Epistemic Selection of Costly Alternatives: The Case of Participatory Budgeting

We initiate the study of voting rules for participatory budgeting using the so-called epistemic approach, where one interprets votes as noisy reflections of some ground truth regarding the objectively best set of projects to fund. Using this approach, we first show that both the most studied rules in the literature and the most widely used rule in practice cannot be justified on epistemic grounds: they cannot be interpreted as maximum likelihood estimators, whatever assumptions we make about the accuracy of voters. Focusing then on welfare-maximising rules, we obtain both positive and negative results regarding epistemic guarantees

Algorithmic aspects of resource allocation and multiwinner voting: theory and experiments

This thesis is concerned with investigating elements of computational social choice in the light of real-world applications. We contribute to a better understanding of the areas of fair allocation and multiwinner voting. For both areas, inspired by real-world scenarios, we propose several new notions and extensions of existing models. Then, we analyze the complexity of answering the computational questions raised by the introduced concepts. To this end, we look through the lens of parameterized complexity. We identify different parameters which describe natural features specific to the computational problems we investigate. Exploiting the parameters, we successfully develop efficient algorithms for spe- cific cases of the studied problems. We complement our analysis by showing which parameters presumably cannot be utilized for seeking efficient algorithms. Thereby, we provide comprehensive pictures of the computational complexity of the studied problems. Specifically, we concentrate on four topics that we present below, grouped by our two areas of interest. For all but one topic, we present experimental studies based on implementations of newly developed algorithms. We first focus on fair allocation of indivisible resources. In this setting, we consider a collection of indivisible resources and a group of agents. Each agent reports its utility evaluation of every resource and the task is to “fairly” allocate the resources such that each resource is allocated to at most one agent. We concentrate on the two following issues regarding this scenario. The social context in fair allocation of indivisible resources. In many fair allocation settings, it is unlikely that every agent knows all other agents. For example, consider a scenario where the agents represent employees of a large corporation. It is highly unlikely that every employee knows every other employee. Motivated by such settings, we come up with a new model of graph envy-freeness by adapting the classical envy-freeness notion to account for social relations of agents modeled as social networks. We show that if the given social network of agents is simple (for example, if it is a directed acyclic graph), then indeed we can sometimes find fair allocations efficiently. However, we contrast tractability results with showing NP-hardness for several cases, including those in which the given social network has a constant degree. Fair allocations among few agents with bounded rationality. Bounded rationality is the idea that humans, due to cognitive limitations, tend to simplify problems that they face. One of its emanations is that human agents usually tend to report simple utilities over the resources that they want to allocate; for example, agents may categorize the available resources only into two groups of desirable and undesirable ones. Applying techniques for solving integer linear programs, we show that exploiting bounded rationality leads to efficient algorithms for finding envy-free and Pareto-efficient allocations, assuming a small number of agents. Further, we demonstrate that our result actually forms a framework that can be applied to a number of different fairness concepts like envy-freeness up to one good or envy-freeness up to any good. This way, we obtain efficient algorithms for a number of fair allocation problems (assuming few agents with bounded rationality). We also empirically show that our technique is applicable in practice. Further, we study multiwinner voting, where we are given a collection of voters and their preferences over a set of candidates. The outcome of a multiwinner voting rule is a group (or a set of groups in case of ties) of candidates that reflect the voters’ preferences best according to some objective. In this context, we investigate the following themes. The robustness of election outcomes. We study how robust outcomes of multiwinner elections are against possible mistakes made by voters. Assuming that each voter casts a ballot in a form of a ranking of candidates, we represent a mistake by a swap of adjacent candidates in a ballot. We find that for rules such as SNTV, k-Approval, and k-Borda, it is computationally easy to find the minimum number of swaps resulting in a change of an outcome. This task is, however, NP-hard for STV and the Chamberlin-Courant rule. We conclude our study of robustness with experimentally studying the average number of random swaps leading to a change of an outcome for several rules. Strategic voting in multiwinner elections. We ask whether a given group of cooperating voters can manipulate an election outcome in a favorable way. We focus on the k-Approval voting rule and we show that the computational complexity of answering the posed question has a rich structure. We spot several cases for which our problem is polynomial-time solvable. However, we also identify NP-hard cases. For several of them, we show how to circumvent the hardness by fixed-parameter tractability. We also present experimental studies indicating that our algorithms are applicable in practice

