Large language models (LLMs) are increasingly used for decision-making tasks where fairness is an essential desideratum. But what does fairness even mean to an LLM? To investigate this, we conduct a comprehensive evaluation of how LLMs perceive fairness in the context of resource allocation, using both synthetic and real-world data. We find that several state-of-the-art LLMs, when instructed to be fair, tend to prioritize improving collective welfare rather than distributing benefits equally. Their perception of fairness is somewhat sensitive to how user preferences are represented, but less so to the real-world context of the decision-making task. Finally, we show that the best strategy for aligning an LLM's perception of fairness to a specific criterion is to provide it as a mathematical objective, without referencing "fairness", as this prevents the LLM from mixing the criterion with its own prior notions of fairness. Our results provide practical insights for understanding and shaping how LLMs interpret fairness in resource allocation problems.

We introduce a model of fair division with market values, where indivisible goods must be partitioned among agents with (additive) subjective valuations, and each good additionally has a market value. The market valuation can be viewed as a separate additive valuation that holds identically across all the agents. We seek allocations that are simultaneously fair with respect to the subjective valuations and under the market valuation. We show that an allocation that satisfies stochastically-dominant envy-freeness up to one good (SD-EF1) with respect to both the subjective valuations and the market valuation does not always exist, but the weaker guarantee of EF1 with respect to the subjective valuations along with SD-EF1 with respect to the market valuation can be guaranteed. We also study a number of other guarantees such as Pareto optimality, EFX, and MMS. In addition, we explore non-additive valuations and extend our model to cake-cutting. Along the way, we identify several tantalizing open questions.

Fairness and efficiency have become the pillars of modern fair division research, but prior work on achieving both simultaneously is largely limited to the unconstrained setting. We study fair and efficient allocations of indivisible goods under additive valuations and various types of allocation feasibility constraints, and demonstrate the unreasonable effectiveness of the maximum Nash welfare (MNW) solution in this previously uncharted territory. Our main result is that MNW allocations are 1/2-envy-free up to one good (EF1) and Pareto optimal under the broad family of (arbitrary) matroid constraints. We extend these guarantees to complete MNW allocations for base-orderable matroid constraints, and to a family of non-matroid constraints (which includes balancedness). We establish tightness of our results by providing counterexamples for the satisfiability of certain stronger desiderata, but show an improved result for the special case of goods with copies (Gafni et al. 2023). Finally, we also establish novel best-of-both-worlds guarantees for goods with copies and balancedness.

We study temporal fair division, whereby a set of agents are allocated a (possibly different) set of goods on each day for a period of days. We study this setting, as well as a number of its special cases formed by the restrictions to two agents, same goods on each day, identical preferences, or combinations thereof, and chart out the landscape of achieving two types of fairness guarantees simultaneously: fairness on each day (per day) and fairness over time (up to each day, or the weaker version, overall). In the most general setting, we prove that there always exists an allocation that is stochastically-dominant envy-free up to one good (SD-EF1) per day and proportional up to one good (PROP1) overall, and when all the agents have identical preferences, we show that SD-EF1 per day and SD-EF1 overall can be guaranteed. For the case of two agents, we prove that SD-EF1 per day and EF1 up to each day can be guaranteed using an envy balancing technique. We provide counterexamples for other combinations that establish our results as among the best guarantees possible, but also leave open some tantalizing questions.

A fundamental task in multi-agent systems is to match n agents to n alternatives (e.g., resources or tasks). This is often done by eliciting agents' ordinal rankings over the alternatives rather than their exact numerical utilities. While this simplifies elicitation, the incomplete information leads to inefficiency, captured by a worst-case measure called distortion. Recent work shows that making just a few cardinal utility queries per agent can significantly improve the distortion, with Amanatidis et al. (2024) achieving O(√n) distortion with two queries per agent. We generalize their result by achieving O(n^(1/λ)) distortion with λ queries per agent, for any constant λ, which is optimal up to a constant factor given a previous lower bound by Amanatidis et al. (2022). We extend this finding to the general social choice problem of selecting one of m alternatives based on n agents' preferences, achieving O((min{n, m})^(1/λ)) distortion with λ queries per agent, for any constant λ, which is also optimal given prior results. Thus, our work settles open questions regarding the optimal distortion achievable with a fixed number of cardinal value queries in both settings.

