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, most especially, 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 statistical machine learning. We further formulate axioms for representative social choice, and present Arrow-like impossibility results and conjectures. Our framework provides a new perspective on the study of social choice, and opens up new research directions at the intersection of social choice theory and statistical learning theory.