Representative Social Choice: From Learning Theory to AI Alignment

TL;DR

This paper introduces a novel framework called representative social choice, which models democratic decision-making for large populations and issues, connecting social choice theory with learning theory and AI alignment.

Contribution

It formulates representative social choice as a statistical learning problem, establishes generalization guarantees, and proves new impossibility theorems, bridging social choice, learning, and AI alignment.

Findings

Many social choice questions can be formulated as learning problems

Generalization properties of social choice mechanisms are established

Arrow-like impossibility theorems are proved using new combinatorial tools

Abstract

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, legislation, 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 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.