arXiv subjects

Warut Suksompong

Publications and source records attributed to Warut Suksompong.

At least 19 recordsLinked to original sources

arXiv2026

Fractional Assignment with $\ell_1$ Preferences

We study a fractional assignment setting where $n$ objects are to be assigned to $n$ agents with unit capacity, and each agent specifies an ideal distribution over the objects. Unlike in classic random assignment, these ideal distributions are not necessarily degenerate, as agents may prefer a mixture of objects rather than any single object. We assume that agents seek to minimize the $\ell_1$ distance between their ideal distribution and the distribution they receive, which is equivalent to maximizing the overlap between the two distributions. We propose two mechanisms, one based on water filling (WF) and the other on quadratic programming (QP), and show that both mechanisms are utilitarian-optimal (and hence Pareto efficient), envy-free, strategyproof, and satisfy equal treatment of equals. Moreover, we highlight a distinct advantage of each mechanism: while the WF mechanism satisfies the stronger property of group-strategyproofness, the QP mechanism is more robust in terms of egalitarian overlap welfare.

econ.TH↗

arXiv2026

Reconfiguration in Fair Division Revisited

We revisit reconfiguration in the fair allocation of indivisible goods, where the goal is to transform one fair allocation into another through a sequence of exchanges while preserving fairness at every step. Our focus is on the hierarchy of envy-freeness up to $k$ goods (EF$k$). We show that for any fixed $k$, two EF1 allocations with the same size vector need not admit a reconfiguration path whose intermediate allocations satisfy EF$k$. This impossibility persists even when the two allocations arise from standard EF1 approaches: the envy cycle elimination algorithm or the maximum Nash welfare solution. In contrast, we prove that allocations with the same size vector produced by recursively balanced picking sequences, including round-robin, are always connected via a path that maintains EF2. We also show that deciding whether an EF1 reconfiguration path exists is NP-hard for any fixed number of agents. Furthermore, we complement these exchange-based results by studying a more permissive model that also allows transfers, establishing additional connectivity guarantees.

cs.GT↗

arXiv2026

Individual Fairness in Budget Aggregation

We consider the problem of aggregating $n$ individual distributions over $m$ alternatives into a collective distribution, also known as budget aggregation. Existing fairness notions in this literature typically do not guarantee fairness to individual agents. To address this, we define two versions of individual fair share guarantees. We show that when agents' utilities are derived from $\ell_t$ metrics for any $t\geq 1$, both these guarantees can be satisfied along with Pareto efficiency, and the corresponding distributions can be computed in polynomial time. On the other hand, for $\ell_1$ utilities, we prove that Pareto efficiency, strategyproofness, and a very weak fairness notion called single-minded positive share are not always compatible for $n,m \ge 3$. For smaller parameters, we provide rules that satisfy these three axioms. We also establish similar impossibility results for $\ell_2$ utilities.

cs.GT↗

arXiv2026

Fair Division with Binary Valuations: Characterizations

We consider the fair allocation of indivisible goods with binary valuations. In this setting, the maximum Nash welfare rule, the leximin rule, and all additive welfarist rules with a strictly concave function coincide. We show that for any number of agents, this rule is the only rule that satisfies envy-freeness up to one good, strategyproofness, neutrality, minimal completeness, and invariance under disapproving unassigned goods (IDU). Moreover, we present an alternative characterization for two agents, where we replace IDU with non-redundancy and resource-monotonicity. In both characterizations, all axioms are necessary.

econ.TH↗

arXiv2026

Reforming an Unfair Allocation by Exchanging Goods

Fairly allocating indivisible goods is a frequently occurring task in everyday life. Given an initial allocation of the goods, we consider the problem of reforming it via a sequence of exchanges to attain fairness in the form of envy-freeness up to one good (EF1). We present a vast array of results on the complexity of determining whether it is possible to reach an EF1 allocation from the initial allocation and, if so, the minimum number of exchanges required. In particular, we uncover several distinctions based on the number of agents involved and their utility functions. Furthermore, we derive essentially tight bounds on the worst-case number of exchanges needed to achieve EF1 when the initial allocation is balanced.

cs.GT↗

arXiv2026

Optimizing the Envy Cycle Elimination Algorithm

In the fair allocation of indivisible goods, a widely used notion of fairness is envy-freeness up to one good (EF1). A classical way to compute an EF1 allocation is the envy cycle elimination (ECE) algorithm, which iteratively assigns a good to an unenvied agent and, after each assignment, resolves any resulting envy cycle. Although the ECE algorithm always produces an EF1 allocation, it leaves considerable freedom in choosing both the next good to allocate and the agent to receive it. We investigate natural heuristics that exploit this flexibility to improve welfare guarantees. For example, we show that if the heuristic jointly selects the good and the receiving agent maximizing the utility, the worst-case utilitarian welfare loss is significantly lower than that of the vanilla algorithm. By contrast, restricting the heuristic to select only one of these two dimensions does not yield comparable improvements. We also complement our theoretical results with empirical average-case analysis.

