Social choice theory offers a wealth of approaches for selecting a candidate on behalf of voters based on their reported preference rankings over options. When voters have explicit utilities for these options, however, using preference rankings may lead to suboptimal outcomes vis-a-vis utilitarian social welfare. Distortion is a measure of this suboptimality, and an extensive literature uses it to develop and analyze voting rules when utilities have minimal structure. However, in many settings, such as common paradigms for value alignment, available options admit a vector representation, and it is natural to suppose that utilities are parametric functions thereof. We undertake the first study of distortion for linear utility functions. Our theoretical contributions are organized into two parts: randomized and deterministic voting rules. We obtain bounds that depend only on dimension of the candidate embedding, and are independent of the numbers of candidates or voters. Additionally, we introduce poly-time instance-optimal algorithms for minimizing distortion given a collection of candidates and votes. We empirically evaluate these in two real-world domains: recommendation systems using collaborative filtering embeddings, and opinion surveys utilizing language model embeddings. Our results benchmark the distortion bounds of several standard rules against our instance-optimal algorithms.

The use of large language models either as decision support systems, or in agentic workflows, is rapidly transforming the digital ecosystem.However, the understanding of LLM decisionmaking under uncertainty remains limited.We study LLM risky choices along two dimensions: (1) prospect representation (based on an explicit representation or outcome history) and (2) decision rationale (explanation).Our study, which involves 20 frontier and open LLMs, is complemented by a matched human subjects experiment, which provides one reference point, while an expected payoff maximizing rational agent model provides another.We find that LLMs cluster into two categories: reasoning models (RMs) and conversational models (CMs).RMs tend towards rational behavior, are insensitive to the order of prospects, gain/loss framing, and explanations, and behave similarly whether prospects are explicit or presented via a history of outcomes.CMs are significantly less rational, slightly more human-like, sensitive to prospect ordering, framing, and explanation, and exhibit a large description-history gap.Paired comparisons of open LLMs suggest that a key factor differentiating RMs and CMs is training for mathematical reasoning.

Many dynamic decision problems, such as robotic control, involve a series of tasks, many of which are unknown at training time. Typical approaches for these problems, such as multi-task and meta reinforcement learning, do not generalize well when the tasks are diverse. On the other hand, approaches that aim to tackle task diversity, such as using task embedding as policy context and task clustering, typically lack performance guarantees and require a large number of training tasks. To address these challenges, we propose a novel approach for learning a policy committee that includes at least one near-optimal policy with high probability for tasks encountered during execution. While we show that this problem is in general inapproximable, we present two practical algorithmic solutions. The first yields provable approximation and task sample complexity guarantees when tasks are low-dimensional (the best we can do due to inapproximability), whereas the second is a general and practical gradient-based approach. In addition, we provide a provable sample complexity bound for few-shot learning. Our experiments on MuJoCo and Meta-World show that the proposed approach outperforms state-of-the-art multi-task, meta-, and task clustering baselines in training, generalization, and few-shot learning, often by a large margin. Our code is available at https://github.com/CERL-WUSTL/PACMAN.

Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational problem posed by reasoning. Inspired by human reasoning, we introduce a method of first-order relational probabilistic inference that satisfies both criteria, and can handle hybrid (discrete and continuous) variables. Specifically, we extend sum-of-squares logic of expectation to relational settings, demonstrating that lifted reasoning in the bounded-degree fragment for knowledge bases of bounded quantifier rank can be performed in polynomial time, even with an a priori unknown and/or countably infinite set of objects. Crucially, our notion of tractability is framed in proof-theoretic terms, which extends beyond the syntactic properties of the language or queries. We are able to derive the tightest bounds provable by proofs of a given degree and size and establish completeness in our sum-of-squares refutations for fixed degrees.

In the context of reinforcement learning from human feedback (RLHF), the reward function is generally derived from maximum likelihood estimation of a random utility model based on pairwise comparisons made by humans. The problem of learning a reward function is one of preference aggregation that, we argue, largely falls within the scope of social choice theory. From this perspective, we can evaluate different aggregation methods via established axioms, examining whether these methods meet or fail well-known standards. We demonstrate that both the Bradley-Terry-Luce Model and its broad generalizations fail to meet basic axioms. In response, we develop novel rules for learning reward functions with strong axiomatic guarantees. A key innovation from the standpoint of social choice is that our problem has a *linear* structure, which greatly restricts the space of feasible rules and leads to a new paradigm that we call *linear social choice*.