Representative Social Choice: From Learning Theory to AI Alignment

2024-10-31

arXiv.org

AI Summary

This paper addresses the fundamental challenge of acquiring and processing full preference profiles in large-scale collective decision-making—e.g., jury trials, indirect elections, and AI alignment—where eliciting preferences from all individuals is infeasible. Method: It pioneers a statistical learning formulation of social choice, introduces a formal axiomatic framework for representativeness, and employs combinatorial analysis to prove an Arrow-type impossibility theorem for representative samples. The approach integrates computational social science, statistical learning theory, mechanism design, and axiomatic modeling. Contribution/Results: The work establishes the first social choice framework with provable generalization error guarantees, thereby relaxing the classical assumption of complete preference knowledge. It provides a statistically grounded, justification-sensitive foundation for democratic representativeness and bridges social choice theory, machine learning, and AI alignment through a unified theoretical lens.

Technology Category

Game Theory and Economic Paradigms: Social Choice / VotingKnowledge Representation and Reasoning: PreferencesMachine Learning: Learning Preferences or Rankings

Application Category

Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environmentsUser Modeling, Personalization and Recommendation: Fairness-aware retrieval and rankingSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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, 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.

Problem

• Modeling democratic representation in large-scale collective decisions
• Applying statistical learning to generalize social choice mechanisms
• Developing axioms and impossibility theorems for representative systems

Innovation

• Representative social choice framework for large-scale decisions
• Formulating social choice as statistical learning problems
• Proving generalization properties using machine learning theory