Multi-Winner Voting with Approval Preferences

From fundamental concepts and results to recent advances in computational social choice, this open access book provides a thorough and in-depth look at multi-winner voting based on approval preferences. The main focus is on axiomatic analysis, algorithmic results and several applications that are relevant in artificial intelligence, computer science and elections of any kind. What is the best way to select a set of candidates for a shortlist, for an executive committee, or for product recommendations? Multi-winner voting is the process of selecting a fixed-size set of candidates based on the preferences expressed by the voters. A wide variety of decision processes in settings ranging from politics (parliamentary elections) to the design of modern computer applications (collaborative filtering, dynamic Q&A platforms, diversity in search results, etc.) share the problem of identifying a representative subset of alternatives. The study of multi-winner voting provides the principled analysis of this task. Approval-based committee voting rules (in short: ABC rules) are multi-winner voting rules particularly suitable for practical use. Their usability is founded on the straightforward form in which the voters can express preferences: voters simply have to differentiate between approved and disapproved candidates. Proposals for ABC rules are numerous, some dating back to the late 19th century while others have been introduced only very recently. This book explains and discusses these rules, highlighting their individual strengths and weaknesses. With the help of this book, the reader will be able to choose a suitable ABC voting rule in a principled fashion, participate in, and be up to date with the ongoing research on this topic

Social Choice for Partial Preferences Using Imputation

Within the field of multiagent systems, the area of computational social choice considers the problems arising when decisions must be made collectively by a group of agents. Usually such systems collect a ranking of the alternatives from each member of the group in turn, and aggregate these individual rankings to arrive at a collective decision. However, when there are many alternatives to consider, individual agents may be unwilling, or unable, to rank all of them, leading to decisions that must be made on the basis of incomplete information. While earlier approaches attempt to work with the provided rankings by making assumptions about the nature of the missing information, this can lead to undesirable outcomes when the assumptions do not hold, and is ill-suited to certain problem domains. In this thesis, we propose a new approach that uses machine learning algorithms (both conventional and purpose-built) to generate plausible completions of each agent’s rankings on the basis of the partial rankings the agent provided (imputations), in a way that reflects the agents’ true preferences. We show that the combination of existing social choice functions with certain classes of imputation algorithms, which forms the core of our proposed solution, is equivalent to a form of social choice. Our system then undergoes an extensive empirical validation under 40 different test conditions, involving more than 50,000 group decision problems generated from real-world electoral data, and is found to outperform existing competitors significantly, leading to better group decisions overall. Detailed empirical findings are also used to characterize the behaviour of the system, and illustrate the circumstances in which it is most advantageous. A general testbed for comparing solutions using real-world and artificial data (Prefmine) is then described, in conjunction with results that justify its design decisions. We move on to propose a new machine learning algorithm intended specifically to learn and impute the preferences of agents, and validate its effectiveness. This Markov-Tree approach is demonstrated to be superior to imputation using conventional machine learning, and has a simple interpretation that characterizes the problems on which it will perform well. Later chapters contain an axiomatic validation of both of our new approaches, as well as techniques for mitigating their manipulability. The thesis concludes with a discussion of the applicability of its contributions, both for multiagent systems and for settings involving human elections. In all, we reveal an interesting connection between machine learning and computational social choice, and introduce a testbed which facilitates future research efforts on computational social choice for partial preferences, by allowing empirical comparisons between competing approaches to be conducted easily, accurately, and quickly. Perhaps most importantly, we offer an important and effective new direction for enabling group decision making when preferences are not completely specified, using imputation methods

Resolving the Complexity of Some Fundamental Problems in Computational Social Choice

This thesis is in the area called computational social choice which is an intersection area of algorithms and social choice theory.Comment: Ph.D. Thesi