cs.GT↗

arXiv2026

Envy-Free Allocation of Indivisible Goods via Noisy Queries

We introduce a problem of fairly allocating indivisible goods (items) in which the agents' valuations cannot be observed directly, but instead can only be accessed via noisy queries. In the two-agent setting with Gaussian noise and bounded valuations, we derive upper and lower bounds on the required number of queries for finding an envy-free allocation in terms of the number of items, $m$, and the negative-envy of the optimal allocation, $Δ$. In particular, when $Δ$ is not too small (namely, $Δ\gg m^{1/4}$), we establish that the optimal number of queries scales as $\frac{\sqrt m }{(Δ/ m)^2} = \frac{m^{2.5}}{Δ^2}$ up to logarithmic factors. Our upper bound is based on non-adaptive queries and a simple thresholding-based allocation algorithm that runs in polynomial time, while our lower bound holds even under adaptive queries and arbitrary computation time.

cs.GT↗

arXiv2026

Decomposition Envy-Freeness in Random Assignment

In random assignment, fairness is often captured by stochastic-dominance envy-freeness (SD-EF). We observe that assignments satisfying SD-EF may admit decompositions that result in each agent envying another agent with high probability. To address this, we introduce decomposition envy-freeness (Dec-EF), which is a property of a decomposition rather than of an assignment matrix. We show that an SD-EF assignment matrix always admits a Dec-EF decomposition when there are at most three agents or the agents have at most two distinct preferences.

econ.TH↗

arXiv2026

On the Fairness of Additive Welfarist Rules

Allocating indivisible goods is a ubiquitous task in fair division. We study additive welfarist rules, an important class of rules which choose an allocation that maximizes the sum of some function of the agents' utilities. Prior work has shown that the maximum Nash welfare (MNW) rule is the unique additive welfarist rule that guarantees envy-freeness up to one good (EF1). We strengthen this result by showing that MNW remains the only additive welfarist rule that ensures EF1 for identical-good instances, two-value instances, as well as normalized instances with three or more agents. On the other hand, if the agents' utilities are integers, we demonstrate that several other rules offer the EF1 guarantee, and provide characterizations of these rules for various classes of instances.

cs.GT↗

arXiv2026

Welfare Loss in Connected Resource Allocation

We study the allocation of indivisible items that form an undirected graph and investigate the worst-case welfare loss when requiring that each agent must receive a connected subgraph. Our focus is on both egalitarian and utilitarian welfare. Specifically, we introduce the concept of egalitarian (resp., utilitarian) price of connectivity, which captures the worst-case ratio between the optimal egalitarian (resp., utilitarian) welfare among all allocations and that among connected allocations. We provide tight or asymptotically tight bounds on the price of connectivity for several large classes of graphs in the case of two agents -- including graphs with vertex connectivity $1$ or $2$ and complete bipartite graphs -- as well as for paths, stars, and cycles in the general case where the number of agents can be arbitrary.

cs.GT↗

arXiv2026

Settling the Score: Portioning with Cardinal Preferences

We study a portioning setting in which a public resource such as time or money is to be divided among a given set of candidates, and each agent proposes a division of the resource. We consider two families of aggregation rules for this setting -- those based on coordinate-wise aggregation and those that optimize some notion of welfare -- as well as the recently proposed independent markets rule. We provide a detailed analysis of these rules from an axiomatic perspective, both for classic axioms, such as strategyproofness and Pareto optimality, and for novel axioms, some of which aim to capture proportionality in this setting. Our results indicate that a simple rule that computes the average of the proposals satisfies many of our axioms and fares better than all other considered rules in terms of fairness properties. We complement these results by presenting two characterizations of the average rule.

cs.GT↗

arXiv2025

Optimal Budget Aggregation with Star-Shaped Preference Domains

We study the problem of aggregating distributions, such as budget proposals, into a collective distribution. An ideal aggregation mechanism would be Pareto efficient, strategyproof, and fair. Most previous work assumes that agents evaluate budgets according to the $\ell_1$ distance to their ideal budget. We investigate and compare different models from the larger class of star-shaped utility functions - a multi-dimensional generalization of single-peaked preferences. For the case of two alternatives, we extend existing results by proving that under very general assumptions, the uniform phantom mechanism is the only strategyproof mechanism that satisfies proportionality - a minimal notion of fairness introduced by Freeman et al. (2021). Moving to the case of more than two alternatives, we establish sweeping impossibilities for $\ell_1$ and $\ell_\infty$ disutilities: no mechanism satisfies efficiency, strategyproofness, and proportionality. We then propose a new kind of star-shaped utilities based on evaluating budgets by the ratios of shares between a given budget and an ideal budget. For these utilities, efficiency, strategyproofness, and fairness become compatible. In particular, we prove that the mechanism that maximizes the Nash product of individual utilities is characterized by group-strategyproofness and a core-based fairness condition.

