Despite extensive theoretical research on proportionality in approval-based multiwinner voting, its impact on which committees and candidates can be selected in practice remains poorly understood. We address this gap by (i) analyzing the computational complexity of several natural problems related to the behavior of proportionality axioms, and (ii) conducting an extensive experimental study on both real-world and synthetic elections. Our findings reveal substantial variation in the restrictiveness of proportionality across instances, including previously unobserved high levels of restrictiveness in some real-world cases. We also introduce and evaluate new measures for quantifying a candidate’s importance for achieving proportional outcomes, which differ clearly from assessing candidate strength by approval score.

Many real-world decision-making problems involve optimizing multiple objectives simultaneously, rendering the selection of the most preferred solution a non-trivial problem: All Pareto optimal solutions are viable candidates, and it is typically up to a decision maker to select one for implementation based on their subjective preferences. To reduce the cognitive load on the decision maker, previous work has introduced the Pareto pruning problem, where the goal is to compute a fixed-size subset of Pareto optimal solutions that best represent the full set, as evaluated by a given quality measure. Reframing Pareto pruning as a multiwinner voting problem, we conduct an axiomatic analysis of existing quality measures, uncovering several unintuitive behaviors. Motivated by these findings, we introduce a new measure, directed coverage. We also analyze the computational complexity of optimizing various quality measures, identifying previously unknown boundaries between tractable and intractable cases depending on the number and structure of the objectives. Finally, we present an experimental evaluation, demonstrating that the choice of quality measure has a decisive impact on the characteristics of the selected set of solutions and that our proposed measure performs competitively or even favorably across a range of settings.

In many applications of AI for Social Impact (e.g., when allocating spots in support programs for underserved communities), resources are scarce and an allocation policy is needed to decide who receives a resource. Before being deployed at scale, a rigorous evaluation of an AI-powered allocation policy is vital. In this paper, we introduce the methods necessary to evaluate index-based allocation policies, which allocate a limited number of resources to those who need them the most. Such policies create dependencies between agents, rendering standard statistical tests invalid and ineffective. Addressing the arising practical and technical challenges, we describe an efficient estimator and methods for drawing valid statistical conclusions. Our extensive experiments validate our methodology in practical settings while also showcasing its statistical power. We conclude by proposing and empirically verifying extensions of our methodology that enable us to reevaluate a past randomized control trial conducted with 10000 beneficiaries for a mHealth program for pregnant women. Our new methodology allows us to draw previously invisible conclusions when comparing two different ML allocation policies.

Maternal mortality remains a significant global public health challenge. One promising approach to reducing maternal deaths occurring during facility-based childbirth is through early warning systems, which require the consistent monitoring of mothers' vital signs after giving birth. Wireless vital sign monitoring devices offer a labor-efficient solution for continuous monitoring, but their scarcity raises the critical question of how to allocate them most effectively. We devise an allocation algorithm for this problem by modeling it as a variant of the popular Restless Multi-Armed Bandit (RMAB) paradigm. In doing so, we identify and address novel, previously unstudied constraints unique to this domain, which render previous approaches for RMABs unsuitable and significantly increase the complexity of the learning and planning problem. To overcome these challenges, we adopt the popular Proximal Policy Optimization (PPO) algorithm from reinforcement learning to learn an allocation policy by training a policy and value function network. We demonstrate in simulations that our approach outperforms the best heuristic baseline by up to a factor of 4.

In this paper, we present PRIORITY2REWARD a Large Language Model (LLM) based application which incorporates health worker preferences for resource allocation planning in public health programs. LLMs are increasingly used to design reward functions based on human preferences in Reinforcement Learning problems. We focus on LLM-designed rewards for Restless Multi-Armed Bandits, a framework for allocating limited resources among agents. In the context of public health, our approach empowers grassroots health workers to tailor automated allocation decisions to community needs. We showcase a simulated application of PRIORITY2REWARD for a large-scale mobile health program in India. The tool allows health workers to enter natural language preferences and leverages LLMs to search for reward functions aligned with the preference. Our tool then dynamically showcases how the LLM generated reward function modifies the policy outcomes with respect to different demographic groups in the population. This can help inform policy implementation at a community level.

