arXiv subjects

Rupert Freeman

Publications and source records attributed to Rupert Freeman.

At least 19 recordsLinked to original sources

arXiv2026

Social Welfare in Budget Aggregation

We study budget aggregation under $\ell_1$-utilities, a model for collective decision making in which agents with heterogeneous preferences must allocate a public budget across a set of alternatives. Each agent reports their preferred allocation, and a mechanism selects an allocation. Early work focused on social welfare maximization, which in this setting admits truthful mechanisms, but may underrepresent minority groups, motivating the study of proportional mechanisms. However, the dominant proportionality notion, single-minded proportionality, is weak, as it only constrains outcomes when agents hold extreme preferences. To better understand proportionality and its interaction with welfare and truthfulness, we address three questions. First, how much welfare must be sacrificed to achieve proportionality? We formalize this via the price of proportionality, the best worst-case welfare ratio between a proportional mechanism and Util, the welfare-maximizing mechanism. We introduce a new single-minded proportional and truthful mechanism, UtilProp, and show that it achieves the optimal worst-case ratio. Second, how do proportional mechanisms compare in terms of welfare? We define an instance-wise welfare dominance relation and use it to compare mechanisms from the literature. In particular, we show that UtilProp welfare-dominates all previously known single-minded proportional and truthful mechanisms. Third, can stronger notions of proportionality be achieved without compromising welfare guarantees? We answer this question in the affirmative by studying decomposability and proposing GreedyDecomp, a decomposable mechanism with optimal worst-case welfare ratio. We further show that computing the welfare-dominant decomposable mechanism, UtilDecomp, is NP-hard, and that GreedyDecomp provides a 2-approximation to UtilDecomp in terms of welfare.

cs.GT↗

arXiv2026

Credit Fairness: Online Fairness In Shared Resource Pools

We study repeated allocation of shared resources among agents with time-varying demands and capped linear utilities. In this setting, independently maximizing the minimum endowment-normalized utility in each round satisfies sharing incentives (agents weakly prefer participating in the mechanism to not participating), strategyproofness (agents have no incentive to misreport their demands), and Pareto efficiency. However, this max-min mechanism can lead to large disparities in the total resources received by agents, even when they have the same average demand. We introduce credit fairness, a property that, together with Pareto efficiency, strengthens sharing incentives by giving agents who lend resources in early rounds priority toward recouping those resources in later rounds. Credit fairness can be achieved in conjunction with either Pareto efficiency or strategyproofness individually, but we show that, under anonymity, it cannot be achieved together with both. We propose a mechanism that is credit fair and Pareto efficient, and evaluate it in a computational resource-sharing setting.

cs.GT↗

arXiv2025

Reallocating Wasted Votes in Proportional Parliamentary Elections with Thresholds

In many proportional parliamentary elections, electoral thresholds (typically 3-5%) are used to promote stability and governability by preventing the election of parties with very small representation. However, these thresholds often result in a significant number of "wasted votes" cast for parties that fail to meet the threshold, which reduces representativeness. One proposal is to allow voters to specify replacement votes, by either indicating a second choice party or by ranking a subset of the parties, but there are several ways of deciding on the scores of the parties (and thus the composition of the parliament) given those votes. We introduce a formal model of party voting with thresholds, and compare a variety of party selection rules axiomatically, and experimentally using a dataset we collected during the 2024 European election in France. We identify three particularly attractive rules, called Direct Winners Only (DO), Single Transferable Vote (STV) and Greedy Plurality (GP).

cs.GT↗

arXiv2024

Harm Ratio: A Novel and Versatile Fairness Criterion

Envy-freeness has become the cornerstone of fair division research. In settings where each individual is allocated a disjoint share of collective resources, it is a compelling fairness axiom which demands that no individual strictly prefer the allocation of another individual to their own. Unfortunately, in many real-life collective decision-making problems, the goal is to choose a (common) public outcome that is equally applicable to all individuals, and the notion of envy becomes vacuous. Consequently, this literature has avoided studying fairness criteria that focus on individuals feeling a sense of jealousy or resentment towards other individuals (rather than towards the system), missing out on a key aspect of fairness. In this work, we propose a novel fairness criterion, individual harm ratio, which is inspired by envy-freeness but applies to a broad range of collective decision-making settings. Theoretically, we identify minimal conditions under which this criterion and its groupwise extensions can be guaranteed, and study the computational complexity of related problems. Empirically, we conduct experiments with real data to show that our fairness criterion is powerful enough to differentiate between prominent decision-making algorithms for a range of tasks from voting and fair division to participatory budgeting and peer review.