econ.TH↗

arXiv2025

Comparing the Fairness of Recursively Balanced Picking Sequences

Picking sequences are well-established methods for allocating indivisible goods. Among the various picking sequences, recursively balanced picking sequences -- whereby each agent picks one good in every round -- are notable for guaranteeing allocations that satisfy envy-freeness up to one good. In this paper, we compare the fairness of different recursively balanced picking sequences using two key measures. Firstly, we demonstrate that all such sequences have the same price in terms of egalitarian welfare relative to other picking sequences. Secondly, we characterize the approximate maximin share (MMS) guarantees of these sequences. In particular, we show that compensating the agent who picks last in the first round by letting her pick first in every subsequent round yields the best MMS guarantee.

cs.GT↗

arXiv2025

On Multi-Level Apportionment

Apportionment refers to the well-studied problem of allocating legislative seats among parties or groups with different entitlements. We present a multi-level generalization of apportionment where the groups form a hierarchical structure, which gives rise to stronger versions of the upper and lower quota notions. We show that running Adams' method level-by-level satisfies upper quota, while running Jefferson's method or the quota method level-by-level guarantees lower quota. Moreover, we prove that both quota notions can always be fulfilled simultaneously.

econ.TH↗

arXiv2025

Fair Allocation of Indivisible Goods with Variable Groups

We study the fair allocation of indivisible goods with variable groups. In this model, the goal is to partition the agents into groups of given sizes and allocate the goods to the groups in a fair manner. We show that for any number of groups and corresponding sizes, there always exists an envy-free up to one good (EF1) outcome, thereby generalizing an important result from the individual setting. Our result holds for arbitrary monotonic utilities and comes with an efficient algorithm. We also prove that an EF1 outcome is guaranteed to exist even when the goods lie on a path and each group must receive a connected bundle. In addition, we consider a probabilistic model where the utilities are additive and drawn randomly from a distribution. We show that if there are $n$ agents, the number of goods $m$ is divisible by the number of groups $k$, and all groups have the same size, then an envy-free outcome exists with high probability if $m = ω(\log n)$, and this bound is tight. On the other hand, if $m$ is not divisible by $k$, then an envy-free outcome is unlikely to exist as long as $m = o(\sqrt{n})$.

cs.GT↗

arXiv2025

Coordinating Charitable Donations with Leontief Preferences

We consider the problem of funding public goods that are complementary in nature. Examples include charities handling different needs (e.g., protecting animals vs. providing healthcare), charitable donations to different individuals, or municipal units handling different issues (e.g., security vs. transportation). We model these complementarities by assuming Leontief preferences; that is, each donor seeks to maximize an individually weighted minimum of all contributions across the charities. Decentralized funding may be inefficient due to a lack of coordination among the donors; centralized funding may be undesirable as it ignores the preferences of individual donors. We present a mechanism that combines the advantages of both methods. The mechanism efficiently distributes each donor's contribution so that no subset of donors has an incentive to redistribute their donations. Moreover, it is group-strategyproof, satisfies desirable monotonicity properties, maximizes Nash welfare, returns a unique Lindahl equilibrium, and can be implemented via natural best-response spending dynamics.

econ.TH↗

arXiv2025

Discrepancy Beyond Additive Functions with Applications to Fair Division

We consider a setting where we have a ground set $M$ together with real-valued set functions $f_1, \dots, f_n$, and the goal is to partition $M$ into two sets $S_1,S_2$ such that $|f_i(S_1) - f_i(S_2)|$ is small for every $i$. Many results in discrepancy theory can be stated in this form with the functions $f_i$ being additive. In this work, we initiate the study of the unstructured case where $f_i$ is not assumed to be additive. We show that even without the additivity assumption, the upper bound remains at most $O(\sqrt{n \log n})$. Our result has implications on the fair allocation of indivisible goods. In particular, we show that a consensus halving up to $O(\sqrt{n \log n})$ goods always exists for $n$ agents with monotone utilities. Previously, only an $O(n)$ bound was known for this setting.

math.CO↗

arXiv2025

Two-Sided Fairness in Many-to-One Matching

We consider a classic many-to-one matching setting, where participants need to be assigned to teams based on the preferences of both sides. Unlike most of the matching literature, we aim to provide fairness not only to participants, but also to teams using concepts from the literature of fair division. We present a polynomial-time algorithm that computes an allocation satisfying team-justified envy-freeness up to one participant, participant-justified envy-freeness, balancedness, Pareto optimality, and group-strategyproofness for participants, even in the possible presence of ties. Our algorithm generalizes both the Gale-Shapley algorithm from two-sided matching as well as the round-robin algorithm from fair division. We also discuss how our algorithm can be extended to accommodate quotas and incomplete preferences.

econ.TH↗