each voter approves an axis-aligned hyper-rectangle: a tolerance interval on every issue. Preferences are revealed only through Planar queries, each comparing a voter's tolerance to a candidate on a single issue. We give an algorithm returning an EJR+ committee for any distribution over rectangular preferences, using only $\mathcal{O}(d\log dk)$ Planar queries per voter in expectation given a sufficiently large electorate, independent of the number of candidates $m$, where $d$ is the number of issues and $k$ the committee size. The algorithm rests on a dimension-agnostic verify-or-fallback framework whose query cost is governed by two properties supplied by interchangeable modules. We describe such modules, yielding end-to-end guarantees for known, unknown, and smooth distributions.

cs.GT↗

arXiv2026

Check, Please: Verifiably Fair Clustering

Popular centroid-based clustering methods are typically optimized for global objectives, and may fail to adequately represent large groups of datapoints. Thus, one needs proportionality notions suited for metric settings. Ideally, such notions should admit polynomial-time algorithms for (a) finding proportional outcomes, and (b) checking if a given outcome is proportional; the latter enables evaluation of traditional algorithms without proportionality guarantees (e.g., $k$-means). A promising approach imports proportionality notions from multiwinner voting with approval ballots. In particular, mPJR, the metric version of the well-known Proportional Justified Representation (PJR) axiom, satisfies (a), but whether it satisfies (b) was open. In this work, we study the computational complexity of auditing proportional representation in clustering. In the approval setting, PJR is coNP-complete to verify; however, it admits a strengthening PJR+, which satisfies (a) and (b). We show these results translate to the metric setting: mPJR is coNP-complete to verify, we define mPJR+, a metric analog of PJR+, and argue mPJR+ satisfies (a) and (b). However, auditing mPJR+ relies on repeated submodular minimization, rendering it impractical at scale, and a natural combinatorial approach is infeasible. As a partial remedy, we propose an mPJR+ verification algorithm exponential in $k$ but quasilinear in the number of datapoints. Motivated by these hardness results, we introduce DC-mPJR+: a proportionality concept offering representation guarantees to a restricted set of coalitions around unselected centers, admitting an $O(mn \log n + mnk)$ verification algorithm. DC-mPJR+ outcomes can be computed efficiently, and any $\gamma$-DC-mPJR+ solution satisfies $(\gamma + 2)$-mPJR+.

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arXiv2026

Fair and Efficient Investment in Public Transportation

We study a stylized model of infrastructure investment in public transportation. In our model, each agent travels between a pair of terminals in a network captured by a weighted graph, where edge weights represent distances. The central planner can improve the travel time along a fixed number of edges, with the goal of maximizing the utilitarian or egalitarian welfare. When there is only one agent, we provide a polynomial-time algorithm that combines Dijkstra's algorithm with a dynamic program. We then demonstrate how to use this algorithm as a subroutine to solve the problem for two agents. Generalizing this idea, we present an XP algorithm parameterized by the number of agents. However, our problem turns out to be W[1]-hard with respect to the number of agents. Nevertheless, we obtain a fixed-parameter tractability result for the special case where all agents travel to a common hub. If the number of agents is variable, we obtain NP-completeness and inapproximability results. We discuss implications of our results for a related model of railway network design.

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arXiv2026

Shortlisting: a Principled Approach

Shortlisting is the process of selecting a subset of alternatives from a larger pool for further consideration or final decision-making. It is widely applied in social choice and multi-agent system scenarios. The growing demand for participatory decision-making and the continuously expanding space of candidates create an urgent need for efficient and fair shortlisting procedures. However, little principled study has been done on this problem. This blue-sky paper aims to highlight the overlooked significance of shortlisting, distinguish it from related problems, provide initial thoughts, and, more importantly, serve as a call to arms. We envision that principled shortlisting can reduce cognitive burden, enable fair collective decisions, encourage broader participation, and ultimately build trust in democratic systems.

cs.GT↗

arXiv2026

Truth-Revealing Participatory Budgeting

Participatory Budgeting (PB) is commonly studied from an axiomatic perspective, where the aim is to design procedurally fair and economically efficient rules for voters with full information regarding their preferences. In contrast, we take an epistemic perspective and consider a framework where PB projects have different levels of underlying quality, indicating how well the project will take effect, which cannot be directly observed before implementation. Agents with noisy information cast votes to aggregate their information, and aim to elect a high-quality set of projects. We evaluate the performance of common PB rules by measuring the expected utility of their outcomes, compared to the optimal set of projects. We find that the quality of approximation improves as the range of project costs shrinks. When projects have unit cost, these common rules can identify the ``best'' set with probability converging to 1. We also study whether strategic agents have incentives to honestly convey their information in the vote. We find that it happens only under very restrictive conditions. We also run numerical experiments to examine the performance of different rules empirically and support our theoretical findings.