cs.GT↗

arXiv2024

Truthful Budget Aggregation: Beyond Moving-Phantom Mechanisms

We study a budget-aggregation setting in which a number of voters report their ideal distribution of a budget over a set of alternatives, and a mechanism aggregates these reports into an allocation. Ideally, such mechanisms are truthful, i.e., voters should not be incentivized to misreport their preferences. For the case of two alternatives, the set of mechanisms that are truthful and additionally meet a range of basic desiderata (anonymity, neutrality, and continuity) exactly coincides with the so-called moving-phantom mechanisms, but whether this space is richer for more alternatives was repeatedly stated as an open question. We answer this question in the affirmative by presenting a class of truthful mechanisms that are not moving-phantoms but satisfy the three properties. Since moving-phantom mechanisms can only provide limited fairness guarantees (measured as the worst-case distance to a fair share solution), one motivation for broadening the class of truthful mechanisms is the hope for improved fairness guarantees. We dispel this hope by showing that lower bounds holding for the class of moving-phantom mechanisms extend to all truthful, anonymous, neutral, and continuous mechanisms.

cs.GT↗

arXiv2023

Project-Fair and Truthful Mechanisms for Budget Aggregation

We study the budget aggregation problem in which a set of strategic voters must split a finite divisible resource (such as money or time) among a set of competing projects. Our goal is twofold: We seek truthful mechanisms that provide fairness guarantees to the projects. For the first objective, we focus on the class of moving phantom mechanisms [Freeman et al., 2021], which are -- to this day -- essentially the only known truthful mechanisms in this setting. For project fairness, we consider the mean division as a fair baseline, and bound the maximum difference between the funding received by any project and this baseline. We propose a novel and simple moving phantom mechanism that provides optimal project fairness guarantees. As a corollary of our results, we show that our new mechanism minimizes the $\ell_1$ distance to the mean (a measure suggested by Caragiannis et al. [2022]) for three projects and gives the first non-trivial bounds on this quantity for more than three projects.

cs.GT↗

arXiv2021

Two-Sided Matching Meets Fair Division

We introduce a new model for two-sided matching which allows us to borrow popular fairness notions from the fair division literature such as envy-freeness up to one good and maximin share guarantee. In our model, each agent is matched to multiple agents on the other side over whom she has additive preferences. We demand fairness for each side separately, giving rise to notions such as double envy-freeness up to one match (DEF1) and double maximin share guarantee (DMMS). We show that (a slight strengthening of) DEF1 cannot always be achieved, but in the special case where both sides have identical preferences, the round-robin algorithm with a carefully designed agent ordering achieves it. In contrast, DMMS cannot be achieved even when both sides have identical preferences.

cs.GT↗

arXiv2021

Computing Possible and Necessary Equilibrium Actions (and Bipartisan Set Winners)

In many multiagent environments, a designer has some, but limited control over the game being played. In this paper, we formalize this by considering incompletely specified games, in which some entries of the payoff matrices can be chosen from a specified set. We show that it is NP-hard for the designer to make these choices optimally, even in zero-sum games. In fact, it is already intractable to decide whether a given action is (potentially or necessarily) played in equilibrium. We also consider incompletely specified symmetric games in which all completions are required to be symmetric. Here, hardness holds even in weak tournament games (symmetric zero-sum games whose entries are all -1, 0, or 1) and in tournament games (symmetric zero-sum games whose non-diagonal entries are all -1 or 1). The latter result settles the complexity of the possible and necessary winner problems for a social-choice-theoretic solution concept known as the bipartisan set. We finally give a mixed-integer linear programming formulation for weak tournament games and evaluate it experimentally.

cs.GT↗

arXiv2021

Phragm\'{e}n's Voting Methods and Justified Representation

In the late 19th century, Swedish mathematician Lars Edvard Phragm\'{e}n proposed a load-balancing approach for selecting committees based on approval ballots. We consider three committee voting rules resulting from this approach: two optimization variants - one minimizing the maximal load and one minimizing the variance of loads - and a sequential variant. We study Phragm\'{e}n's methods from an axiomatic point of view, focusing on properties capturing proportional representation. We show that the sequential variant satisfies proportional justified representation, which is a rare property for committee monotonic methods. Moreover, we show that the optimization variants satisfy perfect representation. We also analyze the computational complexity of Phragm\'{e}n's methods and provide mixed-integer programming based algorithms for computing them.