A key task in certain democratic processes is to produce a concise slate of statements that proportionally represents the full spectrum of user opinions. This task is similar to committee elections, but unlike traditional settings, the candidate set comprises all possible statements of varying lengths, and so it can only be accessed through specific queries. Combining social choice and large language models, prior work has approached this challenge through a framework of generative social choice. We extend the framework in two fundamental ways, providing theoretical guarantees even in the face of approximately optimal queries and a budget limit on the overall length of the slate. Using GPT-4o to implement queries, we showcase our approach on datasets related to city improvement measures and drug reviews, demonstrating its effectiveness in generating representative slates from unstructured user opinions.

Our main contribution is the introduction of the map of elections framework. A map of elections consists of three main elements: (1) a dataset of elections (i.e., collections of ordinal votes over given sets of candidates), (2) a way of measuring similarities between these elections, and (3) a representation of the elections in the 2D Euclidean space as points, so that the more similar two elections are, the closer are their points. In our maps, we mostly focus on datasets of synthetic elections, but we also show an example of a map over real-life ones. To measure similarities, we would have preferred to use, e.g., the isomorphic swap distance, but this is infeasible due to its high computational complexity. Hence, we propose polynomial-time computable positionwise distance and use it instead. Regarding the representations in 2D Euclidean space , we mostly use the Kamada-Kawai algorithm, but we also show two alternatives. We develop the necessary theoretical results to form our maps and argue experimentally that they are accurate and credible. Further, we show how coloring the elections in a map according to various criteria helps in analyzing results of a number of experiments. In particular, we show colorings according to the scores of winning candidates or committees, running times of ILP-based winner determination algorithms, and approximation ratios achieved by particular algorithms.

We introduce the problem of adapting a stable matching to forced and forbidden pairs. Given a stable matching M1, a set Q of forced pairs, and a set P of forbidden pairs, we want to find a stable matching that includes all pairs from Q, no pair from P, and is as close as possible to M1. We study this problem in four classic stable matching settings: Stable Roommates (with Ties) and Stable Marriage (with Ties). Our main contribution is a polynomial-time algorithm, based on the theory of rotations, for adapting Stable Roommates matchings to forced pairs. In contrast, we show that the same problem for forbidden pairs is NP-hard. However, our polynomial-time algorithm for forced pairs can be extended to a fixed-parameter tractable algorithm with respect to the number of forbidden pairs. Moreover, we study the setting where preferences contain ties: Some of our algorithmic results can be extended while other problems become intractable.

We provide the first large-scale data collection of real-world approval-based committee elections. These elections have been conducted on the Polkadot blockchain as part of their Nominated Proof-of-Stake mechanism and contain around one thousand candidates and tens of thousands of (weighted) voters each. We conduct an in-depth study of application-relevant questions, including a quantitative and qualitative analysis of the outcomes returned by different voting rules. Besides considering proportionality measures that are standard in the multiwinner voting literature, we pay particular attention to less-studied measures of overrepresentation, as these are closely related to the security of the Polkadot network. We also analyze how different design decisions such as the committee size affect the examined measures.

Focusing on the bipartite Stable Marriage problem, we investigate different robustness measures related to stable matchings. We analyze the computational complexity of computing them and analyze their behavior in extensive experiments on synthetic instances. For instance, we examine whether a stable matching is guaranteed to remain stable if a given number of adversarial swaps in the agent’s preferences are performed and the probability of stability when applying swaps uniformly at random. Our results reveal that stable matchings in our synthetic data are highly unrobust to adversarial swaps, whereas the average-case view presents a more nuanced and informative picture.

Traditional game-theoretic research for security applications primarily focuses on the allocation of external protection resources to defend targets. This work puts forward the study of a new class of games centered around strategically arranging targets to protect them against a constrained adversary, with motivations from varied domains such as peacekeeping resource transit and cybersecurity. Specifically, we introduce Escape Sensing Games (ESGs). In ESGs, a blue player manages the order in which targets pass through a channel, while her opponent tries to capture the targets using a set of sensors that need some time to recharge after each activation. We present a thorough computational study of ESGs. Among others, we show that it is NP-hard to compute best responses and equilibria. Nevertheless, we propose a variety of effective (heuristic) algorithms whose quality we demonstrate in extensive computational experiments.

