Methods and Open Problems in Differentiable Social Choice: Learning Mechanisms, Decisions, and Alignment

Social choice is no longer a peripheral concern of political theory or economics-it has become a foundational component of modern machine learning systems. From auctions and resource allocation to federated learning, participatory governance, and the alignment of large language models, machine learning pipelines increasingly aggregate heterogeneous preferences, incentives, and judgments into collective decisions. In effect, many contemporary machine learning systems already implement social choice mechanisms, often implicitly and without explicit normative scrutiny. This Review surveys differentiable social choice: an emerging paradigm that formulates voting rules, mechanisms, and aggregation procedures as learnable, differentiable models optimized from data. We synthesize work across auctions, voting, budgeting, liquid democracy, decentralized aggregation, and inverse mechanism learning, showing how classical axioms and impossibility results reappear as objectives, constraints, and optimization trade-offs. We conclude by identifying 36 open problems defining a new research agenda at the intersection of machine learning, economics, and democratic theory.