cs.GT↗

arXiv2021

Incentive-Compatible Forecasting Competitions

We initiate the study of incentive-compatible forecasting competitions in which multiple forecasters make predictions about one or more events and compete for a single prize. We have two objectives: (1) to incentivize forecasters to report truthfully and (2) to award the prize to the most accurate forecaster. Proper scoring rules incentivize truthful reporting if all forecasters are paid according to their scores. However, incentives become distorted if only the best-scoring forecaster wins a prize, since forecasters can often increase their probability of having the highest score by reporting more extreme beliefs. In this paper, we introduce two novel forecasting competition mechanisms. Our first mechanism is incentive compatible and guaranteed to select the most accurate forecaster with probability higher than any other forecaster. Moreover, we show that in the standard single-event, two-forecaster setting and under mild technical conditions, no other incentive-compatible mechanism selects the most accurate forecaster with higher probability. Our second mechanism is incentive compatible when forecasters' beliefs are such that information about one event does not lead to belief updates on other events, and it selects the best forecaster with probability approaching 1 as the number of events grows. Our notion of incentive compatibility is more general than previous definitions of dominant strategy incentive compatibility in that it allows for reports to be correlated with the event outcomes. Moreover, our mechanisms are easy to implement and can be generalized to the related problems of outputting a ranking over forecasters and hiring a forecaster with high accuracy on future events.

cs.GT↗

arXiv2020

Best of Both Worlds: Ex-Ante and Ex-Post Fairness in Resource Allocation

We study the problem of allocating indivisible goods among agents with additive valuations. When randomization is allowed, it is possible to achieve compelling notions of fairness such as envy-freeness, which states that no agent should prefer any other agent's allocation to her own. When allocations must be deterministic, achieving exact fairness is impossible but approximate notions such as envy-freeness up to one good can be guaranteed. Our goal in this work is to achieve both simultaneously, by constructing a randomized allocation that is exactly fair ex-ante and approximately fair ex-post. The key question we address is whether ex-ante envy-freeness can be achieved in combination with ex-post envy-freeness up to one good. We settle this positively by designing an efficient algorithm that achieves both properties simultaneously. If we additionally require economic efficiency, we obtain an impossibility result. However, we show that economic efficiency and ex-ante envy-freeness can be simultaneously achieved if we slightly relax our ex-post fairness guarantee. On our way, we characterize the well-known Maximum Nash Welfare allocation rule in terms of a recently introduced fairness guarantee that applies to groups of agents, not just individuals.

cs.GT↗

arXiv2020

Equitable Allocations of Indivisible Chores

We study fair allocation of indivisible chores (i.e., items with non-positive value) among agents with additive valuations. An allocation is deemed fair if it is (approximately) equitable, which means that the disutilities of the agents are (approximately) equal. Our main theoretical contribution is to show that there always exists an allocation that is simultaneously equitable up to one chore (EQ1) and Pareto optimal (PO), and to provide a pseudopolynomial-time algorithm for computing such an allocation. In addition, we observe that the Leximin solution---which is known to satisfy a strong form of approximate equitability in the goods setting---fails to satisfy even EQ1 for chores. It does, however, satisfy a novel fairness notion that we call equitability up to any duplicated chore. Our experiments on synthetic as well as real-world data obtained from the Spliddit website reveal that the algorithms considered in our work satisfy approximate fairness and efficiency properties significantly more often than the algorithm currently deployed on Spliddit.

cs.GT↗

arXiv2020

No-Regret and Incentive-Compatible Online Learning

We study online learning settings in which experts act strategically to maximize their influence on the learning algorithm's predictions by potentially misreporting their beliefs about a sequence of binary events. Our goal is twofold. First, we want the learning algorithm to be no-regret with respect to the best fixed expert in hindsight. Second, we want incentive compatibility, a guarantee that each expert's best strategy is to report his true beliefs about the realization of each event. To achieve this goal, we build on the literature on wagering mechanisms, a type of multi-agent scoring rule. We provide algorithms that achieve no regret and incentive compatibility for myopic experts for both the full and partial information settings. In experiments on datasets from FiveThirtyEight, our algorithms have regret comparable to classic no-regret algorithms, which are not incentive-compatible. Finally, we identify an incentive-compatible algorithm for forward-looking strategic agents that exhibits diminishing regret in practice.

