Lin Ge

Luise Ge, Daniel Halpern, Gregory Kehne et al.

Most social choice rules assume access to full rankings, while current alignment practice -- despite aiming for diversity -- typically treats voters as anonymous and comparisons as independent, effectively extracting only about one bit per voter. Motivated by this gap, we study social choice under an extreme communication budget in the linear social choice model, where each voter's utility is the inner product between a latent voter type and the embedding of the context and candidate. The candidate and voter spaces may be very large or even infinite. Our core idea is to model the electorate as an unknown distribution over voter types and to recover its moments as informative summary statistics for candidate selection. We show that one pairwise comparison per voter already suffices to select a candidate that maximizes social welfare, but this elicitation cannot identify the second moment and therefore cannot support objectives that account for inequality. We prove that two pairwise comparisons per voter, or alternatively a single graded comparison, identify the second moment; moreover, these richer queries suffice to identify all moments, and hence the entire voter-type distribution. These results enable principled solutions to a range of social choice objectives including inequality-aware welfare criteria such as taking into account the spread of voter utilities and choosing a representative subset.

Zheyuan Zhang, Lin Ge, Hongjiang Li et al.

Large language models (LLMs) have demonstrated remarkable capabilities across diverse tasks, and LLM-based agents further extend these abilities to various practical workflows. While recent progress shows that multi-agent systems (MAS) can outperform single agents by coordinating specialized roles, designing effective MAS remains difficult due to prompt sensitivity and the compounded instability MAS creates. To cope with the challenge, recent efforts in automated prompt design have reduced manual effort. However, multi-agent prompt optimization remains largely unexplored. Challenges like exponentially expanding search space and ambiguous credit assignment together make systematic design intractable without principled methods. Therefore, we introduce M}ulti-Agent PRompt Optimization (MAPRO), a four-stage framework that first formulates MAS prompt optimization as a Maximum a Posteriori (MAP) inference problem and solves it using a language-guided variant of max-product belief propagation algorithm. To address credit assignment and updates the system iteratively, MAPRO employs a topology-aware refinement mechanism that integrates execution feedback and downstream blames to selectively update agent prompts. Through this process, MAPRO progressively converges to a coordinated set of agent-specific prompt policies. Across benchmarks in various tasks, MAPRO achieves state-of-the-art performance, consistently surpassing manually engineered baselines and recent automated alternatives. Beyond performance, our MAP-based formulation also delivers general guidelines for building more reliable and principled multi-agent systems in the future

Luise Ge, Gregory Kehne, Yevgeniy Vorobeychik

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 underlying utilities for these options, however, using preference rankings may lead to suboptimal outcomes vis-à-vis utilitarian social welfare. Distortion is a measure of this suboptimality, and provides a worst-case approach for developing and analyzing voting rules when utilities have minimal structure. However in many settings, such as common paradigms for value alignment, alternatives 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. Specifically, we investigate the distortion of linear social choice for deterministic and randomized voting rules. We obtain bounds that depend only on the 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, benchmarking several standard rules against our instance-optimal algorithms.