The growing interest in employing large language models (LLMs) for decision-making in social and economic contexts has raised questions about their potential to function as agents in these domains. A significant number of societal problems involve the distribution of resources, where fairness, along with economic efficiency, play a critical role in the desirability of outcomes. In this paper, we examine whether LLM responses adhere to fundamental fairness concepts such as equitability, envy-freeness, and Rawlsian maximin, and investigate their alignment with human preferences. We evaluate the performance of several LLMs, providing a comparative benchmark of their ability to reflect these measures. Our results demonstrate a lack of alignment between current LLM responses and human distributional preferences. Moreover, LLMs are unable to utilize money as a transferable resource to mitigate inequality. Nonetheless, we demonstrate a stark contrast when (some) LLMs are tasked with selecting from a predefined menu of options rather than generating one. In addition, we analyze the robustness of LLM responses to variations in semantic factors (e.g. intentions or personas) or non-semantic prompting changes (e.g. templates or orderings). Finally, we highlight potential strategies aimed at enhancing the alignment of LLM behavior with well-established fairness concepts.

Two-sided matching markets have demonstrated significant impact in many real-world applications, including school choice, medical residency placement, electric vehicle charging, ride sharing, and recommender systems. However, traditional models often assume that preferences are known, which is not always the case in modern markets, where preferences are unknown and must be learned. For example, a company may not know its preference over all job applicants a priori in online markets. Recent research has modeled matching markets as multi-armed bandit (MAB) problem and primarily focused on optimizing matching for one side of the market, while often resulting in a pessimal solution for the other side. In this paper, we adopt a welfarist approach for both sides of the market, focusing on two metrics: (1) Utilitarian welfare and (2) Rawlsian welfare, while maintaining market stability. For these metrics, we propose algorithms based on epoch Explore-Then-Commit (ETC) and analyze their regret bounds. Finally, we conduct simulated experiments to evaluate both welfare and market stability.

An important problem on social information sites is the recovery of ground truth from individual reports when the experts are in the minority. The wisdom of the crowd, i.e. the collective opinion of a group of individuals fails in such a scenario. However, the surprisingly popular (SP) algorithm~\cite{prelec2017solution} can recover the ground truth even when the experts are in the minority, by asking the individuals to report additional prediction reports--their beliefs about the reports of others. Several recent works have extended the surprisingly popular algorithm to an equivalent voting rule (SP-voting) to recover the ground truth ranking over a set of $m$ alternatives. However, we are yet to fully understand when SP-voting can recover the ground truth ranking, and if so, how many samples (votes and predictions) it needs. We answer this question by proposing two rank-order models and analyzing the sample complexity of SP-voting under these models. In particular, we propose concentric mixtures of Mallows and Plackett-Luce models with $G (\ge 2)$ groups. Our models generalize previously proposed concentric mixtures of Mallows models with $2$ groups, and we highlight the importance of $G > 2$ groups by identifying three distinct groups (expert, intermediate, and non-expert) from existing datasets. Next, we provide conditions on the parameters of the underlying models so that SP-voting can recover ground-truth rankings with high probability, and also derive sample complexities under the same. We complement the theoretical results by evaluating SP-voting on simulated and real datasets.

Two-sided matching markets describe a large class of problems wherein participants from one side of the market must be matched to those from the other side according to their preferences. In many real-world applications (e.g. content matching or online labor markets), the knowledge about preferences may not be readily available and must be learned, i.e., one side of the market (aka agents) may not know their preferences over the other side (aka arms). Recent research on online settings has focused primarily on welfare optimization aspects (i.e. minimizing the overall regret) while paying little attention to the game-theoretic properties such as the stability of the final matching. In this paper, we exploit the structure of stable solutions to devise algorithms that improve the likelihood of finding stable solutions. We initiate the study of the sample complexity of finding a stable matching, and provide theoretical bounds on the number of samples needed to reach a stable matching with high probability. Finally, our empirical results demonstrate intriguing tradeoffs between stability and optimality of the proposed algorithms, further complementing our theoretical findings.

We consider the problem of recovering the ground truth ordering (ranking, top-$k$, or others) over a large number of alternatives. The wisdom of crowd is a heuristic approach based on Condorcet's Jury theorem to address this problem through collective opinions. This approach fails to recover the ground truth when the majority of the crowd is misinformed. The surprisingly popular (SP) algorithm cite{prelec2017solution} is an alternative approach that is able to recover the ground truth even when experts are in minority. The SP algorithm requires the voters to predict other voters' report in the form of a full probability distribution over all rankings of alternatives. However, when the number of alternatives, $m$, is large, eliciting the prediction report or even the vote over $m$ alternatives might be too costly. In this paper, we design a scalable alternative of the SP algorithm which only requires eliciting partial preferences from the voters, and propose new variants of the SP algorithm. In particular, we propose two versions -- Aggregated-SP and Partial-SP -- that ask voters to report vote and prediction on a subset of size $k$ ($\ll m$) in terms of top alternative, partial rank, or an approval set. Through a large-scale crowdsourcing experiment on MTurk, we show that both of our approaches outperform conventional preference aggregation algorithms for the recovery of ground truth rankings, when measured in terms of Kendall-Tau distance and Spearman's $\rho$. We further analyze the collected data and demonstrate that voters' behavior in the experiment, including the minority of the experts, and the SP phenomenon, can be correctly simulated by a concentric mixtures of Mallows model. Finally, we provide theoretical bounds on the sample complexity of SP algorithms with partial rankings to demonstrate the theoretical guarantees of the proposed methods.

