Social choice theory is the study of preference aggregation across a population, used both in mechanism design for human agents and in the democratic alignment of language models. In this study, we propose the representative social choice framework for the modeling of democratic representation in collective decisions, where the number of issues and individuals are too large for mechanisms to consider all preferences directly. These scenarios are widespread in real-world decision-making processes, such as jury trials, indirect elections, legislation processes, corporate governance, and, more recently, language model alignment. In representative social choice, the population is represented by a finite sample of individual-issue pairs based on which social choice decisions are made. We show that many of the deepest questions in representative social choice can be naturally formulated as statistical learning problems, and prove the generalization properties of social choice mechanisms using the theory of machine learning. We further formulate axioms for representative social choice, and prove Arrow-like impossibility theorems with new combinatorial tools of analysis. Our framework introduces the representative approach to social choice, opening up research directions at the intersection of social choice, learning theory, and AI alignment.

翻译：社会选择理论研究群体中的偏好聚合，既用于人类主体的机制设计，也用于语言模型的民主对齐。本研究提出代表性社会选择框架，用于建模集体决策中的民主代表机制，适用于议题和个体数量过于庞大而无法由机制直接处理所有偏好的场景。这类场景在现实世界决策过程中广泛存在，例如陪审团审判、间接选举、立法程序、公司治理，以及最近兴起的语言模型对齐。在代表性社会选择中，群体通过一个基于个体-议题对构成的有限样本来代表，社会选择决策即基于此样本作出。我们证明，代表性社会选择中许多核心问题可自然地表述为统计学习问题，并运用机器学习理论证明了社会选择机制的泛化性质。我们进一步构建了代表性社会选择的公理体系，并运用新的组合分析工具证明了类似阿罗定理的不可能性定理。本框架引入了社会选择的代表性研究路径，为连接社会选择理论、学习理论与人工智能对齐的研究开辟了新方向。