Vertical Federated Learning as a Social Choice Problem

Centralized data aggregation in modern machine learning increasingly conflicts with privacy laws, security risks, and settings where data pooling is impossible. Federated learning addresses this by bringing models to the data. Unlike horizontal federated learning (HFL), where agents share a feature space across distinct individuals, many real-world scenarios require the opposite: agents hold distinct feature sets for overlapping populations. This decentralized setting defines vertical federated learning (VFL). To enable a VFL central server to aggregate multi-agent predictions without accessing raw data or internal models, we propose a voting-theory-based framework satisfying strict privacy and minimal-invasiveness constraints. In this approach, agents submit round-wise predictions (or “votes”) based on their local features, which the server aggregates into a final decision. We prove that any stationary aggregation rule incurs linear regret, motivating a dynamic generalization where agent weights evolve as evidence accumulates. Consequently, we introduce Trust-Based Perpetual Voting (TBPV), adapting classical Perpetual Voting for accuracy-driven tasks by concentrating influence on agents the server trusts most. This is primarily a theoretical contribution: our experiments are a proof of concept, intended to check that the mechanism behaves as the theory predicts on controlled vertical partitions, rather than to establish state-of-the-art performance.