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arXiv2025

Maximizing the Egalitarian Welfare in Friends and Enemies Games

We consider the complexity of maximizing egalitarian welfare in Friends and Enemies Games -- a subclass of hedonic games in which every agent partitions other agents into friends and enemies. We investigate two classic scenarios proposed in the literature, namely, Friends Appreciation ($\mathsf{FA}$) and Enemies Aversion ($\mathsf{EA}$): in the former, each agent primarily cares about the number of friends in her coalition, breaking ties based on the number of enemies, while in the latter, the opposite is true. For $\mathsf{EA}$, we show that our objective is hard to approximate within $O(n^{1-\epsilon})$, for any fixed $\epsilon>0$, and provide a polynomial-time $(n-1)$-approximation. For $\mathsf{FA}$, we obtain an NP-hardness result and a polynomial-time approximation algorithm. Our algorithm achieves a ratio of $2-\Theta(\frac{1}{n})$ when every agent has at least two friends; however, if some agent has at most one friend, its approximation ratio deteriorates to $n/2$. We recover the $2-\Theta(\frac{1}{n})$ approximation ratio for two important variants: when randomization is allowed and when the friendship relationship is symmetric. Additionally, for both $\mathsf{EA}$ and $\mathsf{FA}$ we identify special cases where the optimal egalitarian partition can be computed in polynomial time.

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arXiv2025

Single-Deviation Stability in Additively Separable Hedonic Games with Constrained Coalition Sizes

We study stability in additively separable hedonic games when coalition sizes have to respect fixed size bounds. We consider four classic notions of stability based on single-agent deviations, namely, Nash stability, individual stability, contractual Nash stability, and contractual individual stability. For each stability notion, we consider two variants: in one, the coalition left behind by a deviator must still be of a valid size, and in the other there is no such constraint. We provide a full picture of the existence of stable outcomes with respect to given size parameters. Additionally, when there are only upper bounds, we fully characterize the computational complexity of the associated existence problem. In particular, we obtain polynomial-time algorithms for contractual individual stability and contractual Nash stability, where the latter requires an upper bound of 2. We obtain further results for Nash stability and contractual individual stability, when the lower bound is at least 2.

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arXiv2025

Multiwinner Voting with Interval Preferences under Incomplete Information

In multiwinner approval elections with many candidates, voters may struggle to determine their preferences over the entire slate of candidates. It is therefore of interest to explore which (if any) fairness guarantees can be provided under reduced communication. In this paper, we consider voters with one-dimensional preferences: voters and candidates are associated with points in $\mathbb R$, and each voter's approval set forms an interval of $\mathbb R$. We put forward a probabilistic preference model, where the voter set consists of $\sigma$ different groups; each group is associated with a distribution over an interval of $\mathbb R$, so that each voter draws the endpoints of her approval interval from the distribution associated with her group. We present an algorithm for computing committees that provide Proportional Justified Representation + (PJR+), which proceeds by querying voters' preferences, and show that, in expectation, it makes $\mathcal{O}(\log( \sigma\cdot k))$ queries per voter, where $k$ is the desired committee size.

cs.GT↗

arXiv2025

Selecting Interlacing Committees

Polarization is a major concern for a well-functioning society. Often, mass polarization of a society is driven by polarizing political representation, even when the latter is easily preventable. The existing computational social choice methods for the task of committee selection are not designed to address this issue. We enrich the standard approach to committee selection by defining two quantitative measures that evaluate how well a given committee interconnects the voters. Maximizing these measures aims at avoiding polarizing committees. While the corresponding maximization problems are NP-complete in general, we obtain efficient algorithms for profiles in the voter-candidate interval domain. Moreover, we analyze the compatibility of our goals with other representation objectives, such as excellence, diversity, and proportionality. We identify trade-offs between approximation guarantees, and describe algorithms that achieve simultaneous constant-factor approximations.