We study two-stage committee elections where voters have dynamic preferences over candidates; at each stage, a committee is chosen under a given voting rule. We are interested in identifying a winning committee for the second stage that overlaps as much as possible with the first-stage committee. We show a full complexity dichotomy for the class of Thiele rules: this problem is tractable for Approval Voting (AV) and hard for all other Thiele rules (including, in particular, Proportional Approval Voting and the Chamberlin–Courant rule). We extend this dichotomy to the greedy variants of Thiele rules. We also explore this problem from a parameterized complexity perspective for several natural parameters. We complement the theory with experimental analysis: e.g., we investigate the average number of changes in the committee as a function of changes in voters’ preferences and the role of ties.

Restless multi-arm bandits (RMABs) are a model for sequentially allocating a limited number of resources to agents modeled as Markov Decision Processes. RMABs have applications in cellular networks, anti-poaching, and in particular, healthcare. For such high-stakes use cases, allocations are often required to treat different groups of agents (e.g., defined by sensitive attributes) fairly. In addition to the fairness challenge, agents’ transition probabilities are often unknown and need to be learned in real-world problems. Thus, group fairness in RMABs requires us to simultaneously learn transition probabilities and how much budget we allocate to each group. Overcoming this key challenge ignored by previous work, we develop a decision-focused-learning pipeline to solve equitable RMABs, using a novel budget allocation algorithm to prevent disparity between groups. Our results on both synthetic and real-world large-scale datasets demonstrate that incorporating fair planning into the learning step greatly improves equity with little sacrifice in utility.

Abstract In the simplest game-theoretic formulation of Schelling’s model of segregation on graphs, agents of two different types each select their own vertex in a given graph so as to maximize the fraction of agents of their type in their occupied neighborhood. Two ways of modeling agent movement here are either to allow two agents to swap their vertices or to allow an agent to jump to a free vertex. The contributions of this paper are twofold. First, we prove that deciding the existence of a swap-equilibrium and a jump-equilibrium in this simplest model of Schelling games is NP-hard, thereby answering questions left open by Agarwal et al. [AAAI ’20] and Elkind et al. [IJCAI ’19]. Second, we introduce two measures for the robustness of equilibria in Schelling games in terms of the minimum number of edges or the minimum number of vertices that need to be deleted to make an equilibrium unstable. We prove tight lower and upper bounds on the edge- and vertex-robustness of swap-equilibria in Schelling games on different graph classes.

Focusing on Stable Roommates (SR), we contribute to the toolbox for conducting experiments for stable matching problems. We introduce the polynomial-time computable mutual attraction distance to measure the similarity of SR instances, analyze its properties, and use it to create a map of SR instances. This map visualizes 460 synthetic SR instances (each sampled from one of ten different statistical cultures) as follows: Each instance is a point in the plane, and two points are close on the map if the corresponding SR instances are similar with respect to our mutual attraction distance to each other. Subsequently, we conduct several illustrative experiments and depict their results on the map, illustrating the map’s usefulness as a non-aggregate visualization tool, the diversity of our generated dataset, and the need to use instances sampled from different statistical cultures. Lastly, we extend our approach to the bipartite Stable Marriage problem.

We analyze the (parameterized) computational complexity of “fair” variants of bipartite many-to-one matching, where each vertex from the “left” side is matched to exactly one vertex and each vertex from the “right” side may be matched to multiple vertices. We want to find a “fair” matching, in which each vertex from the right side is matched to a “fair” set of vertices. Assuming that each vertex from the left side has one color modeling its “attribute”, we study two fairness criteria. For instance, in one of them, we deem a vertex set fair if for any two colors, the difference between the numbers of their occurrences does not exceed a given threshold. Fairness is, for instance, relevant when finding many-to-one matchings between students and colleges, voters and constituencies, and applicants and firms. Here colors may model sociodemographic attributes, party memberships, and qualifications, respectively. We show that finding a fair many-to-one matching is NP-hard even for three colors and maximum degree five. Our main contribution is the design of fixed-parameter tractable algorithms with respect to the number of vertices on the right side. Our algorithms make use of a variety of techniques including color coding. At the core lie integer linear programs encoding Hall like conditions. We establish the correctness of our integer programs, based on Frank’s separation theorem [Frank, Discrete Math. 1982]. We further obtain complete complexity dichotomies regarding the number of colors and the maximum degree of each side.

