We study the problem of selecting a statement that finds common ground across diverse population preferences. Generative AI is uniquely suited for this task because it can access a practically infinite set of statements, but AI systems like the Habermas machine leave the choice of generated statement to a voting rule. What it means for this rule to find common ground, however, is not well-defined. In this work, we propose a formal model for finding common ground in the infinite alternative setting based on the proportional veto core from social choice. To provide guarantees relative to these infinitely many alternatives and a large population, we wish to satisfy a notion of proportional veto core using only query access to the unknown distribution of alternatives and voters. We design an efficient sampling-based algorithm that returns an alternative in the (approximate) proportional veto core with high probability and prove matching lower bounds, which show that no algorithm can do the same using fewer queries. On a synthetic dataset of preferences over text, we confirm the effectiveness of our sampling-based algorithm and compare other social choice methods as well as LLM-based methods in terms of how reliably they produce statements in the proportional veto core.

翻译：本研究探讨如何从多样化群体偏好中选取能够建立共识基础的陈述。生成式人工智能特别适合此项任务，因为它能够访问近乎无限的陈述集合，但诸如哈贝马斯机器这类人工智能系统将生成陈述的选择权交由投票规则决定。然而，该规则达成共识基础的具体含义尚未得到明确定义。本文基于社会选择理论中的比例否决核，提出了一种在无限备选方案情境下寻求共识基础的形式化模型。为在无限多备选方案与大规模群体的背景下提供理论保证，我们期望仅通过对未知备选方案分布与选民分布的查询访问，就能满足比例否决核的概念要求。我们设计了一种高效的基于抽样的算法，该算法能以高概率返回处于（近似）比例否决核内的备选方案，并证明了匹配的下界——这表明任何算法都无法以更少的查询实现相同目标。在基于文本偏好的合成数据集上，我们验证了所提出的抽样算法的有效性，并比较了其他社会选择方法及基于大语言模型的方法在生成符合比例否决核的陈述方面的可靠性。