We consider the challenge of AI value alignment with multiple individuals that have different reward functions and optimal policies in an underlying Markov decision process. We formalize this problem as one of *policy aggregation*, where the goal is to identify a desirable collective policy. We argue that an approach informed by social choice theory is especially suitable. Our key insight is that social choice methods can be reinterpreted by identifying ordinal preferences with volumes of subsets of the *state-action occupancy polytope*. Building on this insight, we demonstrate that a variety of methods — including approval voting, Borda count, the proportional veto core, and quantile fairness — can be practically applied to policy aggregation.

With a rapid growth in the deployment of AI tools for making critical decisions (or aiding humans in doing so), there is a growing demand to be able to explain to the stakeholders how these tools arrive at a decision. Consequently, voting is frequently used to make such decisions due to its inherent explainability. Recent work suggests that using randomized (as opposed to deterministic) voting rules can lead to significant efficiency gains measured via the distortion framework. However, rules that use intricate randomization can often become too complex to explain to the stakeholders; losing explainability can eliminate the key advantage of voting over black-box AI tools, which may outweigh the efficiency gains. We study the efficiency gains which can be unlocked by using voting rules that add a simple randomization step to a deterministic rule, thereby retaining explainability. We focus on two such families of rules, randomized positional scoring rules and random committee member rules, and show, theoretically and empirically, that they indeed achieve explainability and efficiency simultaneously to some extent.

We consider the allocation of homogeneous divisible goods to agents with linear additive valuations. Our focus is on the case where some agents are secretive and reveal no preference information, while the remaining agents reveal full preference information. We study distortion, which is the worst-case approximation ratio when maximizing social welfare given such partial information about agent preferences. As a function of the number of secretive agents k relative to the overall number of agents n, we identify the exact distortion for every p-mean welfare function, which includes the utilitarian welfare (p=1), the Nash welfare (p -> 0), and the egalitarian welfare (p -> -Inf).

Sortition is a form of democracy built on random selection of representatives. Two of the key arguments in favor of sortition are that it provides representation (a random panel reflects the composition of the population) and fairness (everyone has a chance to participate). Uniformly random selection is perfectly fair, but is it representative? Towards answering this question, we introduce the notion of a representation metric on the space of individuals, and assume that the cost of an individual for a panel is determined by the $q$-th closest representative; the representation of a (random) panel is measured by the ratio between the (expected) sum of costs of the optimal panel for the individuals and that of the given panel. For $k/2 < q \le k-\Omega(k)$, where $k$ is the panel size, we show that uniform random selection is indeed representative by establishing a constant lower bound on this ratio. By contrast, for $q \leq k/2$, no random selection algorithm that is almost fair can give such a guarantee. We therefore consider relaxed fairness guarantees and develop a new random selection algorithm that sheds light on the tradeoff between representation and fairness.

A voting rule decides on a probability distribution over a set of m alternatives, based on rankings of those alternatives provided by agents. We assume that agents have cardinal utility functions over the alternatives, but voting rules have access to only the rankings induced by these utilities. We evaluate how well voting rules do on measures of social welfare and of proportional fairness, computed based on the hidden utility functions.

In public-private graphs, users share one public graph and have their own private graphs. A private graph consists of personal private contacts that only can be visible to its owner, e.g., hidden friend lists on Facebook and secret following on Sina Weibo. However, existing public-private analytic algorithms have not yet investigated the dense subgraph discovery of k-truss, where each edge is contained in at least k-2 triangles. This paper aims at finding k-truss efficiently in public-private graphs. The core of our solution is a novel algorithm to update k-truss with node insertions. We develop a classification-based hybrid strategy of node insertions and edge insertions to incrementally compute k-truss in public-private graphs. Extensive experiments validate the superiority of our proposed algorithms against state-of-the-art methods on real-world datasets.