We study the formation of stable outcomes via simple dynamics in cardinal hedonic games, where the utilities of agents change over time depending on the history of the coalition formation process. Specifically, we analyze situations where members of a coalition decrease their utility for a leaving agent (resent) or increase their utility for a joining agent (appreciation). We show that in contrast to classical dynamics, for resentful or appreciative agents, dynamics are guaranteed to converge under mild conditions for various stability concepts. Thereby, we establish that both resent and appreciation are strong stability-driving forces.

To aggregate rankings into a social ranking, one can use scoring systems such as Plurality, Veto, and Borda. We distinguish three types of methods: ranking by score, ranking by repeatedly choosing a winner that we delete and rank at the top, and ranking by repeatedly choosing a loser that we delete and rank at the bottom. The latter method captures the frequently studied voting rules Single Transferable Vote (aka Instant Runoff Voting), Coombs, and Baldwin. In an experimental analysis, we show that the three types of methods produce different rankings in practice. We also provide evidence that sequentially selecting winners is most suitable to detect the "true" ranking of candidates. For different rules in our classes, we then study the (parameterized) computational complexity of deciding in which positions a given candidate can appear in the chosen ranking. As part of our analysis, we also consider the Winner Determination problem for STV, Coombs, and Baldwin and determine their complexity when there are few voters or candidates.

We study the properties of elections that have a given position matrix (in such elections each candidate is ranked on each position by a number of voters specified in the matrix). We show that counting elections that generate a given position matrix is #P-complete. Consequently, sampling such elections uniformly at random seems challenging and we propose a simpler algorithm, without hard guarantees. Next, we consider the problem of testing if a given matrix can be implemented by an election with a certain structure (such as single-peakedness or group-separability). Finally, we consider the problem of checking if a given position matrix can be implemented by an election with a Condorcet winner. We complement our theoretical findings with experiments.

We consider the problem of subset selection where one is given multiple rankings of items and the goal is to select the highest "quality" subset. Score functions from the multiwinner voting literature have been used to aggregate rankings into quality scores for subsets. We study this setting of subset selection problems when, in addition, rankings may contain systemic or unconscious biases toward a group of items. For a general model of input rankings and biases, we show that requiring the selected subset to satisfy group fairness constraints can improve the quality of the selection with respect to unbiased rankings. Importantly, we show that for fairness constraints to be effective, different multiwinner score functions may require a drastically different number of rankings: While for some functions, fairness constraints need an exponential number of rankings to recover a close-to-optimal solution, for others, this dependency is only polynomial. This result relies on a novel notion of "smoothness" of submodular functions in this setting that quantifies how well a function can "correctly" assess the quality of items in the presence of bias. The results in this paper can be used to guide the choice of multiwinner score functions for the subset selection setting considered here; we additionally provide a tool to empirically enable this.

The Mallows model is a popular distribution for ranked data. We empirically and theoretically analyze how the properties of rankings sampled from the Mallows model change when increasing the number of alternatives. We find that real-world data behaves differently from the Mallows model, yet is in line with its recent variant proposed by Boehmer et al. [IJCAI ’21]. As part of our study, we issue several warnings about using the classic Mallows model. For instance, we find that one should be extremely careful when using the Mallows model to generate data for experiments with a varying number of alternatives, as observed trends in such experiments might be due to the changing nature of the generated data.

Abstract Given a set of agents qualifying or disqualifying each other, group identification is the task of identifying a socially qualified subgroup of agents. Social qualification depends on the specific rule used to aggregate individual qualifications . The classical bribery problem in this context asks how many agents need to change their qualifications in order to change the outcome in a certain way. Complementing previous results showing polynomial-time solvability or NP-hardness of bribery for various social rules in the constructive (aiming at making specific agents socially qualified) or destructive (aiming at making specific agents socially disqualified) setting, we provide a comprehensive picture of the parameterized computational complexity landscape. Conceptually, we also consider a more fine-grained concept of bribery cost, where we ask how many single qualifications need to be changed, nonunit prices for different bribery actions, and a more general bribery goal that combines the constructive and destructive setting.