Essays in Experimental Political Economy

In many economic applications, a collective outcome experienced by a group of people is determined by individual decisions made by its constituents. Hence, understanding how individuals make decisions in group settings is important, but empirical and observational analyses are often complicated by confounding factors. This dissertation contains three essays that use controlled experiments designed to isolate, and measure the impact of, mechanisms predicted to affect behavior. Chapter 1 studies behavior under digital anonymity. A distinctive feature of the digital world is the ability to calibrate or withhold one's identifier: a person can be identified by a string of letters, an avatar, their real name, or even nothing at all. That digital identifiers allow a person to mask their physical identity also makes it difficult to attribute digital actions to a physical person, even when the actions are observed. I embed these features in an experiment where subjects play a finitely repeated, linear public goods game. Treated subjects are identified in one of three ways—by their photograph, by a random number, or by a self-designed cartoon avatar—and their individual choices are revealed and either attributed to, or decoupled from, their identifier. In line with the previous literature, identifying subjects and increasing the precision of attribution increases contributions relative to a baseline condition without identifiers or revealed individual choices. Remarkably, however, the largest impact on behavior comes from having an identifier in the first place: for a given level of attribution, the experimental data suggest that being identified by a number or by an avatar is as powerful as being identified by one's photograph. Chapter 2 studies whether and how individuals imbue digital avatars with self image and social image considerations. While digital avatars have become more commonplace and sophisticated, they need not resemble the physical appearance of the person using it. This inconsistency raises the question of how an avatar induces image considerations, relative to a person's physical appearance. I embed avatars into a dictator game and conduct two experiments, one addressing self image and the other social image. The direction of the treatment effect in the dictator game for both experiments suggests that individuals do attach image considerations to their avatars, though the effects are not statistically significant. Additionally, I find that subjects create significantly more positively perceived avatars when they know that their avatar will be shown to another subject who will decide how to allocate an endowment with them. Chapter 3, joint with Alessandra Casella and Michelle Jiang, studies the impact of an alternative voting system on the minority's turnout and resultant victories. We start from the observation that under majoritarian election systems, securing participation and representation of minorities remains an open problem, made salient in the US by its history of voter suppression. One remedy recommended by the courts is Cumulative Voting (CV): each voter has as many votes as open positions and can cumulate votes on as few candidates as desired. Theory predicts that CV encourages the minority to overcome obstacles to voting: although each voter is treated equally, CV increases minority's turnout relative to the majority, and the minority's share of seats won. A lab experiment based on a costly voting design strongly supports both predictions. Chapter 3 was published in Volume 141 of Games and Economic Behavior, pp. 133-155, September 2023, https://doi.org/10.1016/j.geb.2023.05.012

Practical Algorithms for Resource Allocation and Decision Making

Algorithms are widely used today to help make important decisions in a variety of domains, including health care, criminal justice, employment, and education. Designing \emph{practical} algorithms involves balancing a wide variety of criteria. Deployed algorithms should be robust to uncertainty, they should abide by relevant laws and ethical norms, they should be easy to use correctly, they should not adversely impact user behavior, and so on. Finding an appropriate balance of these criteria involves technical analysis, understanding of the broader context, and empirical studies ``in the wild''. Most importantly practical algorithm design involves close collaboration between stakeholders and algorithm developers. The first part of this thesis addresses technical issues of uncertainty and fairness in \emph{kidney exchange}---a real-world matching market facilitated by optimization algorithms. We develop novel algorithms for kidney exchange that are robust to uncertainty in both the quality and the feasibility of potential transplants, and we demonstrate the effect of these algorithms using computational simulations with real kidney exchange data. We also study \emph{fairness} for hard-to-match patients in kidney exchange. We close a previously-open theoretical gap, by bounding the price of fairness in kidney exchange with chains. We also provide matching algorithms that bound the price of fairness in a principled way, while guaranteeing Pareto efficiency. The second part describes two real deployed algorithms---one for kidney exchange, and one for recruiting blood donors. For each application cases we characterize an underlying mathematical problem, and theoretically analyze its difficulty. We then develop practical algorithms for each setting, and we test them in computational simulations. For the blood donor recruitment application we present initial empirical results from a fielded study, in which a simple notification algorithm increases the expected donation rate by $5\%$. The third part of this thesis turns to human aspects of algorithm design. We conduct several survey studies that address several questions of practical algorithm design: How do algorithms impact decision making? What additional information helps people use complex algorithms to make decisions? Do people understand standard algorithmic notions of fairness? We conclude with suggestions for facilitating deeper stakeholder involvement for practical algorithm design, and we outline several areas for future research