cs.LG↗

arXiv2019

Equitable Allocations of Indivisible Goods

In fair division, equitability dictates that each participant receives the same level of utility. In this work, we study equitable allocations of indivisible goods among agents with additive valuations. While prior work has studied (approximate) equitability in isolation, we consider equitability in conjunction with other well-studied notions of fairness and economic efficiency. We show that the Leximin algorithm produces an allocation that satisfies equitability up to any good and Pareto optimality. We also give a novel algorithm that guarantees Pareto optimality and equitability up to one good in pseudopolynomial time. Our experiments on real-world preference data reveal that approximate envy-freeness, approximate equitability, and Pareto optimality can often be achieved simultaneously.

cs.GT↗

arXiv2019

Truthful Aggregation of Budget Proposals

We consider a participatory budgeting problem in which each voter submits a proposal for how to divide a single divisible resource (such as money or time) among several possible alternatives (such as public projects or activities) and these proposals must be aggregated into a single aggregate division. Under $\ell_1$ preferences -- for which a voter's disutility is given by the $\ell_1$ distance between the aggregate division and the division he or she most prefers -- the social welfare-maximizing mechanism, which minimizes the average $\ell_1$ distance between the outcome and each voter's proposal, is incentive compatible (Goel et al. 2016). However, it fails to satisfy the natural fairness notion of proportionality, placing too much weight on majority preferences. Leveraging a connection between market prices and the generalized median rules of Moulin (1980), we introduce the independent markets mechanism, which is both incentive compatible and proportional. We unify the social welfare-maximizing mechanism and the independent markets mechanism by defining a broad class of moving phantom mechanisms that includes both. We show that every moving phantom mechanism is incentive compatible. Finally, we characterize the social welfare-maximizing mechanism as the unique Pareto-optimal mechanism in this class, suggesting an inherent tradeoff between Pareto optimality and proportionality.

cs.GT↗

arXiv2016

Crowdsourced Outcome Determination in Prediction Markets

A prediction market is a useful means of aggregating information about a future event. To function, the market needs a trusted entity who will verify the true outcome in the end. Motivated by the recent introduction of decentralized prediction markets, we introduce a mechanism that allows for the outcome to be determined by the votes of a group of arbiters who may themselves hold stakes in the market. Despite the potential conflict of interest, we derive conditions under which we can incentivize arbiters to vote truthfully by using funds raised from market fees to implement a peer prediction mechanism. Finally, we investigate what parameter values could be used in a real-world implementation of our mechanism.

cs.AI↗

arXiv2016

Fair Public Decision Making

We generalize the classic problem of fairly allocating indivisible goods to the problem of \emph{fair public decision making}, in which a decision must be made on several social issues simultaneously, and, unlike the classic setting, a decision can provide positive utility to multiple players. We extend the popular fairness notion of proportionality (which is not guaranteeable) to our more general setting, and introduce three novel relaxations --- \emph{proportionality up to one issue, round robin share, and pessimistic proportional share} --- that are also interesting in the classic goods allocation setting. We show that the Maximum Nash Welfare solution, which is known to satisfy appealing fairness properties in the classic setting, satisfies or approximates all three relaxations in our framework. We also provide polynomial time algorithms and hardness results for finding allocations satisfying these axioms, with or without insisting on Pareto optimality.

cs.GT↗

arXiv2016

On the Price of Stability of Undirected Multicast Games

In multicast network design games, a set of agents choose paths from their source locations to a common sink with the goal of minimizing their individual costs, where the cost of an edge is divided equally among the agents using it. Since the work of Anshelevich et al. (FOCS 2004) that introduced network design games, the main open problem in this field has been the price of stability (PoS) of multicast games. For the special case of broadcast games (every vertex is a terminal, i.e., has an agent), a series of works has culminated in a constant upper bound on the PoS (Bilo` et al., FOCS 2013). However, no significantly sub-logarithmic bound is known for multicast games. In this paper, we make progress toward resolving this question by showing a constant upper bound on the PoS of multicast games for quasi-bipartite graphs. These are graphs where all edges are between two terminals (as in broadcast games) or between a terminal and a nonterminal, but there is no edge between nonterminals. This represents a natural class of intermediate generality between broadcast and multicast games. In addition to the result itself, our techniques overcome some of the fundamental difficulties of analyzing the PoS of general multicast games, and are a promising step toward resolving this major open problem.

cs.DS↗