Abstract We study the NP-hard Fair Connected Districting problem recently proposed by Stoica et al. [AAMAS 2020]: Partition a vertex-colored graph into k connected components (subsequently referred to as districts) so that in every district the most frequent color occurs at most a given number of times more often than the second most frequent color. Fair Connected Districting is motivated by various real-world scenarios where agents of different types, which are one-to-one represented by nodes in a network, have to be partitioned into disjoint districts. Herein, one strives for “fair districts” without any type being in a dominating majority in any of the districts. This is to e.g. prevent segregation or political domination of some political party. We conduct a fine-grained analysis of the (parameterized) computational complexity of Fair Connected Districting. In particular, we prove that it is polynomial-time solvable on paths, cycles, stars, and caterpillars, but already becomes NP-hard on trees. Motivated by the latter negative result, we perform a parameterized complexity analysis with respect to various graph parameters including treewidth, and problem-specific parameters, including, the numbers of colors and districts. We obtain a rich and diverse, close to complete picture of the corresponding parameterized complexity landscape (that is, a classification along the complexity classes FPT, XP, W[1]-hard, and para-NP-hard).

A recent report of Littmann published in the Communications of the ACM outlines the existence and the fatal impact of collusion rings in academic peer reviewing. We introduce and analyze the problem Cycle-Free Reviewing that aims at finding a review assignment without the following kind of collusion ring: A sequence of reviewers each reviewing a paper authored by the next reviewer in the sequence (with the last reviewer reviewing a paper of the first), thus creating a review cycle where each reviewer gives favorable reviews. As a result, all papers in that cycle have a high chance of acceptance independent of their respective scientific merit. We observe that review assignments computed using a standard Linear Programming approach typically admit many short review cycles. On the negative side, we show that Cycle-Free Reviewing is NP-hard in various restricted cases (i.e., when every author is qualified to review all papers and one wants to prevent that authors review each other's or their own papers or when every author has only one paper and is only qualified to review few papers). On the positive side, among others, we show that, in some realistic settings, an assignment without any review cycles of small length always exists. This result also gives rise to an efficient heuristic for computing (weighted) cycle-free review assignments, which we show to be of excellent quality in practice.

Following up on purely theoretical work, 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.

We analyze the (parameterized) computational complexity of "fair" variants of bipartite many-to-one matching, where each vertex from the "left" side is matched to exactly one vertex and each vertex from the "right" side may be matched to multiple vertices. We want to find a "fair" matching, in which each vertex from the right side is matched to a "fair" set of vertices. Assuming that each vertex from the left side has one color modeling its attribute, we study two fairness criteria. In one of them, we deem a vertex set fair if for any two colors, the difference between the numbers of their occurrences does not exceed a given threshold. Fairness is relevant when finding many-to-one matchings between students and colleges, voters and constituencies, and applicants and firms. Here colors may model sociodemographic attributes, party memberships, and qualifications, respectively. We show that finding a fair many-to-one matching is NP-hard even for three colors and maximum degree five. Our main contribution is the design of fixed-parameter tractable algorithms with respect to the number of vertices on the right side. Our algorithms make use of a variety of techniques including color coding. At the core lie integer linear programs encoding Hall like conditions. To establish the correctness of our integer programs, we prove a new separation result, inspired by Frank's separation theorem [Frank, Discrete Math. 1982], which may also be of independent interest. We further obtain complete complexity dichotomies regarding the number of colors and the maximum degree of each side.

Motivated by putting empirical work based on (synthetic) election data on a more solid mathematical basis, we analyze six distances among elections, including, e.g., the challenging-to-compute but very precise swap distance and the distance used to form the so-called map of elections. Among the six, the latter seems to strike the best balance between its computational complexity and expressiveness.

We use the "map of elections" approach of Szufa et al. (AAMAS 2020) to analyze several well-known vote distributions. For each of them, we give an explicit formula or an efficient algorithm for computing its frequency matrix, which captures the probability that a given candidate appears in a given position in a sampled vote. We use these matrices to draw the "skeleton map" of distributions, evaluate its robustness, and analyze its properties. We further develop a general and unified framework for learning the distribution of real-world preferences using the frequency matrices of established vote distributions.

We study the parameterized complexity of counting variants of Swap- and Shift-Bribery, focusing on the parameterizations by the number of swaps and the number of voters. Facing several computational hardness results, using sampling we show experimentally that Swap-Bribery offers a new approach to the robustness analysis of elections.