Fairness is one of the most desirable societal principles in collective decision-making. It has been extensively studied in the past decades for its axiomatic properties and has received substantial attention from the multiagent systems community in recent years for its theoretical and computational aspects in algorithmic decision-making. However, these studies are often not sufficiently rich to capture the intricacies of human perception of fairness in the ambivalent nature of the real-world problems. We argue that not only fair solutions should be deemed desirable by social planners (designers), but they should be governed by human and societal cognition, consider perceived outcomes based on human judgement, and be verifiable. We discuss how achieving this goal requires a broad transdisciplinary approach ranging from computing and AI to behavioral economics and human-AI interaction. In doing so, we identify shortcomings and long-term challenges of the current literature of fair division, describe recent efforts in addressing them, and more importantly, highlight a series of open research directions.

The classical house allocation problem involves assigning $n$ houses (or items) to $n$ agents according to their preferences. A key criterion in such problems is satisfying some fairness constraints such as envy-freeness. We consider a generalization of this problem wherein the agents are placed along the vertices of a graph (corresponding to a social network), and each agent can only experience envy towards its neighbors. Our goal is to minimize the aggregate envy among the agents as a natural fairness objective, i.e., the sum of all pairwise envy values over all edges in a social graph. When agents have identical and evenly-spaced valuations, our problem reduces to the well-studied problem of linear arrangements. For identical valuations with possibly uneven spacing, we show a number of deep and surprising ways in which our setting is a departure from this classical problem. More broadly, we contribute several structural and computational results for various classes of graphs, including NP-hardness results for disjoint unions of paths, cycles, stars, or cliques, and fixed-parameter tractable (and, in some cases, polynomial-time) algorithms for paths, cycles, stars, cliques, and their disjoint unions. Additionally, a conceptual contribution of our work is the formulation of a structural property for disconnected graphs that we call separability which results in efficient parameterized algorithms for finding optimal allocations.

In fair division of indivisible goods,  ℓ-out-of-d maximin share (MMS) is the value that an agent can guarantee by partitioning the goods into d bundles and choosing the ℓ least preferred bundles. Most existing works aim to guarantee to all agents a constant fraction of their 1-out-of-n MMS. But this guarantee is sensitive to small perturbation in agents' cardinal valuations. We consider a more robust approximation notion, which depends only on the agents' ordinal rankings of bundles. We prove the existence of ℓ-out-of-⌊(ℓ + 1/2)n⌋ MMS allocations of goods for any integer ℓ ≥ 1, and present a polynomial-time algorithm that finds a 1-out-of-⌈3n/2⌉ MMS allocation when ℓ=1. We further develop an algorithm that provides a weaker ordinal approximation to MMS for any ℓ > 1.

The maximin share (MMS) guarantee is a desirable fairness notion for allocating indivisible goods. While MMS allocations do not always exist, several approximation techniques have been developed to ensure that all agents receive a fraction of their maximin share. We focus on an alternative approximation notion, based on the population of agents, that seeks to guarantee MMS for a fraction of agents. We show that no optimal approximation algorithm can satisfy more than a constant number of agents, and discuss the existence and computation of MMS for all but one agent and its relation to approximate MMS guarantees. We then prove the existence of allocations that guarantee MMS for $\frac{2}{3}$ of agents, and devise a polynomial time algorithm that achieves this bound for up to nine agents. A key implication of our result is the existence of allocations that guarantee $\text{MMS}^{\lceil{3n/2}\rceil}$, i.e., the value that agents receive by partitioning the goods into $\lceil{\frac{3}{2}n}\rceil$ bundles, improving the best known guarantee of $\text{MMS}^{2n-2}$. Finally, we provide empirical experiments using synthetic data.

The wisdom of the crowd has long become the de facto approach for eliciting information from individuals or experts in order to predict the ground truth. However, classical democratic approaches for aggregating individual \emph{votes} only work when the opinion of the majority of the crowd is relatively accurate. A clever recent approach, \emph{surprisingly popular voting}, elicits additional information from the individuals, namely their \emph{prediction} of other individuals' votes, and provably recovers the ground truth even when experts are in minority. This approach works well when the goal is to pick the correct option from a small list, but when the goal is to recover a true ranking of the alternatives, a direct application of the approach requires eliciting too much information. We explore practical techniques for extending the surprisingly popular algorithm to ranked voting by partial votes and predictions and designing robust aggregation rules. We experimentally demonstrate that even a little prediction information helps surprisingly popular voting outperform classical approaches.