cs.GT↗

arXiv2025

Not in My Backyard! Temporal Voting Over Public Chores

We study a temporal voting model where voters have dynamic preferences over a set of public chores -- projects that benefit society, but impose individual costs on those affected by their implementation. We investigate the computational complexity of optimizing utilitarian and egalitarian welfare. Our results show that while optimizing the former is computationally straightforward, minimizing the latter is computationally intractable, even in very restricted cases. Nevertheless, we identify several settings where this problem can be solved efficiently, either exactly or by an approximation algorithm. We also examine the effects of enforcing temporal fairness and its impact on social welfare, and analyze the competitive ratio of online algorithms. We then explore the strategic behavior of agents, providing insights into potential malfeasance in such decision-making environments. Finally, we discuss a range of fairness measures and their suitability for our setting.

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arXiv2025

Justified Representation: From Hare to Droop

The study of proportionality in multiwinner voting with approval ballots has received much attention in recent years. Typically, proportionality is captured by variants of the Justified Representation axiom, which say that cohesive groups of at least $\ell\cdot\frac{n}{k}$ voters (where $n$ is the total number of voters and $k$ is the desired number of winners) deserve $\ell$ representatives. The quantity $\frac{n}{k}$ is known as the Hare quota in the social choice literature. Another -- more demanding -- choice of quota is the Droop quota, defined as $\lfloor\frac{n}{k+1}\rfloor+1$. This quota is often used in multiwinner voting with ranked ballots: in algorithms such as Single Transferable Voting, and in proportionality axioms, such as Droop's Proportionality Criterion. A few authors have considered it in the context of approval ballots, but the existing analysis is far from comprehensive. The contribution of our work is a systematic study of JR-style axioms (and voting rules that satisfy them) defined using the Droop quota instead of the Hare quota. For each of the standard JR axioms (namely, JR, PJR, EJR, FPJR, FJR, PJR+ and EJR+), we identify a voting rule that satisfies the Droop version of this axiom. In some cases, it suffices to consider known rules (modifying the corresponding Hare proof, sometimes quite substantially), and in other cases it is necessary to modify the rules from prior work. Each axiom is more difficult to satisfy when defined using the Droop quota, so our results expand the frontier of satisfiable proportionality axioms. We complement our theoretical results with an experimental study, showing that for many probabilistic models of voter approvals, Droop JR/EJR+ are considerably more demanding than standard (Hare) JR/EJR+.

cs.GT↗

arXiv2025

Strengthening Proportionality in Temporal Voting

We study proportional representation in the framework of temporal voting with approval ballots. Prior work adapted basic proportional representation concepts -- justified representation (JR), proportional JR (PJR), and extended JR (EJR) -- from the multiwinner setting to the temporal setting. Our work introduces and examines ways of going beyond EJR. Specifically, we consider stronger variants of JR, PJR, and EJR, and introduce temporal adaptations of more demanding multiwinner axioms, such as EJR+, full JR (FJR), full proportional JR (FPJR), and the Core. For each of these concepts, we investigate its existence and study its relationship to existing notions, thereby establishing a rich hierarchy of proportionality concepts. Notably, we show that two of our proposed axioms -- EJR+ and FJR -- strengthen EJR while remaining satisfiable in every temporal election.

cs.GT↗

arXiv2025

From Independence of Clones to Composition Consistency: A Hierarchy of Barriers to Strategic Nomination

We study two axioms for social choice functions that capture the impact of similar candidates: independence of clones (IoC) and composition consistency (CC). We clarify the relationship between these axioms by observing that CC is strictly more demanding than IoC, and investigate whether common voting rules that are known to be independent of clones (such as STV, Ranked Pairs, Schulze, and Split Cycle) are composition-consistent. While for most of these rules the answer is negative, we identify a variant of Ranked Pairs that satisfies CC. Further, we show how to efficiently modify any (neutral) social choice function so that it satisfies CC, while maintaining its other desirable properties. Our transformation relies on the hierarchical representation of clone structures via PQ-trees. We extend our analysis to social preference functions. Finally, we interpret IoC and CC as measures of robustness against strategic manipulation by candidates, with IoC corresponding to strategy-proofness and CC corresponding to obvious strategy-proofness.