In their AAMAS 2020 paper, Szufa et al. presented a "map of elections" that visualizes a set of 800 elections generated from various statistical cultures. While similar elections are grouped together on this map, there is no obvious interpretation of the elections' positions. We provide such an interpretation by introducing four canonical “extreme” elections, acting as a compass on the map. We use them to analyze both a dataset provided by Szufa et al. and a number of real-life elections. In effect, we find a new parameterization of the Mallows model, based on measuring the expected swap distance from the central preference order, and show that it is useful for capturing real-life scenarios.

To address the dynamic nature of real-world networks, we generalize competitive diffusion games and Voronoi games from static to temporal graphs, where edges may appear or disappear over time. This establishes a new direction of studies in the area of graph games, motivated by applications such as influence spreading. As a first step, we investigate the existence of Nash equilibria in competitive diffusion and Voronoi games on different temporal graph classes. Even when restricting our studies to temporal paths and cycles, this turns out to be a challenging undertaking, revealing significant differences between the two games in the temporal setting. Notably, both games are equivalent on static paths and cycles. Our two main technical results are (algorithmic) proofs for the existence of Nash equilibria in temporal competitive diffusion and temporal Voronoi games when the edges are restricted not to disappear over time.

In hedonic diversity games (HDGs), recently introduced by Bredereck, Elkind, and Igarashi (2019), each agent belongs to one of two classes (men and women, vegetarians and meat-eaters, junior and senior researchers), and agents' preferences over coalitions are determined by the fraction of agents from their class in each coalition. Bredereck et al. show that while an HDG may fail to have a Nash stable (NS) or a core stable (CS) outcome, every HDG in which all agents have single-peaked preferences admits an individually stable (IS) outcome, which can be computed in polynomial time. In this work, we extend and strengthen these results in several ways. First, we establish that the problem of deciding if an HDG has an NS outcome is NP-complete, but admits an XP algorithm with respect to the size of the smaller class. Second, we show that, in fact, all HDGs admit IS outcomes that can be computed in polynomial time; our algorithm for finding such outcomes is considerably simpler than that of Bredereck et al. We also consider two ways of generalizing the model of Bredereck et al. to k ≥ 2 classes. We complement our theoretical results by empirical analysis, comparing the IS outcomes found by our algorithm, the algorithm of Bredereck et al. and a natural better-response dynamics.

Given a set of individuals qualifying or disqualifying each other, group identification is the task of identifying a socially qualified subgroup of individuals. Social qualification depends on the specific rule used to aggregate individual qualifications. The bribery problem in this context asks how many agents need to change their qualifications in order to change the outcome. Complementing previous results showing polynomial-time solvability or NP-hardness of bribery for various social rules in the constructive (aiming at making specific individuals socially qualified) or destructive (aiming at making specific individuals socially disqualified) setting, we provide a comprehensive picture of the parameterized computational complexity landscape. Conceptually, we also consider a more fine-grained concept of bribery cost, where we ask how many single qualifications need to be changed, and a more general bribery goal that combines the constructive and destructive setting.

In the multidimensional stable roommate problem, agents have to be allocated to rooms and have preferences over sets of potential roommates. We study the complexity of finding good allocations of agents to rooms under the assumption that agents have diversity preferences (Bredereck, Elkind, Igarashi, AAMAS'19): each agent belongs to one of the two types (e.g., juniors and seniors, artists and engineers), and agents' preferences over rooms depend solely on the fraction of agents of their own type among their potential roommates. We consider various solution concepts for this setting, such as core and exchange stability, Pareto optimality and envy-freeness. On the negative side, we prove that envy-free, core stable or (strongly) exchange stable outcomes may fail to exist and that the associated decision problems are NP-complete. On the positive side, we show that these problems are in FPT with respect to the room size, which is not the case for the general stable roommate problem.

We initiate the study of external manipulations in Stable Marriage by considering several manipulative actions as well as several manipulation goals. For instance, one goal is to make sure that a given pair of agents is matched in a stable solution, and this may be achieved by the manipulative action of reordering some agents' preference lists. We present a comprehensive study of the computational complexity of all problems arising in this way. We find several polynomial-time solvable cases as well as NP-hard ones. For the NP-hard cases, focusing on the natural parameter "budget" (that is, the number of manipulative actions one is allowed to perform), we also conduct a parameterized complexity analysis and encounter mostly parameterized hardness results.