cs.GT↗

arXiv2025

Streamlining Equal Shares

Participatory budgeting (PB) is a form of citizen participation that allows citizens to decide how public funds are spent. Through an election, citizens express their preferences on various projects (spending proposals). A voting mechanism then determines which projects will be approved. The Method of Equal Shares (MES) is the state of the art algorithm for a proportional, voting based approach to participatory budgeting and has been implemented in cities across Poland and Switzerland. A significant drawback of MES is that it is not \textit{exhaustive} meaning that it often leaves a portion of the budget unspent that could be used to fund additional projects. To address this, in practice the algorithm is combined with a completion heuristic - most often the ``add-one" heuristic which artificially increases the budget until a heuristically chosen threshold. This heuristic is computationally inefficient and will become computationally impractical if PB is employed on a larger scale. We propose the more efficient \textsc{add-opt} heuristic for Exact Equal Shares (EES), a variation of MES that is known to retain many of its desirable properties. We solve the problem of identifying the next budget for which the outcome for EES changes in $O(mn)$ time for cardinal utilities and $O(m^2n)$ time for uniform utilities, where $m$ is the number of projects and $n$ is the number of voters. Our solution to this problem inspires the efficient \textsc{add-opt} heuristic which bypasses the need to search through each intermediary budget. We perform comprehensive experiments on real-word PB instances from Pabulib and show that completed EES outcomes usually match the proportion of budget spent by completed MES outcomes. Furthermore, the \textsc{add-opt} heuristic matches the proportion of budget spend by add-one for EES.

cs.GT↗

arXiv2025

Verifying Proportionality in Temporal Voting

We study a model of temporal voting where there is a fixed time horizon, and at each round the voters report their preferences over the available candidates and a single candidate is selected. Prior work has adapted popular notions of justified representation as well as voting rules that provide strong representation guarantees from the multiwinner election setting to this model. In our work, we focus on the complexity of verifying whether a given outcome offers proportional representation. We show that in the temporal setting verification is strictly harder than in multiwinner voting, but identify natural special cases that enable efficient algorithms.

cs.GT↗

arXiv2024

Towards Fair and Efficient Public Transportation: A Bus Stop Model

We consider a stylized formal model of public transportation, where a set of agents need to travel along a given road, and there is a bus that runs the length of this road. Each agent has a left terminal and a right terminal between which they wish to travel; they can walk all the way, or walk to/from the nearest stop and use the bus for the rest of their journey. The bus can make a fixed number of stops, and the planner needs to select locations for these stops. We study notions of efficiency and fairness for this setting. First, we give a polynomial-time algorithm for computing a solution that minimizes the total travel time; our approach can capture further extensions of the base model, such as more general cost functions or existing infrastructure. Second, we develop a polynomial-time algorithm that outputs solutions with provable fairness guarantees (such as a variant of the justified representation axiom or $2$-approximate core) as long as the agents' costs only depend on the distance they need to walk. Our simulations indicate that our algorithm almost always outputs fair solutions, even for parameter regimes that do not admit theoretical guarantees.

cs.GT↗

arXiv2024

Fair Division of Chores with Budget Constraints

We study fair allocation of indivisible chores to agents under budget constraints, where each chore has an objective size and disutility. This model captures scenarios where a set of chores need to be divided among agents with limited time, and each chore has a specific time needed for completion. We propose a budget-constrained model for allocating indivisible chores, and systematically explore the differences between goods and chores in this setting. We establish the existence of an EFX allocation. We then show that EF2 allocations are polynomial-time computable in general; for many restricted settings, we strengthen this result to EF1. For divisible chores, we develop an efficient algorithm for computing an EF allocation.

cs.GT↗

arXiv2024

Temporal Fair Division of Indivisible Items

We study a fair division model where indivisible items arrive sequentially, and must be allocated immediately and irrevocably. Previous work on online fair division has shown impossibility results in achieving approximate envy-freeness under these constraints. In contrast, we consider an informed setting where the algorithm has complete knowledge of future items, and aim to ensure that the cumulative allocation at each round satisfies approximate envy-freeness -- which we define as temporal envy-freeness up to one item (TEF1). We focus on settings where items can be exclusively goods or exclusively chores. For goods, while TEF1 allocations may not always exist, we identify several special cases where they do -- two agents, two item types, generalized binary valuations, unimodal preferences -- and provide polynomial-time algorithms for these cases. We also prove that determining the existence of a TEF1 allocation is NP-hard. For chores, we establish analogous results for the special cases, but present a slightly weaker intractability result. We also establish the incompatibility between TEF1 and Pareto-optimality, with the implication that it is intractable to find a TEF1 allocation that maximizes any $p$-mean welfare, even for two agents.

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